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Fall 2011

S.I.G.M.A. Seminar
 Thermodynamics on Fractals Link: View Poster Speaker: Gerald Dunne (University of Connecticut) Time: Friday, September 2, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Quantum particles in thermal equilibrium probe the geometry in which they are conﬁned. This idea can be used to address certain questions relating to fractals and a consistent thermodynamics may be defined based on the density of states extracted from the fractal zeta function or heat kernel trace. Comments: Free Pizza (courtesy of Mathematics Department). Come down at 12:30 to mingle with other grad students before the talk.

Algebra Seminar
 The ultrafilter topology on spaces of valuation domains and applications Link: View Poster Speaker: Carmelo Finocchiaro (Universita degli Studi "Roma Tre", Italy) Time: Tuesday, September 6, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs)

UConn Math Club
 Commuting Polynomials Link: View Poster Speaker: Keith Conrad (University of Connecticut) Time: Wednesday, September 7, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: When we compose two functions f(x) and g(x), the order of composition usually matters: f(g(x)) is normally not the same as g(f(x)). If it happens that f(g(x)) = g(f(x)) then we'll say the two functions commute. A simple example of a pair of commuting polynomials is xm and xn for any positive integers m and n, since (xm)n = xmn = (xn)m. Other than the power functions x, x2, x3,..., is there any other collection of commuting polynomials fn(x), with one term of each degree? We will see that there is essentially just one other (interesting) example, and it's related to a formula from trigonometry! Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 Zeta functions of fractal strings and the Riemann hypothesis Link: View Poster Speaker: John Rock (California State Polytechnic University, Pomona) Time: Friday, September 9, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: "Can one hear the shape of a fractal string?" An affirmative answer (in the right context) to this seemingly innocuous question is equivalent to the popular and provocative hypothesis originally posed by Bernhard Riemann—the nontrivial zeros of the Riemann zeta function lie on the line with real part one-half. In this talk, we discuss the zeta functions and complex dimensions of fractal strings and their natural relationship with the structure of the zeros of the Riemann zeta function. Comments: Free Pizza (courtesy of Mathematics Department). Come down at 12:30 to mingle with other grad students before the talk.

Actuarial Science Seminar
 Esscher Approximations for Maximum Likelihood Estimates Link: View Poster Speaker: Jim Bridgeman (University of Connecticut) Time: Friday, September 9, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: The series expansion of a probability density function known to actuaries by Esscher’s name and to statisticians as the saddlepoint approximation typically gets integrated to approximate probability values under the density, with a location parameter in the expansion chosen to optimize convergence of the integrated series. We propose using either the derivative of that same expansion, or alternatively using an exactly analogous series expansion for the derivative of a probability density function, to approximate the value of the point of maximum likelihood for the density. The key is to make the value of the location parameter of the series expansion an unknown and assume it to be the point of maximum likelihood, which which leads to a tractable optimization problem to find its value.

Cluster Algebras Reading Seminar
 On cluster theory and quantum dilogarithm identities; Introduction Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Monday, September 12, 2011 at 3:30 pm Place: MSB 117 (UConn - Storrs)

Logic Seminar
 Degrees which are low for isomorphism Link: View Poster Speaker: Reed Solomon (UConn) Time: Monday, September 12, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: A Turing degree d is low for isomorphism if whenever d can compute an isomorphism between a pair of computable structures, there is a computable isomorphism between these structures. This talk will survey some results from an ongoing project about such degrees with Johanna Franklin and Ted Slaman.

UConn Math Club
 Investigating Randomness Link: View Poster Speaker: Johanna Franklin (University of Connecticut) Time: Wednesday, September 14, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: What does it mean to say that an infinite binary sequence is random? Does it mean that the sequence is hard to describe? Does it have to be unpredictable? Does it have to be indistinguishable from other sequences? In this talk, I'll frame these questions mathematically and explain how all of them can be used to define the same set of binary sequences to be random. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 Efficient Coding of Natural Sound Link: View Poster Speaker: David Ferrone (University of Connecticut) Time: Friday, September 16, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will see how our auditory system begins to process what we hear, e.g. how it encodes signals before they are sent to our brain. This is based on an article of Michael Lewicki (2002) along with enough background to understand it. Comments: Free Pizza (courtesy of Mathematics Department). Come down at 12:30 to mingle with other grad students before the talk.

Analysis and Probability Seminar
 A simplified proof of the relation between scaling exponents in first passage percolation Link: View Poster Speaker: Michael Damron (Princeton) Faculty Sponsor:Ben-Ari Time: Friday, September 16, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two "scaling exponents": one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing paths between the same points. In a recent breakthrough work, Sourav Chatterjee proved this conjecture using a strong definition of the exponents. I will discuss work I just completed with Tuca Auffinger, in which we introduce a new and intuitive idea that replaces Chatterjee's main argument and gives an alternative proof of the relation. One advantage of our argument is that it does not require a non-trivial technical assumption of Chatterjee on the weight distribution.

Actuarial Science Seminar
 On Two Generalizations of Axiomatic Risk Measures Link: View Poster Speaker: Manuel Morales (Universite de Montreal) Time: Friday, September 16, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: The axiomatic definition of risk measures in Artzner et al. (1998) marked the begining of new research field. Among the different generzalizations that followed, we find mainly two schools: Coherent Risk Measures (Artzner et al. (1998)) and Insurance Risk Measures (Wang (1997)). Here, we present two generalizations in each one of these two directions. First, we discuss how we can axiomatically define a risk measure on the space of infinite sequences. The goal of such generalization is to provide a coherent way of defining a risk measure for data samples of any size. This procedure makes no assumption about the underlying loss distribution. In the second generalization, we used the normal inverse Gaussian distribution in order to extend the normal distortion introduced by Wang. As a result, we obtain a distortion-based risk measure that is compatible with a non-gaussian option pricing theory.

Logic Seminar
 Counting rational points on certain Pfaffian surfaces Link: View Poster Speaker: Margaret Thomas (Konstanz) Time: Monday, September 19, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: In this talk, we shall consider the question of bounding the density of rational and algebraic points on sets definable in o-minimal expansions of the real field. After surveying the topic, we shall focus on a conjecture of Wilkie about sets definable in the real exponential field and review the progress that has so far been made towards this. In particular, we shall present some results in this direction for certain surfaces. (These results are joint work with Gareth O. Jones.)

Algebra Seminar
 Cox rings of toric vector bundles Link: View Poster Speaker: Milena Hering (University of Connecticut) Time: Tuesday, September 20, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Cox ring of an algebraic variety X comprises all homogeneous coordinate rings of images of X under maps to projective space. It is a basic question whether this ring is finitely generated (it then is called a "Mori dream space"). While toric varieties are Mori dream spaces, Cox rings of vector bundles on toric varieties with a compatible torus action turn out to not be finitely generated. In, fact there is a beautiful relationship between these rings and Cox rings of blow ups of points in projective space, which have been extensively studied in the context of Hilbert's 14th problem.

UConn Math Club
 Lagrange Multipliers — Why? Link: View Poster Speaker: Patrick Dragon (University of Connecticut) Time: Wednesday, September 21, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: The method of Lagrange multipliers is used in multivariable calculus to optimize one function, subject to the constraint of another. After three courses in college calculus, many students are able to use the method effectively. Yet very few can explain it. This talk is aimed at students who are currently taking or have already taken their third course in calculus. We will start with a review of gradients, directional derivatives, and optimization problems. We will prove that given a surface defined by f(x,y,z)=c, the gradient of f is perpendicular to the surface. This will be the foundation for a geometric interpretation of Lagrange multipliers, and our approach to understanding why the method works. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 Computer, Hello Computer: A brief introduction to Sage Link: View Poster Speaker: Lucas David-Roesler (University of Connecticut) Time: Friday, September 23, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will discuss the basic features of the computer algebra system Sage. We will see how to do basic calculations such as derivatives and integrals as well as creating graphics and some simple animations. Comments: Free Pizza (courtesy of Mathematics Department). Come down at 12:30 to mingle with other grad students before the talk.

Cluster Algebras Reading Seminar
 Stability and Harder-Narasimhan filtration Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Friday, September 23, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Analysis and Probability Seminar
 Polynomial Interpolation and Approximation of Multivariate Band Limited Functions Link: View Poster Speaker: B. A. Bailey (UCONN) Time: Friday, September 23, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: In this presentation, an equivalence between existence of particular exponential Riesz bases for spaces of multivariate bandlimited functions and existence of certain polynomial interpolants for these bandlimited functions is given. Namely, polynomials are constructed which (in the limit) interpolate $(t_n, f(t_n))_n$ for certain classes of unequally spaced data nodes $(t_n)_n$ and corresponding $l_2$ sampled data $(f(t_n))_n$. Existence of these polynomials allows one to construct a simple sequence of approximants for an arbitrary multivariate bandlimited function $f$ which demonstrates $L_2$ and uniform convergence on $R^d$ to $f$. A simpler computational version of this recovery formula is also given, at the cost of replacing $L_2$ and uniform convergence on $R^d$ with $L_2$ and uniform convergence on increasingly large subsets of $R^d$. As a special case, the polynomial interpolants of given $l_2$ data converge in the same fashion to the multivariate bandlimited interpolant of that same data. Concrete examples of pertinent Riesz bases and unequally spaced data nodes are also given.

Actuarial Science Seminar
 Ruin Models Featuring Interest and Diffusion Link: View Poster Speaker: Ilie-Radu Mitric (University of Connecticut) Time: Friday, September 23, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: A number of extensions to the risk theory models are analyzed. Initially, we consider a multi-threshold compound Poisson surplus process with interest earned at a constant rate. Then, we analyze a multi-layer compound Poisson surplus process perturbed by diffusion and examine the behavior of the Gerber-Shiu discounted penalty function. Lastly, we considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix- Exponential (ME) distribution. Under this scenario, we present a general methodology to analyze the Gerber-Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for the absolute ruin probabilities in the generalized Erlang (2) case complement recent results from literature obtained under the classical risk model.

Algebra Seminar
 A combinatorial formula for cluster variables of rank two Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Tuesday, September 27, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: This talk is about the generators of cluster algebras of rank two, the so-called cluster variables. Cluster variables are certain Laurent polynomials in two variables which are defined in a recursive way. Each of these variables corresponds to a (preprojectiv or preinjective) representation of the quiver with two vertices, 1 and 2, and r arrows from 2 to 1, also known as the generalized Kronecker quiver. I will present a direct formula for the cluster variables in terms of certain subpaths of a specific lattice path. This formula is the result of a joint work with Kyungyong Lee.

UConn Math Club
 An Introduction to Elliptic Curves Link: View Poster Speaker: David Pollack (Wesleyan ) Time: Wednesday, September 28, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: What are all rational number solutions to the equation y2 = x3 + 17? An easy rational solution is (x,y) = (2,5). Other rational solutions are less apparent, such as (-64/25,59/125) and (5023/3249,842480/185193)! How were they found? The graph of an equation like y2 = x3 + 17 is called an elliptic curve, and such curves are a central topic in number theory. In recent years elliptic curves played a crucial role in the proof of Fermat's Last Theorem, and they are of great use in cryptography. We'll give an overview of elliptic curves, discussing some of their main properties and ending with several open questions. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 Spectral Graph Theory Link: View Poster Speaker: Daniel Kelleher (University of Connecticut) Time: Friday, September 30, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: "This monograph is an intertwined tale of eigenvalues and their use in unlocking a thousand secrets about graphs. The stories will be told — how the spectrum reveals fundamental properties of a graph, how spectral graph theory links the discrete universe to the continuous one through geometric, analytic and algebraic techniques..." –Fan Chung, Spectral Graph Theory, 1996. Comments: Free Pizza (courtesy of Mathematics Department). Come down at 12:30 to mingle with other grad students before the talk.

Analysis and Probability Seminar
 Interlacing particle systems Link: View Poster Speaker: Jeffrey Kuan (Harvard) Faculty Sponsor:Ben-Ari Time: Friday, September 30, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: We consider an interlacing particle system in the two-dimensional lattice, which can also be interpreted as a growing stepped surface. This model has connections to the representation theory of Lie groups and to the AKPZ equation from mathematical physics. The main results are the discovery of new kernels, and that the fluctuations of the height function converge to the Gaussian free field

Actuarial Science Seminar
 Sounding the Alarm Link: View Poster Speaker: John Robinson (International Association of Black Actuaries (IABA)) Time: Friday, September 30, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: This talk will discuss about post-retirement medical and some of its social implications. Public sector entities have been required to have actuarial valuations of their postretirement benefits performed only since 2008, thanks to GASB 45. This has led to the quantification of many billions of dollars of liabilities which are largely unfunded. The presentation will outline the valuation's objectives and process, and demonstrate why we all need to be concerned about these benefits. A few minutes will also be spent about the International Association of Black Actuaries (IABA).

Algebra Seminar
 Serre's uniformity question and bounds on torsion subgroups of elliptic curves Link: View Poster Speaker: Alvaro Lozano-Robledo (University of Connecticut) Time: Tuesday, October 4, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk I will begin by introducing elliptic curves and discuss the structure theorem of the group of rational points (the Mordell-Weil theorem), which says that the group of rational points is a finitely generated abelian group. Next, I will explain what is known about the torsion subgroup on an elliptic curve, and will introduce a question of Serre (the so-called uniformity question). I will end with applications of Serre's question to finding bounds on the size of torsion subgroups.

UConn Math Club
 Bijective Proofs Link: View Poster Speaker: Steven Pon (University of Connecticut) Time: Wednesday, October 5, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Some mathematical formulas can be proved in different ways, and these different proofs may each have an advantage that makes it “better” than the others. When a formula involves positive integers, one of the most interesting (but not necessarily simple!) ways of proving the formula is a technique called a bijective proof. In this talk I'll introduce bijective proofs and we'll work through some examples, finishing with some unsolved problems. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 Inversion of quasiseparable Vandermonde-like matrices Link: View Poster Speaker: Shirani Perera (University of Connecticut) Time: Friday, October 7, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Specialization of Inversion of Vandermonde matrices which is called inversion of quasiseparable Vandermonde is a known result due to [BEGOT]. But in this result we fill the missing part of specialization of Inversion of Vandermonde-like matrices i.e. quasiseparable Vandermonde-like matrices. To do so we had to identify the structure of displacement operator with generators. Moreover the key thing in here is we identified two-term recurrence relations between columns of basis transformation matrix which is much more favorable by comparing the $k$-term recurrence relations between columns in basis transformation matrix in present. Finally we used the immediate property together with the structure of the displacement operator to invert quasiseparable Vandermonde-like matrices having ${O}(n^2)$ complexity. Comments: Free Pizza (courtesy of Mathematics Department).

Cluster Algebras Reading Seminar
 Hall algebras Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Friday, October 7, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Finite Mixture Models with Insurance Applications Link: View Poster Speaker: Matthew Flynn (Travelers) Time: Friday, October 7, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: Practical insurance modeling applications can run into two challenges: long-tailed loss distributions and modeling samples with a undefined or unlabeled mixes of claim types, resulting in multi-modal loss distributions. Finite mixture models are one promising approach to both of the above challenges. This session will address practical modeling tips, providing examples in several software tools: R, JMP, and SAS.

PDE and Differential Geometry Seminar
 Optimal Regularity and Nondegeneracy for minimizers of an energy arising from the fractional Laplacian Link: View Poster Speaker: Ray Yang (Courant Institute of Mathematical Sciences) Time: Monday, October 10, 2011 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We discuss the optimal regularity and non degeneracy of an energy related to the fractional Laplacian. This work is related to, but addresses a different problem from, recent work of Cafarelli, Roquejo re, and Sire. A variant of the boundary Harnack inequality is also proved, where it is no longer required that the function be 0 along the boundary.

Logic Seminar
 Finding something real in Zilber's field Link: View Poster Speaker: Ahuva Shkop (Ben-Gurion) Time: Monday, October 10, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: In 2004, Zilber constructed a class of exponential fields, known as pseudoexponential fields, and proved that there is exactly one pseudoexponential field in every uncountable cardinality up to isomorphism. He conjectured that the pseudoexponential field of size continuum, K , is isomorphic to the classic complex exponential field. Since the complex exponential field contains the real exponential field, one consequence of this conjecture is the existence of a real closed exponential subfield of K . In this talk, I will sketch the proof of the existence of uncountably many non-isomorphic countable real closed exponential subfields of K and discuss some of their properties.

Algebra Seminar
 Fourth moments and an identity of the divisor function Link: View Poster Speaker: Yichao Zhang (University of Connecticut) Time: Tuesday, October 11, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: This is based on my Ph.D thesis and a joint work with Henry H. Kim. As a different formulation of Lindelof Hypothesis on the Riemann zeta function, moment problems were introduced. Later, people considered general L-functions, starting with the L-functions associated to modular forms, and moment problems were naturally extended. Moment problems are far from being solved in any case, for example, complete solutions only exist for the second and fourth moment of Riemann zeta function and second moment of L-functions associated to modular forms. For higher moments, even reducing the exponents is much harder. In this talk, we shall see an average version of fourth moments problem for L-functions associated to newforms. We shall also include an identity of the divisor function defined over quaternion algebras, which plays an important role in the proof and is of interest in its own right.

Colloquium
 Discussion and Brainstorming: Design curriculums to meet the modern business need Link: View Poster Speaker: Maoli Chang (Affinion Group, Stamford CT) Faculty Sponsor:Wolodymyr Madych Time: Wednesday, October 12, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In 1980, Alvin Toffler postulated that we were entering what he called the Third Wave, the Information Age. He has anticipated the explosion of data and information. It turned out that he was dead on with his prediction. Through the development of computers and advancement of internet and mobile, we have seen more and more data are generated daily, more and more of these data are used to help us to make decisions in all walks of life. No matter what the industry is, no matter what products and services are provided. In 2010 alone, more data were generated than in all of previous human history combined, according to Harvard Business Review. The business community has ever increasing need to make decisions based on information and knowledge. Any decision management has become information decision management. We have overwhelming amount of data. To make the right and best decision has become ever challenging. It requires unparalleled programming skills, analytical skills, modeling skills, and new tools, new software. This has presented a great opportunity for students in Mathematics, Statistics, and Computer Science to play greater and expanded roles.

UConn Math Club
 Rational parametrizations Link: View Poster Speaker: Michael Joseph (University of Connecticut) Time: Wednesday, October 12, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: On the graph of a conic (a curve given by an equation of degree 2, like a circle, ellipse, or hyperbola), it's easy to find real points by picking x almost at random and solving for y. However, if we want to find rational points -- where both x and y are rational, then guessing is often bad: a point where x is rational usually does not have y rational too. We will give, in several concrete examples, a geometric method to describe all the rational points on a conic (whose equation has rational coefficients). This technique of “rational parametrization” is an important mixture of algebra and geometry which is often not seen in standard undergraduate geometry courses. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

S.I.G.M.A. Seminar
 An Introduction to Ramsey Theory Link: View Poster Speaker: Reed Solomon (University of Connecticut) Time: Friday, October 14, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Ramsey theory is a part of combinatorics which looks for certain types of regularities. The simplest example of a theorem in Ramsey theory is the Pigeonhole Principle which says that if you put infinitely many pigeons into finitely many pigeonholes, then some pigeonhole contains infinitely many pigeons. In this talk, we will explore several theorems in Ramsey theory and some applications of these theorems. Comments: Free Pizza (courtesy of Mathematics Department).

Analysis and Probability Seminar
 An Empirical Process Interpretation of a Model of Species Survival Link: View Poster Speaker: Iddo Ben-Ari Faculty Sponsor:Ben-Ari Time: Friday, October 14, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: I will discuss a model of species survival recently proposed by Michael and Volkov, and which was inspired by the Bak-Sneppen model. The model could be viewed as a variant of empirical processes in which the sample size is a random process and, when decreasing, samples of smallest numerical values are discarded. Michael and Volkov proved that the empirical distribution functions converge to the sample distribution conditioned not to be below a certain threshold. I will present a functional central limit theorem for the fluctuations of the empirical distribution functions. These scale to a process which is discontinuous at the threshold. It is Gaussian above the threshold, strictly positive at the threshold, and zero below the threshold.

Cluster Algebras Reading Seminar
 Reineke's Identities Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Friday, October 14, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Summarizing Insurance Scores Using a Gini Index Link: View Poster Speaker: Edward W. (Jed) Frees (University of Wisconsin - Madison and ISO Innovative Analytics) Time: Friday, October 14, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: Joint work with Glenn Meyers and David Cummings (ISO Innovative Analytics) Individuals, corporations and government entities regularly exchange financial risks $y$ at prices $P$. Comparing distributions of risks and prices can be difficult, particularly when the financial risk distribution is complex. For example, with insurance, it is not uncommon for a risk distribution to be a mixture of zeros (corresponding to no claims) and a right-skewed distribution with thick-tails (the claims distribution). However, analysts do not work in a vacuum and, in cases such as insurance, use insurance scores relative to prices, called "relativities," that point to areas of potential discrepancies between the risk and price distributions. Using the relativity ordering, we develop a Lorenz curve and Gini index that can cope with adverse selection and measure potential profit. In 1905, Max Otto Lorenz displayed skewed income distributions using a graph now known as the Lorenz curve. In 1912, Corrado Gini summarized this curve with a statistic now known as the Gini index. Both devices are widely used in welfare economics, among other fields. This work extends these concepts to a financial context by ordering risks. We provide a detailed example using homeowners insurance. We develop theory to calibrate sample sizes, establishing that the number of observations typically encountered in insurance practice are sufficient for reliable estimation. Further, we show that the Gini index can be written in terms of covariance operators, thus expanding the scope of interpretations.

PDE and Differential Geometry Seminar
 Nonnegative solutions of nonlinear elliptic equations and their nodal structure Link: View Poster Speaker: Peter Polacik (University of Minnesota) Time: Monday, October 17, 2011 at 3:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We consider the Dirichlet problem for a class of fully non-linear elliptic equations on a bounded domain $Omega$. We assume that $Omega$ is symmetric about a hyperplane $H$ and convex in the direction perpendicular to $H$. By a well-known result of Gidas, Ni and Nirenberg and its generalizations, all positive solutions are reflectionally symmetric about $H$ and decreasing away from the hyperplane in the direction orthogonal to $H$. For non-negative solutions, this result is not always true. Nonetheless, a lot can be said about the symmetry of such solutions and of their nodal set. After presenting a theorem to that regard, we will show examples of non-negative solutions with non-trivial nodal sets. Also we will discuss a class of homogeneous semi-linear problems which do not admit any such solutions.

Algebra Seminar
 Computing Tropical Resultants Link: View Poster Speaker: Josephine Yu (Georgia Tech) Time: Monday, October 17, 2011 at 4:20 pm Place: TLS 301 (UConn - Storrs) Abstract: (Please note special day - Monday! - and special room - TLS 301 - and special time 4:20 - 5:15) We fix the supports A=(A_1,...,A_k) of a list of tropical polynomials and define the tropical resultant TR(A) to be the set of choices of coefficients such that the tropical polynomials have a common solution. We show that TR(A) equals the tropicalization of the algebraic variety of solvable systems and that its dimension can be computed in polynomial time. The tropical resultant inherits a fan structure from the secondary fan of the Cayley configuration of A and we present algorithms for the traversal of TR(A) in this structure. We also present a new algorithm for recovering a Newton polytope from the support of its tropical hypersurface. We use this to compute the Newton polytope of the sparse resultant polynomial in the case where TR(A) is of codimension 1. Finally we consider the more general setting of specialized tropical resultants and report on experiments with our implementations. This is joint work with Anders Jensen.

Analysis and Probability Seminar
 Sparse regularization in limited angle tomography Link: View Poster Speaker: Juergen Frikel (Helmholtz Zentrum München, Deutsches Forschungszentrum für Gesundheit und Umwelt) Faculty Sponsor:Madych Time: Tuesday, October 18, 2011 at 4:15 pm Place: MSB M118 (UConn - Storrs) Abstract: We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, such as filtered backprojection (FBP), do not perform well in such situations. To stabilize the reconstruction procedure additional prior knowledge about the unknown object has to be integrated into the reconstruction process. In this talk, we will discuss the use of the sparse regularization technique in combination with curvelets. We argue that this technique gives rise to an edge-preserving reconstruction. Moreover, we show that the dimension of the problem can be significantly reduced in the curvelet domain. To this end, we give a characterization of the kernel of limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will present the practical relevance of these results. Comments: UNUSAL time, day and room.

Colloquium
 Parameter Estimation in Exponential Sums Link: View Poster Speaker: Frank Filbir (Helmholtz Institut München) Time: Wednesday, October 19, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Many applications in digital signal processing, NMR spectroscopy, direction finding in antennas, as well as numerical analysis lead to the problem of finding hidden periodicities. The problem can be stated as follows. Let l be a positive integer and assume we are given finitely many samples x(k) for k running from -N to N of a real signal x(t)= ∑j aje-imωjt, where the sum runs from -l to l. The problem consists in determining the ωj's from the samples. This problem has a long history. A first solution was already given by the French mathematician Gaspard de Prony in 1795. For different reasons the problem was considered over and over again. In the 1990's W. B. Jones, O. Njĺstad, and E. B. Saff showed how this problem can be related to orthogonal polynomials on the unit circle. They proposed an algorithm which approximates the ωj's with linear rate of convergence. We will show how this method can be improved by using localized kernels. This talk is based on joint work with Hrushikesh N. Mhaskar, Department of Mathematics, California State University, U.S.A. and Jürgen Prestin, Department of Mathematics, University Lübeck, Germany.

UConn Math Club
 The Strong Pseudoprime Test and the iPhone Link: View Poster Speaker: Jeremy Teitelbaum (University of Connecticut) Time: Wednesday, October 19, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: I will explain the strong pseudoprime test (sometimes called the Miller-Rabin test). This is a method for determining if a number is composite, with a high degree of confidence, and without having to factor the number. As a bonus, I will explain a somewhat convoluted method for putting a reliable primality test onto your iphone. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

Colloquium
 Feynman path integrals in curved spaces Link: View Poster Speaker: Bruce Driver (UCSD) Faculty Sponsor:Gordina Time: Thursday, October 20, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In a first (perhaps second) course on quantum mechanics one learns to quantize a classical mechanical system in the operator formalism via "canonical quantization." However, when dealing with classical systems with non-flat configuration spaces, canonical quantization may be ambiguous due to problems with "operator orderings." On the other hand at first blush, Feynman's path integral interpretation of quantum mechanics does not seem to suffer from these ambiguities. However, there is no free lunch and the same ambiguities reappear in the Feynman picture when one actually tries to precisely define these path integral expressions. This talk will describe some attempts to mathematically interpret Feynman's picture for quantum mechanical systems in geometric settings. Choices will have to be made and these choices lead to different quantizations of the same classical system. (All terms in this abstract will be explained at least at the level needed for this talk.)

S.I.G.M.A. Seminar
 Lambert W Function and Infinite Exponential Link: View Poster Speaker: Michael Joseph (University of Connecticut) Time: Friday, October 21, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Lambert W Function is a function $W(z)$ which satisfies the relation $W(z)e^{(W(z))}=W(z)$ for any complex number $z$. It is defined as an inverse function, similar to square roots, logarithms, and inverse trigonometric functions, as it is the inverse of the function $ze^z$. This function is useful in finding closed form solutions to many equations which contain both exponential and power functions. In this talk, I will discuss this function, with respect to both the real and the complex numbers. I will also discuss the infinite exponential, an interesting mathematical problem related to the W function. Comments: Free Pizza (courtesy of Mathematics Department).

Cluster Algebras Reading Seminar
 The integration map Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Friday, October 21, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Enterprise Risk Management (ERM) for Small Businesses Link: View Poster Speaker: Jay Vadiveloo (Towers Watson and UConn) Time: Friday, October 21, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: Joint presentation with Jai Gangwani. Enterprise Risk Management or ERM is one of the hottest topics these days in the financial world. However, the focus of ERM has always been on large corporations. Small businesses, which are the fastest growing business segment in the US and also the business segment which experiences the highest failure rates, are completely ignored by ERM professionals and in the ERM literature. Our presentation will describe the ERM for Small Businesses initiative that has been developed by the Goldenson Center for Actuarial Research at UConn. A graduate student will share his experiences on an ERM project on the Willimantic Brewing Company that he is currently working on at the Goldenson Center. We will discuss analogies between ERM for Small Businesses and ERM for large corporations, and describe some recent opportunities that have emerged to do this initiative on a larger, funded basis.

Colloquium
 Coloring Some Perfect Graphs Link: View Poster Speaker: Maria Chudnovsky (Columbia) Time: Wednesday, October 26, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: A graph G is called perfect if for every induced subgraph H of G, the chromatic number and the clique number of H are equal. After the recent proof of the Strong Perfect Graph Theorem, and the discovery of a polynomial-time recognition algorithm, the central remaining open question about perfect graphs is finding a combinatorial polynomial-time coloring algorithm. (There is a polynomial-time algorithm known, using the ellipsoid method). Recently, we were able to find such an algorithm for a certain class of perfect graphs, that includes all perfect graphs admitting no balanced skew-partition. The algorithm is based on finding special "extremal" decompositions in such graphs; we also use the idea of "trigraphs".

UConn Math Club
 Formulas for π Link: View Poster Speaker: Jared Weinstein (BU) Time: Wednesday, October 26, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Humanity has been discovering interesting formulas for π since at least the Middle Ages.  We'll present a few of those surprising formulas.  One of them, called the Wallis product, tells us something about probabilities.  To wit, there is a connection between the square root of π and the probability that a Pachinko ball lands directly below where it was dropped. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders! Additional Comments: USG Funded

S.I.G.M.A. Seminar
 Tools of the Trade in Large Lecture Calculus Instruction Link: View Poster Speaker: Amit Savkar (University of Connecticut) Time: Friday, October 28, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Over the last several years, Calculus 1 and Calculus 2 have been taught in large lectures at the University of Connecticut. Last year we developed three online resources: a) Electronic flash cards, b) Clicker question bank, and c) Micro Videos as supplemental material to assist the students in their learning process. After one year we now have data that suggest some of the things that students like and would like to see more of. I will be presenting the student'’s perceptions and their input on the resources that were created for Calculus 1. Comments: Free Pizza (courtesy of Mathematics Department).

Cluster Algebras Reading Seminar
 Derived equivalences and graded equivalences Link: View Poster Speaker: Lucas David-Roesler (University of Connecticut) Time: Friday, October 28, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Variable Selection in GLM with Actuarial Applications Link: View Poster Speaker: Wenyuan Zheng (University of Connecticut) Time: Friday, October 28, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: When pricing an insurance product, companies collect information from potential policyholders to construct a premium structure. Regardless of the type of insurance product, there is always an infinite amount of information that may be gathered from each policyholder (e.g. credit history, medical history, physical exam). It is important to decide which variables are significant to model a fair and equitable pricing structure. Although an informal process of variable selection is often employed, a more formal statistical procedure is recommended to avoid inefficiencies and imprecision. Bayesian variable selection methods offer such a framework and enable the analyst to (1) incorporate prior beliefs about the significance of specific covariates, (2) include information about the relative cost of the covariates, and (3) obtain the probability that each covariate is included in the model. In this talk, initially we provide an introduction to three Bayesian variable selection techniques. Then using data from Singapore automobile insurers, we fit to Generalized Linear Models of claim frequency and severity. Lastly, we extend these procedures to Zero-Modified and Hurdle Poisson models for claim count, and Generalized Gamma model for severity data.

Algebra Seminar
 Automorphisms of Certain Maximal Curves Link: View Poster Speaker: Elisabeth Malmskog (Wesleyan University) Time: Tuesday, November 1, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Hasse-Weil bound restricts the number of points of a curve which are defined over a finite field; if the number of points meets this bound, the curve is called maximal. Giulietti and Korchmaros introduced a curve C_3 which is maximal over F_q^6 and determined its automorphism group. Garcia, Guneri, and Stichtenoth generalized this construction to a family of curves C_n, indexed by an odd integer n at least 3, such that C_n is maximal over F_q^(2n). Rachel Pries, Robert Guralnick, and I determined the automorphism group Aut(C_n) when n > 3; in contrast with the case n = 3, it fixes the point at infinity on C_n. The proof uses ramification groups and results from group theory. I will discuss maximal curves, automorphism groups, and outline our proof.

UConn Math Club
 Sandpiles and Dominos Link: View Poster Speaker: David Perkinson (Reed College) Time: Wednesday, November 2, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: The Abelian Sandpile Model is a mathematical model of a pile of sand developed by physicists around 1990 to exemplify self-organized criticality, a phenomenon which describes a state at the border of stability. The Gutenberg-Richter law in geophysics and Zipf's law in linguistics are often cited as real-world examples. In this talk, I will present work done over the last few years with Reed College students connecting the sandpile model with domino tilings. We will be interested in tiling an m x n checkerboard (m rows and n columns) with dominos. A domino covers exactly two squares of the checkerboard, and a tiling consists of covering the checkerboard with non-overlapping dominos. Three questions to think about as a warm-up before the talk: 1) What are conditions on m and n that ensure a tiling exists? 2) How many ways are there of tiling a 3 x 3 checkerboard? 3) Take a flexible 4 x 4 checkerboard and glue one edge to an opposite edge with a twist, to get a Moebius band. How many ways are there of tiling this twisted checkerboard? Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

Colloquium
 Faculty meeting Link: View Poster Speaker: Evarist Gine-Masdeu Time: Thursday, November 3, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs)

S.I.G.M.A. Seminar
 The Continued Fraction Expansion of $e$ Link: View Poster Speaker: John Haga (University of Connecticut) Time: Friday, November 4, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The continued fraction expansion of e was first described by Euler, who proved that the expansion was accurate by solving a differential equation. This served as a proof that $e$ is irrational. While developing a method to approximate power series by rational functions, Hermite's student Pade defined a class of integrals which, as we will see, can be used to offer an alternative proof as to the accuracy of the continued fraction expansion of $e$. Comments: Free Pizza (courtesy of Mathematics Department).

Analysis and Probability Seminar
 A quasi-invariance result for subelliptic heat kernel measures Link: View Poster Speaker: Tai Melcher (University of Virginia) Faculty Sponsor:Gordina Time: Friday, November 4, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: We will discuss recent Cameron-Martin type quasi-invariance results for subelliptic heat kernel measures on infinite-dimensional analogues of the Heisenberg group. Quasi-invariance results are of interest, for example, in the study of smoothness of measures on infinite-dimensional spaces and have previously been the subject of much study in elliptic settings. In finite dimensions, one typically defines smoothness as absolute continuity with respect to some reference measure and smoothness of the associated density. In infinite dimensions, in the absence of a canonical reference measure, alternative interpretations of smoothness must be made. In particular, in an infinite-dimensional setting, it is natural to interpret quasi-invariance as a smoothness property. Typically the proofs in elliptic cases rely on lower bounds on the Ricci curvature; of course, such lower bounds are unavailable in a subelliptic setting. Our proof replaces this curvature requirement with a curvature-dimension inequality better suited to the subelliptic case. This is joint work with M. Gordina and F. Baudoin.

Cluster Algebras Reading Seminar
 The integration map Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Friday, November 4, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Accounting for Regime and Parameter Uncertainty in Regime-Switching Models Link: View Poster Speaker: Brian Hartman (University of Connecticut) Time: Friday, November 4, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: As investment guarantees become increasingly complex, realistic simulation of the price becomes more critical. Currently, regime-switching models are commonly used to simulate asset returns. Under a regime switching model, simulating random asset streams involves three steps: (i) estimate the model parameters given the number of regimes using maximum likelihood, (ii) choose the number of regimes using a model selection criterion, and (iii) simulate the streams using the optimal number of regimes and parameter values. This method, however, does not properly incorporate regime or parameter uncertainty into the generated asset streams and therefore into the price of the guarantee. To remedy this, we adopt a Bayesian approach to properly account for those two sources of uncertainty and improve pricing. Joint work with Matt Heaton at NCAR.

Logic Seminar
 An Introduction to the Functional Interpretation Link: View Poster Speaker: Henry Towsner (UConn) Time: Monday, November 7, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: The functional interpretation is one of the main tools of modern proof theory, providing a systematic way for extracting constructive information from proofs. This talk will give an introduction to what the functional interpretation is and how it is used, culminating in a recent application to reverse mathematics.

Algebra Seminar
 A combinatorial description of the Casselman-Shalika formula Link: View Poster Speaker: Ben Salisbury (University of Connecticut) Time: Tuesday, November 8, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Casselman-Shalika formula asserts that a certain integral over a $p$-adic matrix group may be expressed as a product over positive roots corresponding to that matrix group. Recently, for the case when the underlying root system is of finite type A, this formula has been reinterpreted as a sum over the highest weight crystal $B(\lambda+\rho)$. It is known that such crystals have a combinatorial realization in terms of semistandard Young tableaux. In this talk, we explain how the realization of $B(\lambda+\rho)$ in terms of semistandard Young tableaux yields a statistic at each vertex defining a coefficient making this expansion possible, without the need to generate the entire crystal graph. Moreover, these coefficients lead to a definition of a polynomial $H_{\lambda+\rho}(-;q) \in \mathbf Z[q^{-1}]$ which recovers data about the relevant representations.

UConn Math Club
 Egyptian Fractions Link: View Poster Speaker: Konstantina Christodoulopoulou (University of Connecticut) Time: Wednesday, November 9, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: Ancient Egyptians had a curious and cumbersome way of expressing fractions: they represented them using only distinct unit fractions. Since then, Egyptian fractions have appeared in various mathematical contexts and many mathematicians have worked on questions related to them. In this talk, I will discuss some of the problems related to Egyptian fractions. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders!

Colloquium
 Graduate student meeting Link: View Poster Speaker: Evarist Gine-Masdeu Time: Thursday, November 10, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs)

S.I.G.M.A. Seminar
 Quadratic Forms Versus Higher-Degree Forms Link: View Poster Speaker: Keith Conrad (University of Connecticut) Time: Friday, November 11, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Quadratic forms (i.e., homogeneous polynomials of degree 2) appear throughout mathematics and they form a vibrant area of research in their own right. Forms of higher degree (i.e., homogeneous polynomials of degree 3 or higher), by comparison, have a far less developed general theory. It is natural to ask why this is so. We will discuss some of the important features of quadratic forms and the extent to which those features can -- or can not -- be extended to forms of higher degree. Comments: Free Pizza (courtesy of Mathematics Department).

Analysis and Probability Seminar
 Discrete Homotopies, Essential Circles, and Finiteness of Fundamental Groups Link: View Poster Speaker: Jay (Leonard) Wilkins (UCONN) Time: Friday, November 11, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: Discrete homotopy theory uses discrete chains and homotopies rather than their usual continuous counterparts. Building on the work of Berestovskii-Plaut regarding uniform spaces, and generalizing the covering spectrum of Sormani-Wei, we use discrete homotopy theory to define epsilon-covering maps and associated groups that describe the topology of a geodesic space at a given scale. These methods are particularly amenable to course geometric tools such as Gromov-Hausdorff convergence. The topology of the covers changes at specific values we call homotopy critical values. In compact geodesic spaces (e.g. Riemannian manifolds) these values are completely determined by lengths of essential circles whose number and multiplicity are controlled in any Gromov-Hausdorff precompact class. As applications, which are new even for Riemannian manifolds, we will - time permitting - 1) describe a new set of generators for the fundamental group of a compact geodesic space, 2) compare and contrast our results to those of Sormani-Wei, 3) introduce a circle spectrum intermediate between the covering and length spectra, and 4) prove a fundamental group finiteness theorem that does not require lower bounds on curvature, volume, or the 1-systole.

Cluster Algebras Reading Seminar
 The integration map 2 Link: View Poster Speaker: Arend Bayer (University of Connecticut) Time: Friday, November 11, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Colloquium
 On Zaremba's Conjecture Link: View Poster Speaker: Alex Kontorovich (Yale) Time: Friday, November 11, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: It is folklore that modular multiplication is “random”. This concept is useful for many applications, such as generating pseudorandom sequences, or in quasi-Monte Carlo methods for multi-dimensional numerical integration. Zaremba's theorem quantifies the quality of this “randomness” in terms of certain Diophantine properties involving continued fractions. His 40-year old conjecture predicts the ubiquity of moduli for which this Diophantine property is uniform. It is connected to Markoff and Lagrange spectra, as well as to families of “low-lying” divergent geodesics on the modular surface. We prove that a density one set satisfies Zaremba's conjecture, using recent advances such as the circle method and estimates for bilinear forms in the Affine Sieve, as well as a “congruence” analog of the renewal method in the thermodynamic formalism. This is joint work with Jean Bourgain.

Actuarial Science Seminar
 Mortality Improvements: Historical Trends and Considerations for Developing Future Assumptions Link: View Poster Speaker: Marianne Purushotham (Towers Watson) Time: Friday, November 11, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: This presentation reviews trends in mortality improvement from a global perspective with a focus on the US, Canada and the UK. In addition, recent trends and the impact of current health and lifestyle changes are discussed with a view toward providing actuaries with potential tools for developing future assumptions.

Logic Seminar
 Invariant Measures Concentrated on Countable Structures Link: View Poster Speaker: Rehana Patel (Wesleyan) Time: Monday, November 14, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: The Erd"os-R'enyi random graph construction can be seen as inducing a probability measure concentrated on the Rado graph (sometimes known as the countable 'random graph') that is invariant under arbitrary permutations of the underlying set of vertices. A natural question to ask is: For which other countable structures does such an invariant measure exist? Until recent work of Petrov and Vershik (2010), the answer was not known even for Henson's countable homogeneous-universal triangle-free graph. We provide a characterisation of countable structures that admit invariant measures, in terms of the notion of (group-theoretic) definable closure. This leads to new examples and non-examples, including a complete list of countable homogeneous graphs and partial orders that satisfy our criterion. Our proof uses infinitary logic to build on Petrov and Vershik's constructions, which involve sampling from certain continuum-sized objects. In the case when the measure is concentrated on a graph, these continuum-sized objects are in fact 'graph limits' in the sense of Lovasz and Szegedy (2006). Joint work with Nathanael Ackerman and Cameron Freer.

Algebra Seminar
 A tour through modern deformation theory Link: View Poster Speaker: Jeremy Pecharich (Mount Holyoke College) Time: Tuesday, November 15, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Deformation theory went through a transformation partially led by Deligne, Drinfeld, Kontsevich, Quillen and Stasheff in the beginning of the 1990s. The philosophy is that any suitably' nice deformation problem in characteristic 0 is governed by a differential graded Lie algebra. We will discuss this philosophy through examples from complex geometry and algebra. If time permits we will discuss joint work with V. Baranovsky and V. Ginzburg on an extension of Gabber's integrability theorem to the non-filtered case.

Mathematics Education
 If It Pleases the Court: The Use of Mathematical Reasoning in the Courtroom Link: View Poster Speaker: Mark Myers (Point Break Associates, LLC) Faculty Sponsor:Cardetti Time: Wednesday, November 16, 2011 at 4:30 pm Place: BPB 131 (Biology/Physics Building) (UConn - Storrs) Abstract: For most of the 300 years since Nicholas Bernoulli submitted his thesis Usu Artis Conjectandi in Jure (“The Use of the Art of Conjecturing in the Law”), the use of mathematics – particularly, probability and statistics – in legal reasoning was contemplated by courts in the U.S. and England with considerable suspicion. However, the passing of the Civil Rights Act in the 1960s ushered in a wave of state and federal cases that presented unique issues of proof, and began the slow process of legitimizing the use of statistical evidence in the courtroom. These decisions, together with the rise of increasingly advanced technologies at issue in the disputes between parties, has opened the door to the introduction of other mathematical arguments that must be harnessed by attorneys, presided over by judges and decided by juries. This talk begins with a review of some of the mathematical principles and techniques that regularly make appearances in U.S. courtrooms – whether applied correctly or incorrectly – sometimes with dispositive consequences. Moreover, the increasing use of mathematics in court raises significant pedagogical questions: For example, what is the most effective way to integrate mathematical training into the curriculum of students entering the legal profession? How can ongoing education most efficiently be structured for judges who must decide cases in an increasingly technical world? And how do the rules and procedures that govern the presentation of expert testimony in court support – or hinder – the ability of jurors to quickly grasp the essence of a mathematical assertion? This talk explores a few of these connections between pedagogy and jurisprudence, with the aim of highlighting opportunities to improve the quality of mathematical discourse in both the legal classroom and the courtroom. Comments: This talk is part of the Speaker Series in Mathematics Education Additional Comments: UNUSUAL time and place!!

Colloquium
 If It Pleases the Court: The Use of Mathematical Reasoning in the Courtroom Link: View Poster Speaker: Mark Myers (Point Break Associates, LLC) Faculty Sponsor:Fabiana Cardetti Time: Wednesday, November 16, 2011 at 4:30 pm Place: BPB 131 (UConn - Storrs) Abstract: For most of the 300 years since Nicholas Bernoulli submitted his thesis Usu Artis Conjectandi in Jure (“The Use of the Art of Conjecturing in the Law”), the use of mathematics – particularly, probability and statistics – in legal reasoning was contemplated by courts in the U.S. and England with considerable suspicion. However, the passing of the Civil Rights Act in the 1960s ushered in a wave of state and federal cases that presented unique issues of proof, and began the slow process of legitimizing the use of statistical evidence in the courtroom. These decisions, together with the rise of increasingly advanced technologies at issue in the disputes between parties, has opened the door to the introduction of other mathematical arguments that must be harnessed by attorneys, presided over by judges and decided by juries. This talk begins with a review of some of the mathematical principles and techniques that regularly make appearances in U.S. courtrooms – whether applied correctly or incorrectly – sometimes with dispositive consequences. Moreover, the increasing use of mathematics in court raises significant pedagogical questions: For example, what is the most effective way to integrate mathematical training into the curriculum of students entering the legal profession? How can ongoing education most efficiently be structured for judges who must decide cases in an increasingly technical world? And how do the rules and procedures that govern the presentation of expert testimony in court support – or hinder – the ability of jurors to quickly grasp the essence of a mathematical assertion? This talk explores a few of these connections between pedagogy and jurisprudence, with the aim of highlighting opportunities to improve the quality of mathematical discourse in both the legal classroom and the courtroom Comments: Please note special time and place.

UConn Math Club
 Bhargava's Generalized Factorials Link: View Poster Speaker: Rebecca Torrey (Amherst College) Time: Wednesday, November 16, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: As an undergraduate at Harvard, Manjul Bhargava introduced a beautiful generalization of the well-known factorial function.  What is this generalization and why is it the “right” generalization?  Come find out! Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders! Additional Comments: USG Funded

Colloquium
 Plumes in kinetic transport: how simple random walk can be too simple Link: View Poster Speaker: Michel Dekking (Technical University of Delft) Time: Thursday, November 17, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: I consider a discrete time process for kinetic transport on the two dimensional integer lattice. A particle can move due to advection in the x-direction and due to dispersion. This happens when the particle is free, but it can also be adsorbed and then does not move. When the dispersion of the particle is modeled by simple random walk, strange phenomena occur. I will resolve these problems and give some more properties of this process and its associated system of partial differential equations.

Cluster Algebras Reading Seminar
 Mutations and DT-invariants Link: View Poster Speaker: Ralf Schiffler (University of Connecticut) Time: Friday, November 18, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Claim Cost Management Link: View Poster Speaker: Asiri Gunathilaka (University of Connecticut) Time: Friday, November 18, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: Insurance companies looking to manage their risk exposure are faced with unprecedented challenges due to ever increasing uncertainty in the economic environment. As insurance companies begin to feel pressure to cut cost in these lean economic times, most companies have recognized importance of having a robust claim cost management process in their grasp. In these uncertain times even the companies with best industry practices seek feedback from independent reviewers to attain competitive advantage by increasing effectiveness of their current strategies while identifying new approaches for claim cost management. Towers Watson is a pioneer in the area of claim cost management consulting. An interdisciplinary research team the Goldenson Center for Actuarial Research at UConn has assembled has undertaken a project that improves Towers Watson product offerings in the area of claim cost management. The team lead by Dr. Jay Vadiveloo include members from both UConn and Towers Watson. Going forward the team will explore applications of predictive modeling for claim cost management. The presentation will cover the overview of the project undertaken by our team and brief description on the direction we are heading towards. Primarily, I am going to introduce the database tool team has developed for best practices reviews performed by Towers Watson.

Colloquium
 What should e', pi', gamma(1/2)', zeta(3)' be, if numbers' are replaced by functions'? Link: View Poster Speaker: Dinesh Thakur (University of Arizona) Faculty Sponsor:Jeremy Teitelbaum Time: Tuesday, November 22, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will describe old and new analogies discovered between number fields and function fields and discuss applications to the question in the title and to the determination of algebraic relations between these analogs Comments: Special Colloquium

Algebra Seminar
 What should e', pi', gamma(1/2)', zeta(3)' be, if numbers' are replaced by `functions'? Link: View Poster Speaker: Dinesh Thakur (University of Arizona) Time: Tuesday, November 22, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: We will describe old and new analogies discovered between number fields and function fields and discuss applications to the question in the title and to the determination of algebraic relations between these analogs. (This is a joint Colloquium/Algebra seminar. All are welcome.)

Algebra Seminar
 Computing a level-13 modular curve over Q via representation theory Link: View Poster Speaker: Burcu Baran (University of Michigan) Time: Monday, November 28, 2011 at 11:00 am Place: MSB 118 (UConn - Storrs) Abstract: For any $n > 0$, let $X_{ns}(n)$ denote the modular curve over $\mathbb{Q}$ associated to the normalizer of a non-split Cartan subgroup of level $n$. The integral points and the rational points of $X_{ns}(n)$ are crucial in two interesting problems: the class number one problem and the Serre's uniformity problem. In this talk we focus on the genus-3 curve $X_{ns}(13)$. It has no $\mathbb{Q}$-rational cusp (as for any level $n > 2$), so to compute an equation for this curve as a quartic in $P_2(\mathbb{Q})$ we use representation theory. Our explicit description of $X_{ns}(13)$ yields a surprising exceptional $\mathbb{Q}$-isomorphism to another modular curve. We also compute the $j$-function on $X_{ns}(13)$; evaluating it at the known $\mathbb{Q}$-rational points, we obtain the expected CM values.

Logic Seminar
 Interpretable groups are definable Link: View Poster Speaker: Janak Ramakrishnan (University of Lisbon) Time: Monday, November 28, 2011 at 4:45 pm Place: Exley Science Center 638 (Wesleyan University) Abstract: We present joint work with K. Peterzil and P. Eleftheriou that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. Moreover, every definable group lives in a cartesian product of one-dimensional definable group-intervals (or one-dimensional definable groups).

Algebra Seminar
 Serre's uniformity problem over Q Link: View Poster Speaker: Burcu Baran (University of Michigan) Time: Tuesday, November 29, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: In this talk I will introduce Serre's uniformity problem over Q, an open problem in the theory of Galois representations of elliptic curves. Past work by Serre, Mazur and Bilu-Parent has led to important progress but has not solved the problem. The remaining and the most dicult part amounts to a problem concerning rational points of modular curves associated to normalizers of non-split Cartan subgroups. I will discuss this case and also briefly introduce my work on these modular curves

UConn Math Club
 Convexity Methods in Analysis Link: View Poster Speaker: Iddo Ben-Ari (University of Connecticut) Time: Wednesday, November 30, 2011 at 5:30 pm Place: MSB 319 (UConn - Storrs) Abstract: A function is called convex if the line segment connecting any two points on its graph lies above the graph. This geometric notion has some far-reaching consequences. For example, a convex function is automatically continuous and if it is not constant then it has a single global minimum. In this talk we'll explore the notion of convexity and meet several classical applications in analysis and probability. Comments: Free Refreshments -- Like UConn Math Club on Facebook for talk reminders! Additional Comments: UConntact page: https://uconntact.uconn.edu/organization/math_club

Colloquium
 Undecidability in number theory Link: View Poster Speaker: Bjorn Poonen (MIT) Time: Thursday, December 1, 2011 at 4:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Hilbert's Tenth Problem asked for an algorithm that, given a multivariable polynomial equation with integer coefficients, would decide whether there exists a solution in integers. Around 1970, Matiyasevich, building on earlier work of Davis, Putnam, and Robinson,showed that no such algorithm exists. But the answer to the analogous question with integers replaced by rational numbers is still unknown, and there is not even agreement among experts as to what the answer should be.

S.I.G.M.A. Seminar
 A Taste of Homological Algebra Link: View Poster Speaker: Sarah Glaz (University of Connecticut) Time: Friday, December 2, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: Homological Algebra, as a research approach in Commutative Algebra, investigates certain properties and objects of the category of all modules over a ring, with a view towards deepening our understanding of the structure of the ring itself. But, as it often happens in mathematics, the study of these properties and objects is also very interesting in its own right. The module properties that are usually termed "homological" include, but are not restricted to, freeness, projectivity, flatness, and injectivity. The associated objects whose behavior is of interest include the functors Hom and tensor product, and the derived functors Ext and Tor. Understanding the homological properties of modules, the associated objects, and the development of module and ring invariants, called homological dimensions, which shed new light on the rings themselves, is the topic of the course Math 5020: Introduction to Homological Algebra, I am offering this Spring semester. This talk's purpose is to give a taste of the subject, by introducing a few semi-rigorous definitions and proofs, and several interesting examples. If time allows I will also touch on a topic of my own research which uses a homological algebra approach. Comments: Free Pizza (courtesy of Mathematics Department).

Analysis and Probability Seminar
 Contact process on modular random graphs Link: View Poster Speaker: David Sivakoff (Duke) Time: Friday, December 2, 2011 at 3:00 pm Place: MSB 319 (UConn - Storrs) Abstract: We studied the contact process (or SIS epidemic) on a pair of dense networks with sparse connections between them. I will give an intuitive derivation for the distribution of the time at which the contact process jumps from one part of the network to the other, and outline the proof.

Cluster Algebras Reading Seminar
 Projective dimension of modules over cluster-tilted algebras Link: View Poster Speaker: Ilke Canakçi (University of Connecticut) Time: Friday, December 2, 2011 at 3:00 pm Place: MSB 117 (UConn - Storrs)

Actuarial Science Seminar
 Longitudinal Modeling of Insurance Claim Counts Using Jitters Link: View Poster Speaker: Emiliano A. Valdez (University of Connecticut) Time: Friday, December 2, 2011 at 4:30 pm Place: MSB 403 (UConn - Storrs) Abstract: Joint work with Peng Shi, Northern Illinois University Modeling insurance claim counts is a critical component in the ratemaking process for property and casualty insurance. This article explores the usefulness of copulas to model the number of insurance claims for an individual policyholder within a longitudinal context. To address the limitations of copulas commonly attributed to multivariate discrete data, we adopt a "jittering" method to the claim counts which has the effect of continuitizing the data. Elliptical copulas are proposed to accommodate the intertemporal nature of the "jittered" claim counts and the unobservable subject-specific heterogeneity on the frequency of claims. Observable subject-specific effects are accounted in the model by using available covariate information through a regression model. The predictive distribution together with the corresponding credibility of claim frequency can be derived from the model for ratemaking and risk classification purposes. For empirical illustration, we analyze an unbalanced longitudinal dataset of claim counts observed from a portfolio of automobile insurance policies of a general insurer in Singapore. We further establish the validity of the calibrated copula model, and demonstrate that the copula with "jittering" method outperforms standard count regression models.

Colloquium
 Equivalence relations, random graphs and stochastic homogenization Link: View Poster Speaker: Vadim Kaimanovich (University of Ottawa) Faculty Sponsor:Teplyaev Time: Thursday, December 8, 2011 at 4:00 am Place: MSB 118 (UConn - Storrs) Abstract: The theory of measured discrete equivalence relations provides a natural setup for studying random graphs, in particular, those of fractal origin. We shall discuss several results related to construction and various approximations of invariant measures of the associated equivalence relations.

S.I.G.M.A. Seminar
 Kac-Moody algebras and the Jacobi triple product identity Link: View Poster Speaker: Ben Salisbury (University of Connecticut) Time: Friday, December 9, 2011 at 1:00 pm Place: MSB 118 (UConn - Storrs) Abstract: The Jacobi triple product identity was introduced and proved in 1829 by C. G. J. Jacobi using Euler's pentagonal number theorem. Since then, other proofs have arisen using both combinatorics and complex analysis. One (possibly surprising) proof comes from using the root system of a particular affine Kac-Moody algebra. A connection such as this (Kac-Moody algebras with identities from number theory) is a topic that has become very popular in recent years, and it turns out that the Jacobi triple product identity is a special case of a so-called MacDonald identity. In this talk, we will detail this particular affine Kac-Moody algebra and show how to prove the identity. Comments: Free Pizza (courtesy of Mathematics Department).