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Spring 2008
Colloquium
Speaker: Iddo Ben-Ari (University of California, Irvine)
Time: Tuesday, January 22, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The following model is known as directed last passage on Z^d. For every nearest neighbor path X() on Z^d with initial position X(0)=0 and every time T=0,1,2,..., a random value V(0,X(0))+... + V(T-1,X(T-1)) is assigned, the V(t,x)'s being independent and identically distributed (IID) random variables. The last passage at time T is the maximal random value, taken over all such paths. The main object of study is its asymptotic behavior as T tends to infinity. The model can be viewed as a spatial extension of sums of IID random variables. It exhibits correspondences and close relations with some other models, including totally asymmetric exclusion, random growth models and random matrices. In this talk I'll discuss this model, focusing on its non-standard large
deviations.
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Colloquium
Speaker: Ralf Schiffler (University of Massachusetts at Amherst)
Time: Thursday, January 24, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk is an introduction to quiver representations. A quiver (or oriented graph) Q=(Q_0,Q_1) is a set of vertices Q_0 and set of arrows Q_1 such that each arrow a in Q_1 starts at some vertex s(a) in Q_0 and ends at some vertex t(a) in Q_0. A representation of the quiver Q consists of a vector space V_i for each vertex i in Q_0 and a linear map f_a from V_{s(a)} to V_{t(a)} for each arrow a in Q_1. We will introduce the category of representations of such a quiver Q, consider an equivalent realization as module category over the path algebra of Q and explain basic Auslander-Reiten theory. We will also illustrate some recent developments that connect quiver representations to cluster algebras.
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Analysis and Probability Seminar
Speaker: (University of Connecticut)
Time: Friday, January 25, 2008 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
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Colloquium
Speaker: Moon Duchin (University of California, Davis)
Time: Monday, January 28, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Given a class of metrics on a surface, a system of curves may be said to be "spectrally rigid" if their lengths determine a metric among those in the class. I will discuss the spectral rigidity problem for translation surfaces, an interesting class of singular flat metrics that arise in the study of Teichmuller theory. This is joint work with Chris Leininger and Kasra Rafi.
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UConn Math Club
Speaker: Keith Conrad (University of Connecticut)
Time: Monday, January 28, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Power series expansions are a basic topic in calculus courses. Another kind of series expansion, Fourier series, are met in courses on partial differential equations but really should be known to all students of mathematics. The definition of a function, the Riemann integral, and even set theory all arose in response to delicate questions about Fourier series.
In this talk, Fourier series will be introduced and their properties compared to those of power series. The contrasts
are quite instructive, particularly the counterexamples to most people's intuition about how limits of functions ought to behave.
Comments: Free Refreshments
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Colloquium
Speaker: Pramod Achar (Louisiana State University)
Time: Tuesday, January 29, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In the 1890's, Henri Poincare discovered a remarkable and surprising symmetry among the cohomology groups of a compact, orientable manifold. In the intervening century, many generalizations of Poincare duality have been found, such as versions that hold on singular spaces (using "intersection cohomology"), or that hold for cohomology of vector bundles (Serre-Grothendieck duality). From the perspective of representation theory, one is often interested in the geometry of spaces equipped with a group action. In this setting, Poincare duality is a powerful tool that has led to many stunning achievements in recent decades. I will try to give a glimpse of these results, and I will discuss new results that may lead to similar applications for Serre-Grothendieck duality.
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Actuarial Science Seminar
Speaker: James Bridgeman (University of Connecticut)
Time: Tuesday, January 29, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In practical Monte-Carlo cash-flow testing applications a natural generalization of the mean-reverting lognormal (aka Black-Karasinki) model for interest rates is to make the mean-reversion target itself a random variable. Calibration of such a model is much easier with closed forms for the integrated future interest rate distribution, or at least for its moments. Deriving such closed forms takes us on a Cook's tour of probability and analysis techniques.
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Colloquium
Speaker: David Dumas (Brown University)
Time: Thursday, January 31, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will discuss the theory of complex projective structures on surfaces (which are also known as Mobius structures) and applications of this theory to related areas of low-dimensional geometry and complex analysis. In particular we will explain connections with classical Teichmuller theory, 3-dimensional hyperbolic geometry and Kleinian groups, and how these connections enable new approaches to some analytic and geometric problems.
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Colloquium
Speaker: Milena Hering (University of Minnesota)
Time: Monday, February 4, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Describing the defining equations of a projective algebraic variety is a classical problem in algebraic geometry. I will explain classical results about the defining equations of algebraic curves, and how these results extend to properties of syzygies (relations) between the defining equations. Then I will present some new results about the syzygies of toric varieties.
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Logic Seminar
Speaker: Asher Kach (University of Connecticut)
Time: Monday, February 4, 2008 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The first part will be mostly expository. After reviewing
Ershov-Tarski invariants (characterizing BAs up to elementary equivalence),
we'll spend a signficant amount of time discussing Ketonen invariants
(characterizing BAs up to isomorphism). In particular, we'll make the
transitions from BAs to linear orders, to rank functions, to measures,
to derived monoids.
The second part of my talk will emphasize recent research. After giving
explicit constructions of the depth zero measures, we'll characterize the
computable depth zero, rank omega BAs. We'll also discuss rank one BAs
and depth one BAs. As time permits, work (joint with Denis Hirschfeldt
and Antonio Montalban) on the Feiner hierarchy and its implications to
computable BAs will be presented.
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Colloquium
Speaker: Álvaro Lozano-Robledo (Cornell University)
Time: Tuesday, February 5, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: An elliptic curve is a plane curve (of genus 1) defined by a cubic polynomial in two variables. The problem of finding the rational points on an elliptic curve has fascinated mathematicians since the time of the ancient Greeks. In 1922, L. Mordell proved that the rational points form a finitely generated abelian group (a fact already "known" by Poincare, although he gave no proof). However, to this day, we do not even know a proven algorithm to find the rank of the group. One of the Clay Millennium problems, the Birch and
Swinnerton-Dyer conjecture, which came out of computer calculations in the 1960s, proposes an analytic way to find the rank.
In this talk we will first discuss the state-of-the-art methods and techniques used to overcome the problems that arise when trying to find the rank. Later we will present results which study, for a fixed elliptic curve, the growth of the rank in towers of fields.
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Colloquium
Speaker: Álvaro Lozano-Robledo (Cornell University)
Time: Tuesday, February 5, 2008 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Hex is a board game which was invented (independently) by Piet Hein and John Nash in the 1940's. The game has two peculiarities: it can never end in a draw and the first player can always win (except that no winning strategy is known!). In this talk I will describe a hands-on mathematics workshop that I prepared for K-12 teachers and students, whose goal was the discovery of the two facts about Hex mentioned above. I will also describe two additional mathematics workshops on the concepts of infinity and Pascal's triangle. The goal of all three workshops was to let the audience discover interesting and surprising facts, and come up with their own explanations through hands-on activities.
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Mathematics Education
Speaker: Alvaro Lozano-Robledo (Cornell University)
Time: Tuesday, February 5, 2008 at 5:15 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Hex is a board game which was invented (independently) by
Piet Hein and John Nash in the 1940's. The game has two peculiarities:
it can never end in a draw and the first player can always win (except
that no winning strategy is known!). In this talk I will describe a
hands-on mathematics workshop that I prepared for K-12 teachers and
students, whose goal was the discovery of the two facts about Hex
mentioned above. I will also describe two additional mathematics
workshops on the concepts of infinity and Pascal's triangle. The goal
of all three workshops was to let the audience discover interesting
and surprising facts, and come up with their own explanations through
hands-on activities.
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UConn Math Club
Speaker: Oscar Levin (University of Connecticut)
Time: Wednesday, February 6, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Goodsteins theorem is a rather surprising result about particular sequences of natural numbers. Not only is the result surprising, but the proof of the theorem turns out to use ordinal numbers (a part of set theory) in a surprising way. What is even more surprising is that this use of set theory is necessary for a proof at all. In this talk we will try to unravel what this means. No knowledge of ordinal numbers will be assumed.
Comments: Free Refreshments
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Colloquium
Speaker: Karen Lange (University of Chicago)
Time: Friday, February 8, 2008 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: All people will encounter and use mathematics throughout their lives. Too often, however, people are led to believe that mathematics isn't for them, and they give up on the subject. I believe my role as a mathematician and educator is to ignite others' interest in mathematics (by engaging them in ways based on their interests and background) and to support them through the challenges of learning mathematics. I believe there is a place for everyone in mathematics, and I will discuss my experiences working to encourage people, from middle schoolers to college students to teachers, to embrace their relationship with mathematics.
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Mathematics Education
Speaker: Karen Lange (University of Chicago)
Time: Friday, February 8, 2008 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: All people will encounter and use mathematics throughout their lives. Too often, however, people are led to believe that mathematics isn't for them, and they give up on the subject. I believe my role as a mathematician and educator is to ignite others' interest in mathematics (by engaging them in ways based on their interests and background) and to support them through the challenges of learning mathematics. I believe there is a place for everyone in mathematics, and I will discuss my experiences working to encourage people, from middle schoolers to college students to teachers, to embrace their relationship with mathematics.
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Colloquium
Speaker: Karen Lange (University of Chicago)
Time: Friday, February 8, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Reverse mathematics and computable model theory both attempt to measure the strength of classical mathematical principles, the former from a proof-theoretic perspective and the latter from a computable one. I will present computability results on the Homogeneous Model Theorem (HMT), an existence theorem for general model-theoretic structures found throughout mathematics. I will discuss how these results provide insight into the reverse mathematical strength of HMT. In particular, I will discuss how HMT compares with the Atomic Model Theorem studied by Hirschfeldt, Shore, and Slaman.
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Colloquium
Speaker: Başak Gürel (Université de Montréal)
Time: Monday, February 11, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The existence problem for periodic orbits is one of the central questions in Hamiltonian dynamical systems. For systems describing the motion of a charged particle in a magnetic field, i.e., for the so-called twisted geodesic flows, this question was first addressed by V.I. Arnold in the early 80s. Arnold's work initiated an extensive study of the existence problem for periodic orbits of twisted geodesic flows via variational and dynamical systems methods as well as in the context of symplectic topology.
In this talk we will discuss various aspects of this problem and related results, focusing, in particular, on recent theorems obtained by symplectic topological (or, more precisely, Floer homological) methods.
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Colloquium
Speaker: Nicolas Guay (University of Edinburgh)
Time: Tuesday, February 12, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: One of the major breakthroughs in representation theory in the 20th century was the discovery by V. Kac and R. Moody of a new class of Lie algebras which encompasses the fundamental family of semisimple Lie algebras. Examples of such Kac-Moody algebras are given by affine Lie algebras, which admit various types of generalizations. Over the last fifteen years, mathematicians have been interested in deformations of certain double affine structures in Lie theory. I will present examples of such mathematical objects: quantum toroidal algebras, double affine Hecke algebras, symplectic reflection algebras etc. I will also survey some of the developments in this active area of research and connections with other topics in mathematics.
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UConn Math Club
Speaker: Perry Susskind (Connecticut College)
Time: Wednesday, February 13, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Which came first, the straight line or the ability to measure the distance between points? The geometry of the plane — straight lines, angles, figures such as triangles, the shortest distance between a pair of points — is inseparable from the manner in which distance is measured. Further, transformations that do not change distances between points (such as translations or rotations) may be used to define the geometry of the plane. Such transformations are called rigid motions. Changing the way that distance is measured, or changing the kinds of transformations that are deemed to be rigid motions, results in a quite different geometry called hyperbolic geometry.
Comments: Free Refreshments
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Logic Seminar
Speaker: Asher Kach (University of Connecticut)
Time: Monday, February 18, 2008 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: The first part will be mostly expository. After reviewing
Ershov-Tarski invariants (characterizing BAs up to elementary equivalence),
we'll spend a signficant amount of time discussing Ketonen invariants
(characterizing BAs up to isomorphism). In particular, we'll make the
transitions from BAs to linear orders, to rank functions, to measures,
to derived monoids.
The second part of my talk will emphasize recent research. After giving
explicit constructions of the depth zero measures, we'll characterize the
computable depth zero, rank omega BAs. We'll also discuss rank one BAs
and depth one BAs. As time permits, work (joint with Denis Hirschfeldt
and Antonio Montalban) on the Feiner hierarchy and its implications to
computable BAs will be presented.
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UConn Math Club
Speaker: Aaron Silberstein (Harvard)
Time: Monday, February 18, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In the quadratic formula you learned in high school, there is a square root you need to use. We will ask, more generally, what it means to solve a polynomial using radicals (square roots, cube roots, and so on). In doing so, we will understand another facet of the quadratic formula and figure out how to solve any cubic equation.
Comments: Free Refreshments
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Algebra Seminar
Speaker: Keith Conrad (University of Connecticut)
Time: Tuesday, February 19, 2008 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: When K is a local field, every maximal compact subgroup of GLn(K)
is conjugate to GLn(O), where O is the ring of
integers of K. We will discuss what can be said about compact subgroups of
GLn(Cp), where Cp
is the p-adic complex numbers.
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Actuarial Science Seminar
Speaker: Sudath Ranasinghe/ Chris Macklem (Phoenix Life)
Time: Tuesday, February 19, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The secondary market for life insurance has exploded onto financial planning scene. Clearly the market’s basic premise – the consumer’s right to resell unwanted or unneeded life insurance has been validated by the U.S. insurance market. The market and its associated products especially life settlements, are attracting significant attention from professionals outside of the life insurance industry. Life Settlements allow a policyholder to sell his/her policy in the secondary market for greater than cash value. This has attracted the attention of the capital market. By allowing companies to compete for unwanted or unneeded policies, the secondary market has generated greater consumer choice, a wider range of products and favorable valuations for consumers.
In this presentation, we give background on the life settlements market including market origin, key players, and an overview of typical life settlement transaction. Finally, the perspective of a life insurance company participating in the market will be presented.
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S.I.G.M.A. Seminar
Speaker: $Unique empty (University of Connecticut)
Time: Wednesday, February 20, 2008 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Many mathematical objects come equipped with a variety of mathematical structures -- algebraic, topological, differentiable, etc. A broad question is this: under what circumstances must a mapping from one such object to another that preserves some of these structures also preserve some of the others? We shall sample results from this area, going back to the best-known "classical" result that every scalar-valued homomorphism of a Banach algebra is continuous and winding up with a result published in 2007. Along the way there may be a few surprises...
Comments: Free Donuts (courtesy of GSS)
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Analysis and Probability Seminar
Speaker: Luke Rogers (University of Connecticut)
Time: Friday, February 22, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: I will talk about joint work with Bob Strichartz, in which we produce a
theory of distributions on fractafolds based on a p.c.f. fractal. In
particular we are able to prove analogues of the classical structure
theorems, which identify distributions (locally) as powers of the
Laplacian applied to continuous functions, and show that distributions of
point support are "derivatives" of Dirac masses.
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Logic Seminar
Speaker: Brooke Andersen (Dartmouth College)
Time: Monday, February 25, 2008 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We consider a notion of Turing reducibility which is always total on
recursively enumerable oracles. This notion of reducibility is implied by
truth-table reducibility, but is different from truth-table, weak
truth-table, bounded search and Turing reducibilities on r.e. sets.
Moreover, it is not transitive. We add a condition, called positivity, to
make this notion transitive and see that this is still different from
other strong notions of reducibility. I will show how we can use complete
sets to distinguish this reducibility from other notions. This is work
for my thesis. This reducibility was first studied by Marcia Groszek,
Rebecca Weber and Pete Winkler.
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Algebra Seminar
Speaker: Mizan Khan (Eastern Connecticut State University)
Time: Tuesday, February 26, 2008 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The modular hyperbola Hn is
the set of pairs (x,y) such that xy =1 mod n
with x and y running from 1 to n-1.
This simply defined set of points has connections to a variety of other
mathematical topics including Kloosterman sums, quasirandomness, and
consecutive Farey fractions.
These connections have inspired a closer look at the distribution of the
points of the hyperbola, and many questions remain open.
In this talk, we examine the propensity of these points to collect on
lines of slope 1 and -1. This is joint work with Dennis Eichhorn, Alan
Stein and Christian Yankov.
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Actuarial Science Seminar
Speaker: Yang Ho Choi (University of Connecticut)
Time: Tuesday, February 26, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Black-Scholes Model, one of the most popular option pricing models, assumes that the volatility of the underlying asset is constant. This assumption is far from perfect. Unlike the asset price, the volatility of an asset is not directly observable. This presentation will discuss schemes for attempting to keep track of the current level of volatility from historical data. In addition, these historical data can be used to forecasts of the future values of volatility.
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S.I.G.M.A. Seminar
Speaker: David R. Solomon (University of Connecticut)
Time: Wednesday, February 27, 2008 at 4:30 pm
Place: MSB 303 (UConn - Storrs)
Abstract: For a finite set A, we have a good idea of what it means
to specify how many elements the set A has in the sense that the size
is characterized by a natural number. What if A is an infinite set?
If A is countable, we can specify its size by saying it has the same
size as the natural numbers. What if A is an uncountable set such as
the reals? In this talk, we will look at an extension of the natural
numbers, called the cardinal numbers, which serve to measure the size
of infinite sets. We will consider the size of the reals from this
perspective and talk about the work that Godel and Cohen did in
trying to answer this question.
Comments: Free Donuts (courtesy of GSS)
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UConn Math Club
Speaker: Ajay Shenoy (University of Connecticut)
Time: Wednesday, February 27, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Through the use of mathematical modeling and nonlinear dynamics, doctors and mathematicians can join forces.
After introducing the basics of dynamical modeling with ordinary differential equations in mathematical biology, I will present original research conducted during the summer of 2007 directed at modeling and treating the most common form of leukemia in the Western world. This research includes a model of the untreated disease, modeling of treatments, and ideal treatment regimes for combating the disease.
Comments: Free Refreshments
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UConn Math Club
Speaker: Neal Lima (University of Connecticut)
Time: Wednesday, March 5, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In classical geometry, the Greeks asked whether it was
possible to make constructions using only the “purest” tools: an unmarked straightedge and a compass. They were able to make a number of basic constructions with these restricted tools, e.g., bisecting any angle or constructing the vertices of an equilateral triangle.
But there were a few construction problems the Greeks were not able to carry out in this way (e.g., trisecting a general angle). In this talk we’ll use algebra to show some geometric construction problems are impossible to solve with the Greek tools.
Comments: Free Refreshments
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UConn Math Club
Speaker: Many Speakers
Time: Saturday, March 8, 2008 at 5:30 pm
Place: MSB 319 (Brown University)
Abstract: On March 8th, the first Saturday of our spring break, the UConn Math Club is chartering a bus to Providence to attend the Symposium for Undergraduates in the Mathematical Sciences at Brown. Speakers are coming from Bowdoin, Brown, MIT, NYU, UC Irvine, and UConn.
Our bus will leave UConn at 7:30 AM on Mar. 8 and will return that evening no later than 10:30 PM. If you are interested in joining us, please register at http://www.math.brown.edu/sums/, where there is further information about the talks, and also send an email to uconnmathclub@gmail.com by February 22nd, providing your name and a phone number. (Students in the residence halls have to vacate on Mar. 7, so if you are in the residence halls and do not have alternate local housing, please indicate this in your email and we will try to find temporary accommodations near UConn on the night before and after the symposium.)
Comments: Banquet Dinner
Additional Comments: USG Funded
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PDE and Image Analysis Seminar
Speaker: Bernd Kawohl (the University of Cologne, Germany)
Time: Monday, March 17, 2008 at 3:30 pm
Place: E2 321 (UConn - Storrs)
Abstract: In mathematical image processing we are often presented with amazing examples of image enhancement algorithms. Yet, when applied to different noisy images, they can produce unwanted effects. The analysis of such algorithms lags behind their intuitive development. Two essentially different models have found wide recognition: a variational approach according to Mumford and Shah and an approach via nonlinear diffusion equations. One of these equations is nonparabolic and was suggested by Perona and Malik. In my talk I point out a connection between these two seemingly unrelated approaches and explain some connections with total variation flow.
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Colloquium
Speaker: Hui Li (University of Luxembourg)
Time: Tuesday, March 18, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will introduce symplectic manifolds, Hamiltonian group action, symplectic quotients. We will discuss certain topological property of symplectic manifolds and symplectic quotients. We will discuss quantizations of symplectic manifolds and symplectic quotients, and other problems related if time permits.
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Actuarial Science Seminar
Speaker: Hubert Mueller (Towers Perrin)
Time: Tuesday, March 18, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: This presentation will cover the following topics: (1) recent market trends with Economic Capital (EC), (2) the role of EC when implementing Enterprise Risk Management (ERM), (3) calculating EC using stress testing, (4) adding value from EC, and finally, (5) some recent ERM case studies.
Comments: Click below for slides and report
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Colloquium
Speaker: David Futer (Michigan State University & MSRI)
Time: Wednesday, March 19, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Powerful theorems of Thurston, Perelman, and Mostow tell us that almost every 3-manifold admits a hyperbolic metric, and that this metric is unique. Thus, in principle, there is a 1-to-1 correspondence between a combinatorial description of a 3-manifold and its geometry. On the other hand, a concrete dictionary between combinatorial features and geometric measurements has been much harder to obtain.
I will survey some recent results that explicitly relate the combinatorics of a knot diagram to geometric features of the knot complement and related closed 3-manifolds. There are also interesting connections to the behavior of surfaces and the Jones polynomial of the knot.
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S.I.G.M.A. Seminar
Speaker: Asher Kach (University of Connecticut)
Time: Wednesday, March 19, 2008 at 5:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: After establishing some notation and definitions that apply to
tournaments more broadly, we'll focus our attention on single-elimination
and round-robin tournaments. There is a surprisingly rich mathematical
theory in both cases, partially fueled by professional tournaments like
March Madness. Some highlights of the talk will include examining
mathematically why the NCAA basketball championship is designed the way it
is and showing that every indebted club has either a bum or three
deadbeats.
Though the mathematics is fascinating (at least to the speaker), none of
it will be incredibly sophisticated or high-powered.
Comments: Free Donuts (courtesy of GSS)
Additional Comments: Note the later start time.
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UConn Math Club
Speaker: Adam Gamzon (UMass Amherst)
Time: Wednesday, March 19, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In 1900, David Hilbert proposed 23 problems to the
mathematical community which he considered important.
Just two years later the third of these problems was the first to be solved. The third problem poses the question: if two polyhedra have the same volume then are they equidecomposable? In this talk, we will explain the meaning of this question as well as give a solution.
Comments: Free Refreshments
Additional Comments: USG Funded
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Colloquium
Speaker: Alexander Russell (University of Connecticut)
Time: Thursday, March 20, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk will discuss some basic features of topological quantum field theories and, specifically, the topological invariants they induce. After warming up with knots, we will outline a surprising geometric interpretation of semi-simple algebras as the defining algebras for (TQFT-type) two-dimensional manifold invariants. Finally, we will touch upon the more challenging three-dimensional case, discussing the relationship with Hopf algebras and 6j-symbols. The talk will assume no familiarity with quantum field theories or quantum mechanics.
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Colloquium
Speaker: Arend Bayer (University of Utah)
Time: Friday, March 21, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: One of the most classical questions in algebraic geometry is how to count the number of curves inside an algebraic variety. In the last 15 years, various new approaches (Gromov-Witten invariants, Donaldson-Thomas invariants, ...) to this classical question have emerged.
We will show how one can unite some of these approaches by working with "stability conditions" inside the "derived category of coherent sheaves". This is a typical example of how the derived category, once thought of as general abstract non-sense, captures a lot of geometric information in a well-organized manner.
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Logic Seminar
Speaker: Andrei Morozov (Sobolev Institute of Mathematics and Novosibirsk State University)
Time: Monday, March 24, 2008 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: We give a characterization of countable structures Sigma-definable witout
parameters over the ordered field of reals, the field of complex numbers,
and skew field of quaternions. It appears that over R, all such structures
are hyperarithmetical and they can have arbitrary high hyperarithmetical
complexity, although if we assume some natural restrictions on the
definition, then all such structures have isomorphic computable copies.
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Algebra Seminar
Speaker: David Pollack (Wesleyan University)
Time: Tuesday, March 25, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Classical modular forms of small slope can be lifted to p-adic overconvergent
modular forms. Ash and Stevens have proven an analogous result for modular symbols
for GL3. We will review the situation for GL2 and give a new, constructive, proof
of the GL3 result. A consequence of this proof is an algorithm to compute
arbitrarily accurate approximations to the overconvergent lift of a given symbol.
This is joint work with Robert Pollack.
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Actuarial Science Seminar
Speaker: Jeyaraj Vadiveloo (University of Connecticut)
Time: Tuesday, March 25, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The purpose of the presentation is to have a discussion about building the Watson Wyatt-UConn Actuarial Center, a unique partnership between Watson Wyatt and the University of Connecticut. The mission and purpose of the Center will be discussed, and the operational issues associated with building such a Center will be explored. The talk will also discuss some typical projects undertaken by the Center involving students, faculty and industry professionals. We want the talk to be interactive in order to explore creative suggestions from the audience on how to build this entity into a world class Center of Excellence.
<Extra Information>
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S.I.G.M.A. Seminar
Speaker: JC Beall (University of Connecticut (Philosophy))
Time: Wednesday, March 26, 2008 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk is intended to be a rather informal talk on
Russell's paradox and its philosophical import. I begin by noting that
"Russell's paradox" is ambiguous between a (mathematical) set-
theoretic paradox and a related, more general exemplification-
theoretic paradox. (Think of exemplification as the relation that
holds between an object and its properties. E.g., you're reading this
abstract iff you exemplify the property of emph{reading this
abstract}, etc.) The set-theoretic paradox, though more famous (think
Frege), is not really a paradox -- or at least needn't be treated as a
(current) problem for mathematics. The exemplification-theoretic
paradox is more interesting, and has no special tie to mathematics.
What Russell's exemplification-theoretic paradox teaches us is that
the logic of our exemplification theory must be non-classical. In the
talk, I sketch some of the issues that confront a non-classical
exemplification theory (particularly, Curry's paradox). I close by
answering the question of whether we -- or, more accurately, *you* qua
mathematicians -- cripple mathematics by accepting a non-classical
logic for our broader language.
Comments: Free Donuts (courtesy of GSS)
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UConn Math Club
Speaker: Cameron Freer (Harvard)
Time: Wednesday, March 26, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The Compactness Theorem is a result in mathematical logic that
enables us to deduce results about infinite structures from those about finite structures (and conversely). We'll discuss this theorem, and use it to show a version of the Four-Color theorem for infinite maps. We'll also show how to prove Ramsey's theorem from an infinite version of it.
Comments: Free Refreshments
Additional Comments: USG Funded
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Colloquium
Speaker: Victor Pan (Lehman College, CUNY)
Time: Thursday, March 27, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Multiplicative preconditioning is a popular technique that facilitates the solution of a linear system of equations, but it is generally expensive and flourishes mostly for special input classes. We propose and study randomized additive preconditioning for solving linear systems of equations, with extensions to computation of eigenvectors and determinats. Compared to the classical multiplicative preconditioners, our preconditioners are much easier to generate. They work for a larger class of inputs, which includes rectangular and rank deficient matrices. Furthermore they readily preserve sparseness and structure of the inputs. We cover their generation and applications, show their links to aggregation and some other techniques of matrix computations, and demonstrate the power of this approach by numerical experiments.
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Analysis and Probability Seminar
Speaker: $Unique empty (University of Connecticut)
Time: Friday, March 28, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: The standard (real) Stone-Weierstrass theorem says that if E is a vector
space of continuous functions on a compact Hausdorff space X that contains the
constant functions and separates the points of X , and if E is either a lattice or
an algebra under pointwise operations, then E is dense in C (X ). The lattice
and algebra conditions can be reformulated to say that E is closed under com-
position with the absolute value function and the squaring function respectively.
In 1963 de Leeuw and Katznelson generalized both versions by showing that if
E is closed under composition with some non-affine continuous function, then
E is dense in C (X ). Of course, if it is also hypothesized that E is uniformly
closed – equivalently, that E is complete in the supremum norm – then the con-
clusion becomes E = C (X ). But what if E is complete in some other norm that
dominates the supremum norm? This makes E into a (real) Banach function
space, and from the early 1960s on there has been slow and steady progress on
the following problem: If a non-affine function φ operates by composition on a
Banach function space E, under what additional conditions on φ and/or E can
we deduce that E = C (X )? We shall recount some of this history, with the
emphasis being on conditions on E, and perhaps discuss some work in progress
along these lines.
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PDE and Image Analysis Seminar
Speaker: Qiuyi Dai (Hunan Normal University)
Time: Monday, March 31, 2008 at 3:00 pm
Place: E2 321 (UConn - Storrs)
Abstract: In this talk, we concern with the existence, uniqueness and non-degeneracy of positive solutions to semi-linear elliptic equations. A necessary and sufficient condition for the existence of positive solutions to problems we consider is given. Meanwhile, conditions for the uniqueness of positive solutions to the above mentioned problem is also figured out.
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Mathematics Education
Speaker: Kathy Gavin, Tutita Casa, and Jill Adelson (University of Connecticut)
Time: Monday, March 31, 2008 at 4:00 pm
Place: Gentry 144 (UConn - Storrs)
Abstract: The math begins after the game ends! Come learn about Project M^3, a 6-year national Javits research study with the aim of creating challenging and motivational curriculum units for mathematically talented students in grades 3-5. We will share how the units were developed to focus on students’ deep conceptual understanding of big mathematical ideas. Participants will have opportunities to engage in some sample activities and explore student work to get a better understanding of how talented elementary students approach mathematics.
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Actuarial Science Seminar
Speaker: David Liner/ Louis Lombardi (University of Connecticut)
Time: Tuesday, April 1, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The archaic methodologies of formulaic reserving cannot accurately capture the true risk of today's complex insurance products. Thus, there has been a recent movement for a principle-based reserving approach that requires stochastic modeling techniques. A level amount of fixed income portfolio credit risk is often assumed in the current stochastic models utilized by the industry. This project will evaluate the impact of a dynamic bond rating transition matrix assumption, a key driver of credit risk, on the surplus requirements for a single premium deferred annuity product. The dynamic bond rating transition matrix assumption will more accurately capture the credit rating degradation of the fixed income securities purchased to support the liabilities.
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S.I.G.M.A. Seminar
Speaker: Vicentiu Pasol (University of Connecticut)
Time: Wednesday, April 2, 2008 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract:
In the attempt to construct p-adic objects which are related to the
classical arithmetic objects, such as modular forms, one uses p-adic
distributions as an important tool. A specific type of distributions are
considered and examples are shown to emphasize the analogy with the
classical modular forms.
This is just a small preview of what will be covered in next Fall's Math 321 class. However in this talk, no familiarity with modular forms or p-adic distributions will be assumed.
Comments: Free Donuts (courtesy of GSS)
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UConn Math Club
Speaker: Avraham Bourla (UConn)
Time: Wednesday, April 2, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The four color theorem, one of the most famous theorems in mathematics,
asserts that four colors suffice to color every map so that two
countries with a common boundary are colored differently.
Even though this theorem cannot be proved in an hour, we will see how
we can shed light on the subject of map coloring by introducing the notion
of graphs and by discussing another famous theorem in mathematics, Euler's
polyhedra theorem.
Comments: Free Refreshments
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Colloquium
Speaker: Sergei Treil (Brown University)
Time: Thursday, April 3, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The theory of singular integral operators, in particular, a theorem by Arocena – Cotlar – Sadosky about two weight estimates of Hilbert transform is applied to the investigation of delicate spectral properties in perturbation theory of self-adjoint operators. As an application new result about the absence of the embedded singular spectrum for rank one perturbations is obtained.
The talk is based on a joint work with C. Liaw.
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Analysis and Probability Seminar
Speaker: Richard Nickl (University of Connecticut)
Time: Friday, April 4, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: Let X_1,...,X_n be an i.i.d. sample from the distribution F on R. Under no assumptions on the underlying data-generating process, we construct a purely-data driven adaptive estimator that efficiently estimates the distribution function F in sup-norm loss and, at the same time, estimates its density (if it exists) at the best rate of convergence, also in sup-norm loss. The estimator we consider is based on a suitable modification of Lepski's method applied to a kernel estimator. Some of the techniques involved are sharp exponential inequalities for both the density and the distribution function of the 'linear' estimators underlying the adaptive procedure. These inequalities in turn are based on Talagrand's inequality and the respective moment bounds. To increase the applicability of the estimator, considering Rademacher processes to estimate expectations can be helpful, in a similar vein as in recent work by V. Koltchinskii. (This is joint work with E. Giné).
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PDE and Image Analysis Seminar
Speaker: Konstantin A. Lurie (Department of Mathematical Sciences, Worcester Polytechnic Institute)
Time: Monday, April 7, 2008 at 3:00 pm
Place: E2 321 (UConn - Storrs)
Abstract: The notion of composite materials is a commonplace in material design in statics where they are defined as heterogeneous structures assembled in space from different original materials. The composites appear, as necessary participants, in almost all optimal material layouts in statics. In dynamics, however, such formations are not adequate because they cannot appropriately react upon(or be adjusted to) the temporal changes that occur in the environment. To meet the challenges put forth by this important factor, a concept of dynamic materials (DM) was introduced through the recent decades. DM are defined as the structures assembled from conventional materials in both space and time. This means that the material constants in the assemblage may be both space and time dependent. When this dependence occurs on a micro scale in space-time, a DM becomes a dynamic composite(DC).
DM are thermodynamically open systems: to maintain them, it is necessary to secure a non-stop exchange of energy and momentum between the DM and the environment. Depending on the circumstances, the energy may be pumped into a DM, or it may be extracted from it. In this talk, I will discuss the means that may be and are used to build up DM; these formations rarely appear in nature ( the fundamental exception being a living tissue); they mostly emerge as a product of modern technology. The features that are common to both DM and conventional materials.
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Algebra Seminar
Speaker: Kyu-Hwan Lee (University of Connecticut)
Time: Tuesday, April 8, 2008 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
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Actuarial Science Seminar
Speaker: Emiliano Valdez (University of Connecticut)
Time: Tuesday, April 8, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: This paper, joint work with Edward W. (Jed) Frees and Peng Shi, both from the University of Wisconsin - Madison, demonstrates actuarial applications that can be performed when modern statistical methods are applied to detailed, micro-level automobile insurance records. We consider 1993-2001 data consisting of policy, claims and payment files from a major Singapore insurance company. A hierarchical statistical model, developed in prior work (Frees and Valdez, 2008), is fit using the micro-level data. This model allows us to study the accident frequency, loss type and severity jointly and to incorporate individual characteristics such as age, gender and driving history that explain heterogeneity among policyholders.
Based on this hierarchical model, one can analyze the risk profile of either a single policy (micro-level) or a portfolio of business (macro-level). This paper investigates three types of actuarial applications. First, we demonstrate the calculation of the predictive mean of losses for individual risk rating. This allows the actuary to differentiate prices based on policyholder characteristics. The nonlinear effects of coverage modifications such as deductibles, policy limits and coinsurance are quantified. Moreover, our flexible structure allows us to ``unbundle'' contracts and price more primitive elements of the contract, such as coverage type. The second application concerns the predictive distribution of a portfolio of business. We demonstrate the calculation of various risk measures, including value at risk and conditional tail expectation, that are useful in determining economic capital for insurance companies. Third, we examine the effects of several reinsurance treaties. Specifically, we show the predictive loss distributions for both the insurer and reinsurer under quota share and excess-of-loss reinsurance agreements. In addition, we present an example of portfolio reinsurance, in which the combined effect of reinsurance agreements on the risk characteristics of ceding and reinsuring company are described.
Comments: Click below for copy of paper
<Extra Information>
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S.I.G.M.A. Seminar
Speaker: Thomas Roby (University of Connecticut)
Time: Wednesday, April 9, 2008 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: One of the most powerful techniques for analyzing a
enumerative sequence is to use a *generating function*. This is just a
formal power series whose coefficients match the sequence, i.e., "a
clothesline on which we hang the terms of a sequence" (H. Wilf). We can
then apply algebraic and analytic techniques to help us understand the
properties of the sequence--often to the point of deriving an explicit
formula. We will look at several examples, including famous sequences
associated with Leonhard Paul Euler, and Eugene Charles Catalan.
Comments: Free Donuts (courtesy of GSS)
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UConn Math Club
Speaker: Joseph Pomianowski (University of Connecticut)
Time: Wednesday, April 9, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In 1917, as a century of foreign domination was about to end in Poland,
there appeared an article "On the Needs of Mathematics in Poland," which
led to the founding of the Polish School of Mathematics. We will describe the background to this School and one of its most important contributors – Stefan Banach. Then we will lightly touch on some of Banach's work: Banach Spaces and the Contraction Mapping Theorem.
Comments: Free Refreshments
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Colloquium
Speaker: Richard Shore (Cornell University)
Time: Thursday, April 10, 2008 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We will discuss two related measures of complexity for mathematical theorems and constructions. One asks what proof techniques (or formally axioms) are needed to prove specific theorems. The other asks (for existence proofs) how complicated (in the sense of computability) are the objects that are asserted to exist.
For this talk we will consider some illustrative examples from Combinatorics. In particular, we will consider several theorems of matching theory such as those of Frobenius, (M. and P.) Hall and König. While in the finite case these theorems seem both different and yet somehow the same, an analysis of the countable case in terms of computability or provability clearly distinguishes among them and assigns precise levels to their complexity.
At the most complicated level we will consider lies the König Duality Theorem: Every bipartite graph has a matching such that one can choose a vertex from each edge of the matching so as to produce a cover, i.e. a set with an element from every edge. This theorem cannot be proven using algorithmic methods even when combined with compactness (König's lemma for binary trees) or full König's lemma. We will show that it requires highly nonelementary methods as typified by constructions by transfinite recursion, choice principles and, for some versions, even more.
If time permits, we may also mention the calibration of some results of Ramsey theory that lie at the other (low) end of our classification scheme: Ramsey's theorem for n-tuples for different n and some consequences such as the theorems of Dilworth and Erdős-Szekeres. (Every infinite partial order has an infinite chain or antichain and every infinite linear order has an infinite ascending or descending sequence.)
We will not use, or even consider, any formal systems and no knowledge of logic is presupposed. We will work instead with an intuitive notion of what it means for a function to be computable, i.e. there is a computer program that calculates it given time and space enough and no mechanical failures. We will also explain the relevant combinatorial notions.
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Analysis and Probability Seminar
Speaker: Matt Cecil (University of Connecticut)
Time: Friday, April 11, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: Let $G$ be a simply connected Lie group with Lie algebra $mathfrak{g}$.
The universal enveloping algebra $U$ of $mathfrak{g}$ is often identified
with the left-invariant differential operators on $G$. It will be shown
that $G$ can be embedded in a certain completion of $U$ by ``lifting"
$G$-valued paths using iterated integrals. While this result falls in the
realm of Lie/representation theory, the motivation and potential
applications are analytic and probabilistic in nature. In particular,
this result is inspired by the proof of the Taylor map, a result
exhibiting a Hilbert space isomorphism between the space of holomorphic
functions on a complex Lie group $G$ which are square integrable with
respect to heat kernel measure and the dual of the completion of $U$ in a
particular inner product.
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PDE and Image Analysis Seminar
Speaker: Pengwen Chen (University of Connecticut)
Time: Monday, April 14, 2008 at 3:30 pm
Place: E2 321 (UConn - Storrs)
Abstract: Several models with the convex formulation are proposed for image analysis. In numerical imple-
mentation, these models do not have local minimizers which are not global minimizers. For instance,
Monge-Kantorovich(MK) mass transport model has been proposed to deal with image registration/
matching problems. In this paper, we present a novel image matching model which is essentially a
coupling of MK model with a well-known Hellinger distance function in the probability theory. The
optimal matching is the one which minimize the Hellinger distance between two images. A primal-
dual approach is employed to analyze the existence and uniqueness/non-uniqueness of the optimal
matching. A numerical algorithm is also provided to compute the optimal matching.
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Actuarial Science Seminar
Speaker: David McMichael (MetLife Auto and Home)
Time: Tuesday, April 15, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We will present a brief overview of Actuarial Research at MetLife Auto & Home. Topics will include personnel, tools, business problems, and future challenges.
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S.I.G.M.A. Seminar
Speaker: Matthew Jura (University of Connecticut)
Time: Wednesday, April 16, 2008 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: It is well-known that Arithmetic (the natural numbers with addition and
multiplication) is undecidable. That is, there is a formula &phi in
the language of Arithmetic such that no procedure exists to decide whether
&phi is true or false. The goal of this talk is to show that
Presburger Arithmetic (the natural numbers with addition) is in fact
decidable. The idea is that we can transform formulas of Presburger
Arithmetic into formulas of WS1S, which in turn can be transformed into
finite state automata. The talk is designed for a general audience.
Comments: Free Donuts (courtesy of GSS)
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UConn Math Club
Speaker: Ed Taylor (Wesleyan)
Time: Wednesday, April 16, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Computational geometry is a relatively new field, and it is even newer to me. Recently a colleague of mine — and his students! — got me interested in this subject, and I would like to share a problem and its solution that I am told is emblematic of this field. The basic problem
is to provide a formula — in terms of the number of walls of the
gallery — of the least number of guards required to guarantee that any gallery with this number of walls is guarded.
Being mathematics, we will have to abstract what we mean by a “gallery” and a “guard”. The solution is beautiful in its elegance and it appeals to one's every day common sense. Owing to my recent introduction to the field I will inevitably have to give a short shrift to certain important considerations: in particular I will not talk about algorithmic issues related to this problem.
Comments: Free Refreshments
Additional Comments: USG Funded
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Special Talks
Speaker: Thomas Pietraho (Bowdoin College)
Time: Thursday, April 17, 2008 at 4:00 pm
Place: IMS 120 (UConn - Storrs)
Abstract: Statistics has developed standard ways of measuring the difference between the means of two populations,...and so has the state of Texas. We will discuss and weigh the merits of both approaches, and gauge the impact on the No Child Left Behind Act.
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Analysis and Probability Seminar
Speaker: Erin Terwilleger (University of Connecticut)
Time: Friday, April 18, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: We obtain a multidimensional extension of Lacey and Thiele's result on the boundedness of a model sum operator which plays a crucial role in the boundedness of the bilinear Hilbert transform in one dimension. The proof is a simplification of the original proof of Lacey and Thiele. We take ideas and inspiration from the original along with other recent techniques to obtain the higher dimensional analog. We will also discuss some various results in the area of multilinear operators.
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Mathematics Education
Speaker: Heather Hill (Harvard Graduate School of Education)
Time: Monday, April 21, 2008 at 4:00 pm
Place: Gentry 246 (UConn - Storrs)
Abstract: In this talk, we will explore the question “What mathematical
knowledge do K-8 teachers need to know in order to teach?” To do so,
we will solve some of the mathematics problems teachers encounter in
their daily work, and consider what these problems imply for the
mathematical preparation of teachers. We also describe an effort to
build and validate a multiple-choice assessment of teacher knowledge
in this important arena.
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Algebra Seminar
Speaker: Kate Stange (Brown University)
Time: Tuesday, April 22, 2008 at 3:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. I'll give the background on these and present a higher-dimensional analogue over arbitrary fields. Suppose E is an elliptic curve over a field K, and P1, ..., Pn are points on E defined over K. To this information we associate an n-dimensional array of values of K satisfying a complicated nonlinear recurrence relation. These are called elliptic nets. All elliptic nets arise from elliptic curves in this manner. I'll explore some of the properties of elliptic nets and the geometric information they contain, including a connection to generalised Jacobians, the Poincare biextension and the Tate-Lichtenbaum and Weil pairings on the elliptic curve.
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Actuarial Science Seminar
Speaker: James Bridgeman (University of Connecticut)
Time: Tuesday, April 22, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In late 2006 the British government's mammoth Stern Review on the Economics of Climate Change generated headlines but then quickly faded from view after knowledgeable critics unraveled its methodology. An analysis of what they did provides insight into the present value concept, and into ways that it can be used and abused.
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UConn Math Club
Speaker: Recent UConn Alumni (University of Connecticut)
Time: Wednesday, April 23, 2008 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Anyone planning to be a math teacher after college is invited to this panel discussion. Recent UConn Math Ed. graduates will talk about their experiences teaching math in high school and junior high school. They will give practical advice and answer any questions you may have.
Comments: Free Refreshments
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Analysis and Probability Seminar
Speaker: Denglin Zhou (University of Waterloo)
Time: Friday, April 25, 2008 at 3:00 pm
Place: MSB 311 (UConn - Storrs)
Abstract: Strichartz proves a surprising result that Fourier series on
the Sierpinski gasket can have better convergence properties than classical
Fourier series. This is a
result of the existence of gaps in the spectrum of the Laplacian. In this talk
I will go over Kigami's approach to define a Laplacian as a renormalized limit
of difference operators. For some fractals, the
spectra of the Laplacians can be determined through a process called Spectral
Decimation, which is associated with a rational function and a finite set. A
general criterion for the existence of gaps in the spectrum of Laplacians has
been proved recently. Many of the known examples on which the Laplacians admit
spectral decimation satisfy the criterion. In particular, the infinite family
of Vicsek sets, whose spectral
decimation functions can be written in terms of Chebyshev polynomials, have
been shown to
satisfy the criterion and thus have gaps in their spectrum.
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UConn Math Club
Speaker: Marc Yor (Université Pierre et Marie Curie)
Time: Monday, April 28, 2008 at 3:30 pm
Place: IMS 20 (UConn - Storrs)
Abstract: Wolfgang Doeblin was a promising young probabilist who died at 25 during World War II. While at the front, Doeblin sent a manuscript to the French Academy of Sciences which remained unread until 2000. In it, Doeblin anticipated prominent later work of the Japanese mathematician Ito.
A 1-hour film will be shown about Doeblin's life and mathematics. After a break, in a half-hour film Prof. Marc Yor will explain Doeblin's manuscript "On Kolmogorov’s equation". This second film is meant for those with a good background in probability.
Comments: Note the room and time! Refreshments at 3:00 in MSB 118
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Colloquium
Speaker: Film by Agnes Handwerk and Harrie Willems (Cosponsored by the Statistics Department)
Time: Monday, April 28, 2008 at 3:30 pm
Place: IMS 20 (UConn - Storrs)
Abstract: Wolfgang Doeblin was a promising young probabilist who died at 25 during World War II. While at the front, Doeblin sent a manuscript to the French Academy of Sciences which remained unread until 2000. In it, Doeblin anticipated prominent later work of the Japanese mathematician Ito. A two-part film (with a short intermission) will be shown about Doeblin's life and mathematics. The first part will be an hour long and broadly accessible. In the second part of the film, the French mathematician Marc Yor will explain Doeblin's manuscript "On Kolmogorov’s equation" for about a half hour. The second part is meant for those with a good background in probability.
Comments: Refreshments at 3:00 in MSB 118
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Logic Seminar
Speaker: Charles Steinhorn (Vassar College)
Time: Monday, April 28, 2008 at 4:45 pm
Place: Exley Science Center 618 (Wesleyan University)
Abstract: It has been widely thought that o-minimal structures might lie at the first level of a hierarchy of ordered structures, in analogy with strongly minimal structures. In joint work with A. Onshuus, we develop a framework for ordered structures of finite rank. In particular, we analyze linear orders definable in o-minimal structures, and this will be the focus of the first part of the talk. This analysis appears to have an interesting application in mathematical economics---joint work with T. Brihaye, C. Michaux, and Onshuus---discussion of which is the subject of the second part of the talk.
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Actuarial Science Seminar
Speaker: Jeffrey Leitz, F.S.A. (Founder, Walbridge Capital Advisors, LLC)
Time: Tuesday, April 29, 2008 at 4:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: This brief overview of hedge funds will present examples of the marketing tools used by managers to attract qualified investors. This talk is by invitation only to select faculty and graduate students of the Mathematics Dept. of the University of Connecticut. The information provided at this seminar is solely for general information purposes and does not create a business or professional services relationship, nor does it constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial instruments, and may not be construed as such. For further information please contact the West Hartford office of Walbridge Capital Advisors at 860.490.2892.
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