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Fall 2009

Algebra Seminar
The rank of a quiver representation Link: View Poster
Speaker: Ryan Kinser (University of Connecticut)
Time: Tuesday, September 8, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)

S.I.G.M.A. Seminar
Brownian Motion Link: View Poster
Speaker: Richard Bass (University of Connecticut)
Time: Wednesday, September 9, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In the 1840's Robert Brown conjectured that the chaotic motion of particles suspended in colloidal solutions was due to the impact of molecules. This talk will be about the mathematical model of Brownian motion. First I'll tell you what Brownian motion is, then what some of its peculiar behavior is, and then some applications, to analysis, PDE, and financial math. In fact, in some sense, the collapse of the stock market in the fall of last year can be blamed on the misuse of Brownian motion models.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
The Arithmetic-Geometric Mean Inequality Link: View Poster
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, September 9, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The arithmetic-geometric mean inequality is the most famous elementary inequality in math. The inequality compares two kinds of averages, and the picture below is a visual explanation of the simplest case of it: ½(a + b) ≥ (ab)1/2. Anyone interested in mathematics should know the arithmetic-geometric mean inequality, so if you don't then come to this talk! Even if you already know it, you will learn something new about it.

We will work through a proof of the arithmetic-geometric mean inequality and then describe some of its applications in geometry, algebra, and analysis.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club


S.I.G.M.A. Seminar
Writing Teaching Philosophy Statements Link: View Poster
Speaker: Catherine Ross (University of Connecticut)
Time: Wednesday, September 16, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: We are very happy to welcome Dr. Catherine Ross, Associate Director of ITL and Director of the UConn TA Program, who has graciously offered to run a workshop on writing teaching statements. A good teaching statement is essential in the application process of almost all academic jobs. For more information on the importance of teaching statements, check out this article from the AMS Notices: http://www.math.uconn.edu/TAProgram/CareerInformation/Teaching-Statements-DEREK_BRUFF.pdf
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
The Apollonian gasket revealed Link: View Poster
Speaker: Avraham Bourla (University of Connecticut)
Time: Wednesday, September 16, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Apollonius of Perga (circa 250-200 BC) studied methods of circle packing,such as finding two circles which are mutually tangent to three other circles. His solution was lost, but later scientists (including Newton) developed techniques to solve it. In this talk, we will learn how to generate the fractal known as the Apollonian gasket, which is the infinite iteration of this circle packing procedure.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Algebra Seminar
Representation rings of quivers Link: View Poster
Speaker: Ryan Kinser (University of Connecticut)
Time: Thursday, September 17, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)

PDE and Image Analysis Seminar
Gradient Estimates for the Perfect and Insulated Conductivity Problems Link: View Poster
Speaker: Biao Yin (University of Connecticut)
Time: Monday, September 21, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Stimulating from the study of composite material, we investigate the gradient estimates for the perfect conductivity problem and the insulated conductivity problem. Under these two degenerate cases of the conductivity problem, the gradients of the solutions will blow-up as two inclusions approach to each other. In this talk, the optimal blow-up rates will be derived.

Algebra Seminar
Stability conditions for a quiver, the "local projective plane", and Gamma_1(3) Link: View Poster
Speaker: Arend Bayer (University of Connecticut)
Time: Tuesday, September 22, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will discuss stability conditions for the category of representations of a specific quiver (related to the local projective plane), and its derived category. We show that Gamma_1(3) acts on this derived category. According to Bridgeland, there is a space parametrizing stability conditions for this quiver and its derived category. I will give a description of this space, and describe its relation (predicted by mirror symmetry) to the moduli space of elliptic curves with Gamma_1(3)-level structure. (Joint work with Emanuele Macri, Utah.)

UConn Math Club
Knots and the Fourth Dimension Link: View Poster
Speaker: Constance Leidy (Wesleyan)
Time: Wednesday, September 23, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Take a piece of string, jumble it up, then seal the ends together. The result is a knot. Notice that you can't untie the knot because you've permanently sealed the ends together. (If we don't jumble at all, we'll just end up with a circle, which we call the unknot.) We call two knots equivalent if you can move one jumbled piece of string to look exactly like the other without cutting it open.

Knots naturally live in 3-space. We'll discuss a different equivalence relation called concordance involving the fourth dimension. A knot that is concordant to the unknot is called a slice knot. I will discuss some joint work with T. Cochran, S. Harvey, and myself that show that knots in a certain family whose slice status was previously unknown are in fact not slice.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club


Colloquium
Noise Sensitivity, Noise Stability, Percolation and some connections to TCS Link: View Poster
Speaker: Gil Kalai (Hebrew University and Yale University)
Faculty Sponsor: Blei
Time: Thursday, September 24, 2009 at 4:00 pm
Place: Mathematical Science Building MSB 118 (UConn - Storrs)
Abstract: Noise sensitivity was defined in a paper by Benjamini, Kalai, and Schramm (1999). A closely related notion was considered by Tsirelson and Vershik. I will describe the notion of noise sensitivity of Boolean functions and some basic results and problems related to it. A fun way to explain it (especially after 2000) is in terms of the probability that small mistakes in counting the votes in an election will change the outcome. We will consider the following: 1) The definition of noise sensitivity, and how it is described in terms of the Fourier transform. 2) Noise sensitivity of the crossing event in Percolation (BKS 99, Schramm and Steiff 2005, and finally Garban, Pete, Schramm 2008 - http://front.math.ucdavis.edu/0803.3750 ), the scaling limit for the Spectral distribution (Schramm and Smirnov, 2007, GPS 2008), and dynamic percolation. (ScSt (2005), GPS (2008)). Other cases of noise sensitivity. 3) Noise stability of the majority function, of weighted majority. A conjecture regarding the situation for functions described by monotone depth monotone threshold circuits. 4) The "majority is stabelest theorem" (Mossel, O'Donnell, Oleszkiewicz 05 http://front.math.ucdavis.edu/0503.5503) and the connection to hardness of approximation.

PDE and Image Analysis Seminar
A novel kernel correlation model with the correspondence estimation Link: View Poster
Speaker: Pengwen Chen (University of Connecticut)
Time: Monday, September 28, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We present a multiple linked iterative closest point method to estimate the correspondence and the rigid/nonrigid transformation between point-sets/shapes. The estimation task is carried out through maximizing a similarity function which is the product of square root functions and a kernel correlation. Intuitively this correspondence estimation framework is modified from the well-known mass transport problem. The local mean square error analysis and robustness analysis are provided to show its superior performance to the kernel correlation method.

S.I.G.M.A. Seminar
Examples in algebra using topology Link: View Poster
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, September 30, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: I will discuss a few conjectures in algebra whose resolution uses examples that involve topology.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
The Riemann Rearrangement Theorem Link: View Poster
Speaker: Paul Ellis (UConn)
Time: Wednesday, September 30, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Everyone knows that a + b = b + a. The order in which you add does not matter. This is also true for any finite sum of numbers a1 + a2 + ... + an. But what can happen when we reorder the terms in a convergent infinite series? Come to this talk to find out the very surprising answer!
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Analysis and Probability Seminar
Approximation and interpolation with polyharmonic and similar kernels Link: View Poster
Speaker: Thomas Hangelbroek (Texas A&M)
Time: Friday, October 2, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: I'll discuss some recent results involving approximation with kernels obtained as fundamental solutions of elliptic di erential operators. Such kernels can e ectively treat scattered data in a variety of interesting settings. They are a powerful tool for approximation in high dimensions and on esoteric domains like Lie groups, graphs and manifolds. I will discuss some of the settings where precise approximation results are known, and I will detail one of the main problems facing this kind of approximation: the e ect of the boundary. New results will also be discussed concerning the stability of boundary-free in- terpolation. Under mild assumptions on the geometry of the data, this kind of interpolation can be shown to have a uniformly bounded Lebesgue constant (i.e., the L1 operator norm of the projection operator can be bounded independent of the cardinality of the data). However, much stronger results may hold. When the spacing of the data sites is permitted to vary spatially, interpolation is stable in a more re ned sense, one that takes into account the local spacing of the data sites. Thus, a certain penalized" Lebesgue constant (an operator norm on a weighted L1 space) is uniformly bounded, too. Such stability results dovetail nicely with known error estimates { leading to Lebesgue lemmas" which show that interpolation is near-best approximation. We present one such, showing that the (theoretical) local approximation results obtained recently by Devore and Ron hold for interpolation as well.

PDE and Image Analysis Seminar
Lane-Emden problem : survey about symmetries Link: View Poster
Speaker: Christopher Grumiau (Institut de Math ematique - UMons Mons (Belgium))
Time: Monday, October 5, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Here is the link to the abstract. The Slides of the talk is also provided.

Algebra Seminar
D-ratio of a rational map and a upper bound of height Link: View Poster
Speaker: Chong Gyu Lee (Brown University)
Time: Tuesday, October 6, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: When f: P^n -> P^n be a morphism of degree d, then we have a good relation between height of a point and its image by f; there are two constants C_1 and C_2 satisfying
1/d h( f(P) ) - C_1 < h( P ) < 1/d h ( f(P) ) + C_2.
This is one of most important inequality in Arithmetic Dynamics.
If f: P^n -> P^n is a rational map, then the second inequality - h( P ) < 1/d h ( f(P) ) + C_2 - is invalid because the above inequality comes from functorial property of Weil Height Machine and the geometric definition of a morphism. However, if we extend domain of a rational map to get a morphism, then we can use the functorial property so that we can find weaker inequality for rational map:
We can define the degree of a morphism g: P^n -> P^n as a number satisfying g^* H = deg g H. In other word, we can say that degree of g is the ratio between coefficient of g^*H and H = id^* H where id is the identity man on P^n. Likewise, when we have a rational map f : P^n -> P^n, find an resolution of indeterminacy of f - a projective variety V and a birational map pi : V -> P^n satisfying phi = f circ pi is a morphism. Then, Pic(V) is a free Z-module of rank r and hence we can represent phi^*H and pi^*H with generator of Pic(V);
pi^*H = H_V + sum a_i E_i and phi^*H = deg f H_V + sum b_i E_i
Then, min(b_i / a_i) will work as the degree of a morphism in height inequality. For other convenience, we define D-ratio as
D(f) = deg f imes max (a_i /b_i).
With D-ratio of f, we can prove weaker inequality; there are two constants C_1 and C_2 satisfying
1/d h( f(P) ) - C_1 < h( P ) < r(f) /d h ( f(P) ) + C_2
where r(f) is the D-ratio of f.
This inequality will give us some applications in Arithmetic Dynamics - the height boundedness of preperiodic points of a rational map f, proof of Kawaguchi's Conjecture, improvement of Silverman's result for jointly regular pair of rational maps, etc.

S.I.G.M.A. Seminar
The Effect of Global Warming on Financial Discounting Methodology Link: View Poster
Speaker: James Bridgeman (University of Connecticut)
Time: Wednesday, October 7, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The UK government’s October, 2006, Stern Review on the Economics of Climate Change made startling claims about the present value today of climate change effects predicted to emerge primarily 150 years or more in the future. The ensuing debate included challenges to and defenses of the particular methodology used and parameter values selected to perform the discounting of future values. Noticing an overlooked faux pas in the presentation we uncover the likely motivation for choosing the most mystifying of the parameters values, and provide a lesson on the underpinnings of a basic tool in the actuarial craft. There’s nothing sophisticated in the mathematics and it will be accessible to all.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
Preparing for Graduate School in Math Link: View Poster
Speaker: Math Department Members (UConn)
Time: Wednesday, October 7, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: If you are considering graduate school in mathematics after college, come to this panel discussion where you will hear from members of the UConn math department about their experiences planning for and applying to graduate school. The discussion will then be opened to answer your questions. A packet containing a suggested reading list and some general advice will be distributed too.
Comments: Free Refreshments

Mathematics Education
The learning of fractions: How can it be built on the learning of whole numbers? Link: View Poster
Speaker: Liping Ma
Time: Thursday, October 8, 2009 at 4:30 pm
Place: Dodd Center Konover Auditorium (UConn - Storrs)
Abstract: There may be two approaches to teaching fractions: Teaching fractions "in parallel" with whole numbers or first teaching students about whole numbers, then building their understanding of fractions. The first is a well-known and widely used approach in U.S. elementary schools. This talk will describe the second approach: How students' understanding of the concept of fraction as well as their skill in computing with fractions may be built on their learning of whole numbers and how students' learning of whole numbers may be carefully designed so that it serves as a sound foundation for learning fractions.

Colloquium
The learning of fractions: How can it be built on the learning of whole numbers? Link: View Poster
Speaker: Liping Ma
Faculty Sponsor: Cardetti and Vinsonhaler
Time: Thursday, October 8, 2009 at 4:30 pm
Place: Dodd Center Konover Auditorium (UConn - Storrs)
Abstract: There may be two approaches to teaching fractions: Teaching fractions "in parallel" with whole numbers or first teaching students about whole numbers, then building their understanding of fractions. The first is a well-known and widely used approach in U.S. elementary schools. This talk will describe the second approach: How students' understanding of the concept of fraction as well as their skill in computing with fractions may be built on their learning of whole numbers and how students' learning of whole numbers may be carefully designed so that it serves as a sound foundation for learning fractions.
Comments: Co-sponsored by the Center for Research in Mathematics Education (CRME) and UConn's Teachers for a New Era (TNE)

UConn Math Club
Projective Space Link: View Poster
Speaker: Amanda Beeson (Williams)
Time: Monday, October 12, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: What would happen if we were to add a single point at infinity to the real line? What about if we added a line at infinity to the real plane? What kind of spaces do we get? What is geometry like in these spaces? For example, do any two non-parallel lines still meet in only one point? We will discuss these questions and more!
Comments: Note the day! Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Algebra Seminar
A survey of Robinson-Schensted algorithms in types B/C Link: View Poster
Speaker: Eric Sommers (University of Massachusetts - Amherst)
Time: Tuesday, October 13, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: For the general linear group, the Robinson-Schensted algorithm is a map from the symmetric group to pairs of same-shape standard Young tableaux. It is known both to describe the Kazhdan-Lusztig cells in the symmetric group and to give a parametrization of the orbital varieties (these are certain varieties arising from nilpotent orbits). For types B/C, the story is more complicated and there is a family of algorithms introduced by van Leeuwen for each natural number, extending work of Garfinkle. In this talk, I will describe these algorithms and how they relate to questions about Kazhdan-Lusztig cells and orbital varieties for the symplectic and odd orthogonal groups.

S.I.G.M.A. Seminar
Large Deviations, Small Probabilities Link: View Poster
Speaker: Iddo Ben Ari (University of Connecticut)
Time: Wednesday, October 14, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: What is large deviations? Roughly speaking, quantitative study of (certain) rare events. Here's a classical example. We all know (law of large numbers) that the proportion of Heads in a sequence of (independent, identically distributed) coin tosses converges to the deterministic constant 1/2, as the number of tosses tends to infinity. Large deviations studies the rate of convergence. This is done by looking at the rates at which the probabilities of observing proportions larger (or smaller) than 1/2 decay to zero. In this talk I will tell you a little about this beautiful and important theory and its applications. Time permitting, I will talk about my work in the field and problems I'm interested in.
Comments: Free Donuts (courtesy of GSS)

Analysis and Probability Seminar
The Hitting Time Theorem Link: View Poster
Speaker: Mike Keane (Wesleyan University)
Time: Friday, October 16, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In this lecture, based on joint work with Remco van der Hofstad which appeared in 2008 in the American Mathematical Monthly, I would like to explain our elementary proof of the hitting time theorem. This theorem states that for a left-continuous random walk on the integers starting at an integer k greater than zero, the conditional probability that the walk hits zero for the first time at time n, given that it does hit zero at time n, is equal to k/n. Our proof, unlike others, is entirely probabilistic.

Colloquium
A simple lemma in calculus and its application in Kaehler geometry Link: View Poster
Speaker: Xiuxiong Chen (University of Wisconsin at Madison)
Faculty Sponsor: Gui
Time: Friday, October 16, 2009 at 4:00 pm
Place: Mathematical Science Building MSB 118 (UConn - Storrs)
Abstract: In this lecture, I will first explain a simple lemma in calculus about convex function. It turns out that this lemma holds for all dimension (including inifinite dimension) manifold with non-positive curvature. This has important and surprising application in Kaehler geometry.

Algebra Seminar
On the structure of Witt-Burnside rings Link: View Poster
Speaker: Lance Miller (University of Connecticut)
Time: Tuesday, October 20, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The (classical) Witt vectors are a functorial construction which takes perfect fields of characteristic p to p-adically complete domains of characteristic 0. In particular, finite fields of characteristic p go to finite unramified extensions of Q_p. This functor was generalized by Dress and Siebeneicher to a functor W_G associated to any profinite group G, with Witt's construction being the special case G = Z_p. In this talk we will explore some examples of W_G(k) when G is a pro-p group and k is a field of characteristic p and see some properties that are surprising when compared to the classical case.

S.I.G.M.A. Seminar
Examples in Effective Algebra Link: View Poster
Speaker: Amy Turlington (University of Connecticut)
Time: Wednesday, October 21, 2009 at 3:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Effective algebra is a branch of mathematical logic which lies in the intersection of algebra and computability theory. In this talk, I will give an introduction to the area by presenting two basic results, using groups and linear orders as examples. No knowledge of computability theory is assumed.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
The Pigeonhole Principle and Ramsey Theory Link: View Poster
Speaker: Stu Sidney (UConn)
Time: Wednesday, October 21, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Starting with an old socks-in-the-drawer riddle, we will work our way up to the Happy Ending Theorems of Esther Klein, Paul Erdos, and George Szekeres: given any integer p that is greater than or equal to 4, any sufficiently large set of points in the plane such that no three points are on the same line must contain a subset of p points which are the vertices of a convex p-sided polygon.

The main tools which will be developed along the way are the pigeonhole principle and its muscular consequence, Ramsey theory.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club


Algebra Seminar
The moduli space of points on the projective line and quadratic Groebner bases. Link: View Poster
Speaker: Milena Hering (University of Connecticut)
Time: Tuesday, October 27, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The ring of invariants for the action of the automorphism group of the projective line on the n-fold product of the projective line is a classical object of study. The generators of this ring were determined by Kempe in the 19th century. However, the ideal of relations has been only understood very recently in work of Howard, Millson, Snowden and Vakil. They prove that the ideal of relations is generated by quadratic equations. This raises the natural question, whether the ideal of relations also admits a quadratic Groebner basis. I will report on work with Ben Howard on this question.

Actuarial Science Seminar
Time-inconsistent preferences in consumption, investment and life insurance models Link: View Poster
Speaker: Oriol Roch (Universitat de Barcelona)
Time: Tuesday, October 27, 2009 at 4:20 pm
Place: BPB 131 (UConn - Storrs)
Abstract: The assumption of a constant discount rate of time preference has been questioned by empirical findings about how agents change their preferences over time. For instance, it has been argued that individuals are highly impatient about consuming between today and tomorrow but are much more patient about choices advanced further in the future. Therefore, rates of time preference should decline faster in the short-run than in the long-run and, as a consequence, preferences change with time in such a way that a decision maker at a given time will have different preferences compared with the same agent at any different moment in time. However, as pointed out by Strotz (1956), the use of standard optimal control techniques for problems with other discount factors than the exponential function with a constant rate can lead to time-inconsistent decisions for the decision maker. In this paper, making use of the necessary conditions for consistent policies derived in Marín-Solano and Navas (2009), we depart from the work of Richard (1975) where optimal consumption, portfolio and life insurance rules were studied for an investor with an arbitrary but known distribution of lifetime, and generalize investor's time preferences by considering a variable non-increasing time rate within a stochastic framework.

Mathematics Education
Justification as a disciplinary practice and a learning practice: Negotiating its meaning in classroom. Link: View Poster
Speaker: Megan Staples (UConn Neag School of Education)
Time: Wednesday, October 28, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In this talk, I explore the notion of justification as a disciplinary practice and as a learning practice. As a disciplinary practice, justification has many purposes: it is used to validate claims, provide insight into a phenomenon or result, and systematize knowledge (Hanna, 1990). As a learning practice, justification may be used for these purposes, but also for other classroom-relevant purposes such as assessment, promoting particular mathematical dispositions, and pursuing specific content learning goals. By examining teachers’ views of justification (its attributes, what comprises a “good justification,” etc.) as well as video excerpts from classroom lessons, I try to clarify the nature of justification as a learning practice in k-16 classrooms. A framework for thinking about justification as a learning practice will be presented. Participant feedback on the implications for mathematics education and teacher development will be elicited.

S.I.G.M.A. Seminar
Path algebras and cluster-tilted algebras Link: View Poster
Speaker: Ralf Schiffler (University of Connecticut)
Time: Wednesday, October 28, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: This talk is about representation theory of finite dimensional algebras. An algebra A is a ring which is also a vector space (aha! finite dimensional algebra means the vector space has a finite basis). Representation theory deals with the modules over A. We will use quivers (oriented graphs) to construct a large class of finite dimensional algebras as path algebras and to give a very handy description of their modules. Then we will look at a generalization of finite dimensional path algebras, called cluster-tilted algebras, which have interesting connections to various areas of mathematics.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
Unsolved mysteries of mathematics: the rank of an elliptic curve Link: View Poster
Speaker: Christine McMeekin (UConn)
Time: Wednesday, October 28, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: How does one do research in math? Contrary to popular belief, there are still many questions in pure mathematics which remain unanswered to this day. I will be presenting an introduction to one such question involving elliptic curves and a property of elliptic curves called the rank.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Colloquium
Tropicalisation of rational varieties Link: View Poster
Speaker: Alicia Dickenstein (Universidad de Buenos Aires)
Faculty Sponsor: Hering
Time: Thursday, October 29, 2009 at 4:00 pm
Place: Mathematical Science Building MSB 118 (UConn - Storrs)
Abstract: The tropicalisation trop(V) of an affine or projective algebraic variety V is a polyhedral complex, together with intersection theoretic data, that encodes important information about V as its dimension, its degree, and its asymptotic directions. When V is a hypersurface, trop(V) carries the same information as the Newton polytope of a defining equation for V. The problem of describing trop(V) for a rational variety in terms of a given rational parametrization has been recently studied by Sturmfels-Tevelev-Yu and Esterov-Khovanskii. Based on Kapranov's theorem, we present a naive approach to the problem using curve valuations, which allows us to slightly generalize their results. The advantage of this point of view is that even if we get complete results only when the polynomials defining the parametrization are generic with respect to their Newton polytopes, the proofs can be extended to deal with more general cases. This is joint work in progress with Bernard Mourrain.

PDE and Image Analysis Seminar
Lp-estimates for higher-order elliptic and parabolic systems with BMO coefficients Link: View Poster
Speaker: Hongjie Dong (Brown)
Time: Monday, November 2, 2009 at 3:15 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain.

The leading coefficients are assumed to be merely measurable in the time variable and have small mean oscillations with respect to the spatial variables in small balls or cylinders. This is joint work with Doyoon Kim (USC).


Algebra Seminar
The Constant Terms of Eisenstein Series on Loop Groups over a Function Field. Link: View Poster
Speaker: Phil Lombardo (University of Connecticut)
Time: Tuesday, November 3, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In 2001, Howard Garland published a paper in which he constructed Eisenstein series on arithmetic quotients of loop groups. He obtained a formula for the constant terms of these series, and showed the existence of a meromorphic continuation and a functional equation. In this talk, we generalize his work by defining Eisenstein series on loop groups over a function field, and computing a formula for the constant term.

S.I.G.M.A. Seminar
Investigating the model of high school mathematics teacher preparation in China Link: View Poster
Speaker: Su Liang (University of Connecticut)
Time: Wednesday, November 4, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The preparation of a high school math teacher is an area of study that is still open for improvement and refinement. The research on preparation of high school mathematics teachers calls for enrichment by studying other countries, especially, those countries where high school students have high performance in mathematics. China is one of these countries. Research on high school math teacher preparation in China is still an open field. This study will examine high school mathematics teacher preparation in China, and provide an in-depth look at several characteristic aspects of this model. In particular, this study will provide an overview of the entire model, and an in-depth analysis of the in-service training, which is part of this model.
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
Depleted harmonic series and a neat theorem about primes Link: View Poster
Speaker: John Haga (UConn)
Time: Wednesday, November 4, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: The sum of reciprocals 1/n where n does not contain 9 as a digit converges. Such a sum is called a depleted harmonic series.

There's nothing special about 9 here. We can consider the sum of all 1/n where n doesn't have the block of digits 12121212121212 in it. That sum also converges. Combining this with a theorem about primes which goes back to Euler, we will see that there are infinitely many primes which contain 12121212121212 as a block of its digits.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club


Colloquium
Twisted Euler Products Link: View Poster
Speaker: Solomon Friedberg (Boston College)
Faculty Sponsor: Lee
Time: Thursday, November 5, 2009 at 4:00 pm
Place: Mathematical Science Building MSB 118 (UConn - Storrs)
Abstract: Euler products are the foundation of the Langlands program and a great deal of modern number theory. In this talk I shall introduce twisted Euler products, a new construction, and explain how such twisted products arise. They offer hints of an unexpected connection between number theory and quantum groups.

Analysis and Probability Seminar
Link: View Poster
Speaker: Iddo Ben Ari (University of Connecticut)
Time: Friday, November 6, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)

Algebra Seminar
Affine dual equivalence and k-Schur positivity Link: View Poster
Speaker: Sami Assaf (MIT)
Time: Tuesday, November 10, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The k-Schur functions were first introduced by Lapointe, Lascoux and Morse in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono as the weighted generating function of starred strong tableaux. This definition has been shown to correspond to the Schubert basis for the affine Grassmannian and at t=1 it is equivalent to the k-tableaux characterization of Lapointe and Morse. Using this new definition for k-Schur functions, we prove the symmetry and Schur positivity of k-Schur functions combinatorially using the theory of dual equivalence graphs. Central to our proof is our discovery of an analog of dual equivalence for the affine symmetric group.

S.I.G.M.A. Seminar
TBA Link: View Poster
Speaker: Avraham Bourla (University of Connecticut)
Time: Wednesday, November 11, 2009 at 4:30 pm
Place: MSB 118 (UConn - Storrs)
Comments: Free Donuts (courtesy of GSS)

UConn Math Club
Pick's Formula Link: View Poster
Speaker: Milena Hering (UConn)
Time: Wednesday, November 11, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Pick’s formula gives the area A of a lattice polygon in terms of the number of its interior points, I, and the number of lattice points on its boundary, B: the formula is A = I + B/2 – 1. In this talk I will give a proof of Pick’s formula and sketch some of its relations with algebraic geometry, as well as generalizations to higher-dimensional lattice polytopes.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Mathematics Education
Conflicts between Mathematics Educators and Mathematicians, and Ways to Overcome Them Link: View Poster
Speaker: Wilfried Schmid (Harvard University)
Time: Thursday, November 12, 2009 at 4:30 pm
Place: Biology Physics BPB 131 (UConn - Storrs)
Abstract: Though neither mathematics educators nor mathematicians hold uniform views on K-12 mathematics educators, in both groups there exists what might be called a mainstream consensus. I shall outline the disagreements between the two communities, analyze their origins and consequences, and describe successful efforts to defuse them.

Colloquium
Conflicts between Mathematics Educators and Mathematicians, and Ways to Overcome Them Link: View Poster
Speaker: Wilfried Schmid (Harvard University)
Faculty Sponsor: Cardetti and Vinsonhaler
Time: Thursday, November 12, 2009 at 4:30 pm
Place: Biology/Physics Building BPB 131 (UConn - Storrs)
Abstract: Though neither mathematics educators nor mathematicians hold uniform views on K-12 mathematics educators, in both groups there exists what might be called a mainstream consensus. I shall outline the disagreements between the two communities, analyze their origins and consequences, and describe successful efforts to defuse them.
Comments: Co-sponsored by the Center for Research in Mathematics Education (CRME) and UConn's Teachers for a New Era (TNE)

PDE and Image Analysis Seminar
Scattering for the fourth-order wave equation Link: View Poster
Speaker: Benoit Pausader (Brown)
Time: Monday, November 16, 2009 at 3:00 pm
Place: MSB 319 (UConn - Storrs)
Abstract: We consider the fourth-order wave equation utt+Δ2u+mu+|u|p-1u=0 and we prove that finite energy leads to solution which scatter in the subcritical case 1+8/n < p <1+8/(n-4) when n ≥ 2. For high dimensions, we use a Double-Duhamel formula and a Morawetz-type inequality due to Levandosky and Strauss. For low dimensions, we use concentration-compactness type arguments and a virial-type identity to exclude traveling waves.

PDE and Image Analysis Seminar
Stability and instability in th Stefan problem with surface tension Link: View Poster
Speaker: Mahir Hadzic (Brown)
Time: Monday, November 16, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: Stefan problem with surface tension is one of the best-known parabolic free boundary problems, describing phase transitions. Using a high-order energy method, we first prove the nonlinear stability of flat stationary surfaces. On the other hand, stationary spheres may be unstable and we then provide a full characterization of nonlinear stability/instability of steady spheres.
Comments: In case of scheduling problems, the alternate room will be TLS 301.

Logic Seminar
Generalized Indiscernible Sequences in Stable and NIP Theories Link: View Poster
Speaker: Lynn Scow (UC Berkeley)
Time: Monday, November 16, 2009 at 5:05 pm
Place: Exley Science Center 618 (Wesleyan)
Abstract: In the 1970s, S. Shelah gave the following characterization of stable theories: a theory is stable if and only if any indiscernible sequence in a model of the theory is an indiscernible set. I will present a similar characterization of NIP theories, as theories in qwhich any random ordered graph-indiscernible in a model of the theory remains indiscernible strictly with respect to the order. In this talk I will explain what I mean by a random ordered graph-indiscernible and I will indicate how the result is proved using the Nesetril-Rodl theorem. If time permits, I will discuss an additional example of a characterization of stable theories by generalized indiscernibles that generalizes more faithfully on Shelah's.

Algebra Seminar
The Tame Hecke Algebra Link: View Poster
Speaker: Martin Nikolov (University of Connecticut)
Time: Tuesday, November 17, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: The tame subgroup of the Iwahori subgroup and the tame Hecke algebra will be introduced. I will talk about the presentation of this algebra by means of generators and relations. This has applications concerning  irreducible admissible representations of unramified reductive p-adic groups, which have a nonzero vector fixed by the tame subgroup.

Colloquium
The Linear Algebra of Internet Search Engines Link: View Poster
Speaker: Lesley Ward (University of South Australia)
Time: Wednesday, November 18, 2009 at 3:00 pm
Place: IMS 20 (UConn - Storrs)
Abstract: We often want to search the web for information on a given topic. Early web-search algorithms worked by counting up the number of times the words in a query topic appeared on each webpage. If the topic words appeared often on a given page, that page was ranked highly as a source of information on that topic. More recent algorithms rely on Link Analysis. People make judgments about how useful a given page is for a given topic, and they express these judgments through the hyperlinks they choose to put on their own webpages. Link-analysis algorithms aim to mine the collective wisdom encoded in the resulting network of links. I will discuss the linear algebra that forms the common underpinning of three link-analysis algorithms for web search. I will also present some work on refining one such algorithm, Kleinberg's HITS algorithm. This is joint work with Joel Miller, Greg Rae, Fred Schaefer, Ayman Farahat, Tom LoFaro, Tracy Powell, Estelle Basor, and Kent Morrison. It originated in a Mathematics Clinic project at Harvey Mudd College.
Comments: Note the room!

Colloquium
The Riemann Hypothesis Link: View Poster
Speaker: Keith Conrad (University of Connecticut)
Time: Wednesday, November 18, 2009 at 4:00 pm
Place: IMS 20 (UConn - Storrs)
Abstract: In November 1859, an 8-page paper by Riemann was published which described the distribution of primes using complex analysis.  In this paper Riemann stated what has become arguably the most important unsolved problem in mathematics: the Riemann hypothesis.  In this talk, marking the 150th anniversary of Riemann's paper, I will explain what the Riemann hypothesis is and why it is considered so important.
Comments: Note the room!

UConn Math Club
Bernoulli Numbers and Their Applications Link: View Poster
Speaker: Li-Mei Lim (Brown)
Time: Wednesday, November 18, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: Bernoulli numbers are certain rational numbers that come up in several interesting and classical problems.  In this talk, we'll define the Bernoulli numbers, and explore their connection to the sums 1k+2k+...+(n-1)k, to the mysterious and wonderful Riemann Zeta function, and (time permitting) to the deeply complex Fermat's Last Theorem.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Colloquium
Integral quadratic forms: from local to global Link: View Poster
Speaker: Wai Kiu Chan (Wesleyan University)
Faculty Sponsor: Lee
Time: Thursday, November 19, 2009 at 4:00 pm
Place: Mathematical Science Building MSB 118 (UConn - Storrs)
Abstract: An integral quadratic form is called regular if it represents all integers which cannot be ruled out by congruence considerations. Examples are the sum of four squares and other universal quadratic forms. The goal of this talk is to describe some of the recent advances in the study of regular quadratic forms and generalizations, with emphasis on various finiteness results.

Logic Seminar
Definite Forms in Valued Fields Link: View Poster
Speaker: Laurel Miller-Sims (Smith College)
Time: Monday, November 30, 2009 at 5:05 pm
Place: Exley Science Center 618 (Wesleyan)
Abstract: Given a valued field (K,v), we say that a rational function f(x) in K(x) is integral or infinitesimal definite on the definable set S if v(f(b)) ≥ 0 or v(f(b))>0, respectively, for each b in S. I will give algebraic characterizations of integral definite and infinitesimal definite rational functions in various model-complete theories of valued fields, analogous to the Positivstellensatz and Negativstellensatz for real closed fields.

UConn Math Club
Fourier series, Fourier transforms, and applications Link: View Poster
Speaker: Erin Terwilleger (UConn)
Time: Wednesday, December 2, 2009 at 5:30 pm
Place: MSB 319 (UConn - Storrs)
Abstract: In the beginning of the 19th century, Joseph Fourier developed an infinite series of sine and cosine functions to describe heat flow in a long, thin rectangular plate. However, his assertions ran contrary to the prevailing understanding of functions and infinite series. It took some time for the mathematical world to accept his findings, but today we know Fourier series are extremely important and have led to a whole branch of mathematics called Fourier Analysis. In this talk, I will introduce Fourier series and the Fourier transform and show some applications.
Comments: Free Refreshments
Additional Comments: Email: uconnmathclub@gmail.com Facebook group: UConn Math Club

Colloquium
TBA Link: View Poster
Speaker: Laura Matusevich (Texas A & M University)
Faculty Sponsor: Milena Hering
Time: Friday, December 4, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)

Logic Seminar
How many sprays cover the plane? Link: View Poster
Speaker: Jim Schmerl (University of Connecticut)
Time: Monday, December 7, 2009 at 5:05 pm
Place: Exley Science Center 618 (Wesleyan)
Abstract: I will talk about de la Vega's recent (FM,2009) answer to this question and my improvement to it. If  c  is a point in the plane, then a subset  X  of the plane is a spray (centered at c) if, whenever C is a circle centered at c , then the intersection of X and C is finite.

Algebra Seminar
New parts of Hecke rings Link: View Poster
Speaker: Benjamin Lundell (Cornell University)
Time: Tuesday, December 8, 2009 at 4:00 pm
Place: MSB 118 (UConn - Storrs)
Abstract: In 1970s, Barry Mazur studied certain completed Hecke algebras and related their ring-theoretic properties to deep arithmetic results. In this talk, we will discuss recent progress towards answering a modified version of a question of Mazur's about the rank of such a Hecke algebra and some of the arithmetic corollaries.