University of Georgia
Department of Mathematics

Seminar Schedule
November 6- November 10, 2006

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

 

MONDAY, November 6, 2006

Topology
2:30pm, Room 304
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact topology and the invariant of Ozsvath and Szabo, continued

Algebra
2:30pm, Room 410
Speaker: Jonathan Kujawa, University of Georgia
Title of talk: Support Varieties for Lie superalgebras
Abstract: We will discuss ongoing work with Nakano and Boe on support varieties for Lie superalgebras over the complex numbers. We will discuss what is known, what is not known, and what we would like to know. We will not assume any prior knowledge of Lie superalgebras or their support varieties for this talk. We aim to be accessible to all who are interested.


Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea


TUESDAY, November 7, 2006

VIGRE Graduate Student Seminar
2:00pm, Room 302
Speaker: Jonathan Hanke, Duke University
Title of talk: How many ways can you write a number as a sum of 4 squares?
Abstract: I hope to give a conceptual explanation of the formula for the number of ways to write a positive integer as a sum of 4 integer squares. In addition to philosophy, there will be lots of concrete computations with something for everyone. In particular, we will combine tools from seemingly unrelated areas of mathematics such as - Clock/modular arithmetic with prime numbers - Infinite sums, products, and transcendental numbers - Calculus and the geometry of 4-dimensional space to compute the number of ways of writing 1 and 2 as a sum of four squares. This talk should assume only undergraduate mathematics, and is meant to be a fun talk for first-year graduate students, who want to see something interesting in the land of number theory!

Arithmetic Geometry/Number Theory Special Seminar
3:30pm., Room 304
Speaker: Jonathan Hanke, Duke University
Title of talk: The 290-Theorem and Representing Numbers by Quadratic Forms.
Abstract: This talk will describe several finiteness theorems for quadratic forms, and progress on the question: "Which positive definite integer-valued quadratic forms represent all positive integers?". The answer to this question depends on settling the related question "Which integers are represented by a given quadratic form?" for finitely many forms. The answer to this question can involve both arithmetic and analytic techniques, though only recently has the analytic approach become practical. We will describe the theory of quadratic forms as it relates to answering these questions, its connections with the theory of modular forms, and give an idea of how one can obtain explicit bounds to describe which numbers are represented by a given quadratic form. http://www.sciencenews.org/articles/20060311/bob9.asp


Analysis
3:30pm, Room 222
No Meeting this week

WEDNESDAY, November 8, 2006

Algebraic Geometry
2:30pm, Room 410
No Meeting this week

Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies

Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Zubeyir Cinkir, University of Georgia
Title of talk: More Insight on the "Tau Constant" of a Metrized Graph
Abstract: We will discuss the proofs of some of the key theorems that we mentioned last week. In order to give more insight, our main focus is to discuss the ideas that are used rather than the computations. We will also present illustrative examples. In this talk, we will assume that the audiences attended the last week's talk or know the basic concepts related to the tau constant tau(G) for a metrized graph G.


THURSDAY, November 9, 2006

VIGRE-Algebraic Geometry
2:00pm, Room 410

Wavelets and Splines
2:30pm, Room 524
Speaker: Ming-Jun Lai, University of Georgia
Title of talk: Bivariate Splines for Forecasting
Abstract: Consider a real-valued time series observed p times a period over n periods sampled over a 2D domain. For example, the ozone concentrations over 1000 locations in the U.S. are measured every hour per day for over 90 days. We want to see the patterns and prediction of the concentration distribution over the U.S. We use bivariate splines to fit the given data and use the principle component analysis to extract patterns from the data.

VIGRE - Quantum Mechanics
3:30pm, Room 410

 

FRIDAY, November 10, 2006

Probability Theory
2:30pm, Room 323
Speaker: DongHoon Shin, University of Georgia
Title of talk: Optimal Adaptive LQG Control, continued

Geometry
2:30pm, Room 410
Speaker: Elizabeth Denne, Harvard University
Title of talk: The Distortion of a Knotted Curve
Abstract: The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed that any closed curve has distortion at least $\pi/2$ and asked whether every knot type can be built with distortion less than, say, 100. Here we use the existence of an essential secant to show that any nontrivial knot in space has distortion at least 4.06466. Examples show that distortion under 7.15839 suffices to build a trefoil knot.

VIGRE-Algebra
2:30pm, Room 304