Seminar Schedule
September 17 - September 21, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, September 17, 2007
Algebra
2:30pm, Room 410
Speaker: Benjamin Jones, University of Georgia
Title of talk: Singular Chern Classes of Schubert Varieties: Part 3
Topology
2:30pm, Room 303
Speaker: Will Kazez, University of Georgia
Title of talk: Surfaces in contact 3-manifolds*
Abstract: *This lecture will be the first in a series of lectures by local topologists that are intended to introduce graduate students (and each other) to the sort of research we do.* I will discuss neighborhoods of points, lines and surfaces in contact 3-manifolds, with the goal of explaining how cut-and-paste contact topology is carried out.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea, Cookies
TUESDAY, September 18, 2007
VIGRE - Graduate Student Seminar
2:00pm, Room 304
Speaker: Lev Konstantinovskiy, University of Georgia
Title of talk: The Hilbert Function
Abstract: Given a polynomial ring S and an ideal I, there is a vector space of polynomials of degree n in the quotient ring S/I. Define h(n) to be the dimension of this vector space. It is a function of integers, called the Hilbert function of I. Given the ring S, which functions can be Hilbert functions? We will discuss MacAulay's result on the maximal growth of h. Another question is: Given a ring S and a function h, which ideals have this Hilbert function?
FRG Analysis and Additive Combinatorics Working Group
3:30pm, Room 410
Speaker: Neil Lyall, University of Georgia
Title of talk: Sarkozy's Theorem
Abstract: This is the first meeting of an informal seminar series, specifically aimed at graduate students. It is our intent to give expository lectures on a number of related results from analytic number theory, combinatorics and harmonic analysis (depending on the participants'/speakers' interests).
At the first meeting we shall use the Hardy-Littlewood circle method to prove Sarkozy's theorem: If A is a subset of positive density in the integers, then there exists two elements a and a' in A such that a-a' is a perfect square. The argument we plan to present (a modification of one due to Ben Green), although elementary, in fact gives better quantitative bounds than those which were originally obtained by Sarkozy (but alas fall way short of the best bounds that are currently known). On the positive side, this argument is relatively simple and can be easily extended to prove a more general (and new) result on the existence of certain polynomial configurations in difference sets (or sumsets). If time permits we may briefly discuss these generalizations.
WEDNESDAY, September 19, 2007
Algebraic Geometry
2:30pm, Room 410
No meeting this week
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Dino Lorenzini, University of Georgia
Title of talk: Riemann-Roch zeta functions.
Abstract:I will review the 2-variable zeta function for curves over finite fields, and discuss the properties of the analogue zeta-function for finite graphs.
Mathematical Physics
3:45pm, Room 302
Speaker: Robert Varley, University of Georgia
Title of talk: Entropy in statistical mechanics and thermodynamics
Math Club Seminar
5:00-6:30pm, Conner Hall 104
MATH AND THE BRAIN, A double feature with biological and mathematical insights
Speakers: Professor James Lauderdale (Cellular Biology) http://www.uga.edu/cellbio/lauderdale.html
Professor Andrew Sornborger (Department of Mathematics/Faculty of Engineering) http://www.engr.uga.edu/people/ats Title: Visualizing Thought -or- What Can Neuroscientists Learn from the CIA?
Abstract: If the brain were a computer chip, we could simply map out all of the circuits that caused it to function and figure out how they relate to thought and behavior. In real life, however, figuring out how brains work is much more complicated. Our talk will describe the kind of things that we do in order to understand real brains in real animals. Our labs work together to visualize brain activity in a small tropical fish called a zebrafish. In order to see a brain at work, we use zebrafish whose neurons glow with a fluorescent jellyfish protein, high-tech laser microscopy and mathematics. Using a tag-team format, we will show how mathematics, such as methods originally developed to eavesdrop on the Russians, and biology can combine to give new insights into how brains work.
Pizza and refreshments will be served after the talk.
THURSDAY, September 20, 2007
VIGRE – Algebraic Geometry
3:30pm, Room 323
Applied Math
2:00pm, Room 302
Speaker: Scott Dugan, University of Georgia, Cellular Biology
Title of talk: Mathematical models of embryonic patterning systems
Abstract: During vertebrate embryogenesis, morphogen gradients and molecular clocks each play key, but distinct roles in pattern formation. Morphogen gradients specify a diverse array of cell types in a concentration dependent manner. Molecular clocks, by contrast, control the temporal formation of morphogenetic events, such as somite formation. Despite these dramatic differences, both systems can be described as the interaction between activating and inhibitory gene networks. We have modeled pattern formation by the TGF-beta morphogen, Squint, which is thought to act by a reaction-diffusion mechanism. Squint signals activate an autoregulatory loop in responding cells, leading to the production of new Squint signals, as well as the expression of a secreted inhibitor, called Lefty, which limits the action of Squint. At the level of the individual cells, we find parameters in which exogenous Squint induces oscillatory behavior. Although such parameter values are in the minority, we demonstrate that they are scattered throughout the parameter space. When we modeled the behavior of populations of cells in response to a diffusive gradient of Squint, we found that cells react statically in the vast majority of parameters, as in a classic reaction-diffusion model. As in the single cell model, we observed conditions throughout the parameter space in which the morphogen induces oscillatory behavior in the responding cells. In these cases, cells close to the source respond by producing static levels of Squint and Lefty, but cells far from the source produce periodic pulses of these factors, as in a molecular clock. These results suggest a new mechanism by which morphogen gradients may pattern tissues over time. This is the first of two talks on embryonic patterning. I will present the biological context in a form appropriate for non-biologists, and Malcolm Adams will discuss the mathematical models of this system the following week.
VIGRE – Tropical Geometry
2:00pm, Room 304
VIGRE – Circle Packing
3:30pm, Room 222
VIGRE-Number Theory
2:30pm, Room 326
FRIDAY, September 21, 2007
VIGRE-Algebra
1:30pm, Room 302
Geometry
2:30pm, Room 410
Speaker: TBA
Title of talk: TBA