University of Georgia
Department of Mathematics
Seminar Schedule
February 12– February 16, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, February 12, 2007
Joint Algebraic Geometry / Algebra / Topology seminar
2:30pm, Room 304
Speaker: Grigory Mikhalkin, Toronto
Title of talk: Tropical structures on polyhedral complexes
Abstract: From a geometric point of view algebraic varieties
over the real (max,+)-semifield (also known as the tropical semifield) can be
viewed as polyhedral complexes equipped with integer affine structure. In the
talk we'll analyse this structure using the moduli space of stable curves as
our main example.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Tea and Cookies
TUESDAY, February 13, 2007
VIGRE-Graduate
Student Seminar
2:00pm, Room 304
Speaker: Aaron Abrams, Emory University
Title of talk: Can you tile a square with an odd number
of triangles of equal area?
Abstract: Or how about this one: can you color each point of
the plane with one of three colors, in a nontrivial way, such that no straight
line contains points of all three colors? (What should ``nontrivial'' mean?)
These questions and more will be answered. We will use a bit of topology, a
bit of number theory, and a bit of magic.
WEDNESDAY, February 14, 2007
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Number Theory/Arithmetic Geometry
3:30pm, Room 304
Speaker: Pete Clark, University of Georgia
Title of talk: Ramanujan Graphs I
Abstract: This is the first of a sequence of lectures on Ramanujan
graphs, which are finite graphs characterized by having a "spectral gap"
-- i.e., the difference between the largest and second largest eigenvalues of
the adjacency matrix -- which is asymptotically optimal. Such graphs serve as
a meeting ground for many topics: combinatorics, group theory, automorphic forms
and representations, harmonic analysis, and arithmetic geometry; they are also
of real-world interest, with applications to the design of well-connected, sparse
networks.
This first talk will be pitched at a general mathematical audience: I will discuss basic definitions, provide some motivation, and state a result (of mine, but which will probably not be surprising to several experts in the field) which simultaneously generalizes the work of Lubotzky-Phillips-Sarnak, Morgenstern and Pizer: this seems to represent the limit of what can be shown about k-regular Ramanujan graphs using current technology.
VIGRE – Quantum Mechanics
4:00pm, Room 302
THURSDAY, February 15, 2007
VIGRE – ODE
2:00pm, Room 326
VIGRE – Moduli spaces
2:00pm, Room 304
VIGRE – Geometry
2:00pm, Room 410
FRIDAY, February 16, 2007
Applied
Math Seminar
12:20pm-1:10pm, Room 326
(Pizza at 12:10pm)
Speaker: Malcolm Adams, University of Georgia
Title of talk: The Replicator Equations from Evolutionary
Game Theory
Abstract: The replicator equations are a system of ordinary
differential equations that describe the evolution of n competing populations
in terms of the relative fitness of the various components of the population.
I will give a brief derivation of these equations and discuss some properties
and classical examples. If time permits, I will also describe recent results
of myself and Sornborger on the long term behavior of solutions for a certain
class of these equations.
Geometry
2:30pm, Room 410
Speaker: Jason Parsley, Wake Forest University
Title of talk: Vector Field invariants in R^3
Abstract: In this talk, we explore the construction of general
finite type invariants for vector fields on domains in R^3. As our motivating
example, we aim to understand the helicity of a vector field, which measures
how much the flowlines coil and wrap around one another and is related to the
linking numbers of curves. Helicity is invariant under volume-preserving diffeomorphisms
of the domain. We examine this invariance using a (possibly) new approach via
configuration spaces and the formalized structure of Bott-Taubes integration,
used for defining finite-type invariants for knots. This formulation naturally
suggests an approach to constructing new vector field invariants. This talk
is joint work with Jason Cantarella.
VIGRE–Algebra
3:30pm, Room 304
VIGRE - Hodge Theoretic questions in Algebraic Geometry
3:30pm, Room 303