Seminar Schedule
August 20-24, 2007
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, August 20, 2007
Topology
2:30pm, Room 303
Organizational meeting
Algebra
2:30pm, Room 410
Organizational meeting
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Fall Departmental Meeting
3:30pm, Room 304
TUESDAY, August 21, 2007
VIGRE seminar
2 - 3:15 pm, Room 304
There will be two 35 minute talks, introducing the VIGRE groups.
Speaker: Valery Alexeev, University of Georgia
Title of talk: Tropical geometry
Abstract: Tropical geometry is a "hot", fairly new and popular field whose main attractions are: a very low starting point, almost no prerequisites needed wealth of applications in topology, algebraic geometry, combinatorics, physics, probability theory
wide-open areas for original research a large community of people interested
This combination makes it an attractive place for a student to start original research. Known applications in physics include an amazingly easy way to compute Gromov-Witten invariants and, in a perpendicular direction, a way to describe shapes of dimer crystals.
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Speaker: Dino Lorenzini, University of Georgia
Title of talk: Algebraic Graph Theory
Abstract: Associated to a graph G on n vertices are two (n x n)-matrices, the adjacency matrix A and the Laplacian matrix L. Both A and L have a set of eigenvalues, and a Smith normal form over the integers. Much has been written on the relationships between the eigenvalues and the combinatorics/topology of the graph. In this seminar, we will investigate the information encoded in the Smith normal form of the Laplacian of a graph. Links with recent geometrically inspired theories could also be discussed, depending on the interests of the participants. Prerequisites: a basic course in linear algebra, and a willingness to try things out.
WEDNESDAY, August 22, 2007
Algebraic Geometry
2:30pm, Room 410
Speaker: Matt Baker, Georgia Tech
Title of talk: Graphs as discrete analogues of algebraic curves
Abstract: I will discuss the notion of linear equivalence of divisors on a finite graph, and state a graph-theoretic version of the Riemann-Roch theorem. I will then discuss harmonic morphisms between graphs, including a graph-theoretic analogue of the Riemann-Hurwitz formula, and discuss the functorial maps on Jacobians and harmonic 1-forms induced by a harmonic morphism. Finally, I will state several equivalent characterizations of the notion of a "hyperelliptic graph". This is all joint work with Serguei Norine.
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
Arithmetic Geometry/Number Theory
3:30pm, Room 304
Speaker: Matt Baker, Georgia Tech
Title of talk: Connections between graphs and algebraic curves
Abstract: I will discuss a "specialization map" on a regular semistable arithmetic surface which takes divisors on the generic fiber to divisors on the dual graph of the special fiber. I will then state the "specialization lemma", which says that the dimension of a linear system cannot decrease under specialization. This result has some interesting applications, including a generalization of Ogg's results concerning Weierstrass points on modular curves and a "Brill-Noether theorem" in tropical geometry
Mathematical Physics
3:45pm, Room 302
Organizational meeting
VIGRE-Algebra
3:30pm, Room 303
THURSDAY, August 23, 2007
VIGRE Graduate Student Seminar
2:00pm, Room 323
Speaker: Elham Izadi, University of Georgia
Title of talk: Introduction to Algebraic Geometry
Abstract: The VIGRE research group that I will run this year will concentrate on elementary problems in Algebraic Geometry. Most of the problems that we will work on will be concerned with explicitly desingularizing examples of algebraic varieties by blowing them up (an algebraic variety is the set of common zeros of some polynomials in several variables). For instance we will desingularize plane curves, some hypersurfaces in projective space, subvarieties of Grassmannians. We will start by covering some necessary background about what it means to be singular and nonsingular, what is a blow up etc. There are no prerequisites for the VIGRE group other than enthusiasm and hard work. You can start at any level and do as much as you can. We will split the interested students into groups of two or three (according to people's backgrounds and interests) who will work together on the same problem.
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VIGRE-Number Theory
3:30pm, Room 304
Speaker: Pete Clark, University of Georgia
Introductory meeting
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Circle Packing, Sa’ar Hersonsky, University of Georgia
I will not be giving an introductory talk. Please go to this webpage.
http://www.math.uga.edu/~saarh/CirclePacking.html
If you are still interested, and willing to put 2-3 hours per week during the Fall and next Spring, come and see me in Room 408 on Tuesday, August 21, 2007 between 4:30-5:30 pm.
Applied Math
2:00pm, Room 302
Organizational meeting
FRIDAY, August 24, 2007
Geometry
2:30pm, Room 410
Organizational Meeting
Please come to discuss speakers and organizers for the fall semester.