Seminar Schedule
October 30 - November 3, 2006
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, October 30, 2006
Topology
2:30pm, Room 304
Speaker: Gordana Matic, University of Georgia
Title of talk: Contact topology and the invariant of Ozsvath
and Szabo, Part 2
Algebra
2:30pm, Room 410
No Meeting this week
Faculty and Graduate Student Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, October 31, 2006
VIGRE
Graduate Student Seminar
2:00pm, Room 302
Speaker: Xuechao Li, University of Georgia
Title: Edge coloring in Graph Theory
Abstract: My talk includes introducing some basic concepts
in Graph Theory, coloring problems in graph theory, conjectures on edge coloring
and current results on those conjectures.
Analysis
3:30pm, Room 222
Speaker: Ed Azoff, University of Georgia
Title of talk: Descriptive Set Theory in Harmonic Analysis,
continued
WEDNESDAY, November 1, 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: "Tau Constant", An Invariant of
Metrized Graphs
Abstract: On a weighted graph G, i.e. a metrized graph, the
diagonal value of the Arakelov-Green's function g_{m}(x,y) is a constant for
a certain "canonical measure" m on G. This constant is called "the
tau constant", denoted as tau(G), introduced by M.Baker and R.Rumely, studied
in Summer 2003 REU at UGA and related to S. Zhang's work on the reduction of
curves.
There are a number of ways to describe tau(G). In terms of spectral theory, it is the trace of the inverse of the continuous Laplacian on G. Also, it is closely related to the resistance and the voltage functions on G when G is considered as an electrical network.
Our main focus is to show the existence of a universal positive lower bound to tau(G) for any G with length(G)=1.
We will show how tau(G) changes under various graph operations e.g., doubling edges, deleting and contracting edges, union of graphs along one or two points. We will establish some identities which we call "the deletion and the contraction identities". We will show that tau(G) >= length(G)/12*(1-4/N)2 , where the edge connectivity N > 4.
We will show how tau(G) is related to the discrete Laplacian and present an effective Matlab program computing tau(G). We will present several families of graphs with equal edge lengths and having tau constants asymptotically approaches to length(G)/108.
We will also present an application by giving the relation between tau(G) and
an another constant that was used in one of S. Zhang's papers.
THURSDAY, November 2, 2006
VIGRE-Algebraic Geometry
2:00pm, Room 410
Wavelets and Splines
2:30pm, Room 524
No Meeting this week
VIGRE - Quantum Mechanics
3:30pm, Room 410
FRIDAY, November 3, 2006
Probability Theory
2:30pm, Room 323
Speaker: DongHoon Shin, University of Georgia
Title of talk: Optimal Adaptive LQG Control
Geometry
2:30pm, Room 410
Speaker: David Shea Vick, University of Pennsylvania
Title of talk: The Converse to the Four-Vertex
Theorem
Abstract: The Four-Vertex Theorem is one of the earliest results
in global differential geometry. It states that the curvature function of a
simple closed curve in the plane must have four "vertices", that is,
at least two local maxima and two local minima. The converse to the Four-Vertex
Theorem says that if \kappa is a continuous function on the circle S^1 with
at least two local maxima and two local minima, then \kappa can be realized
as the curvature function of a simple closed curve in the plane. A version of
the Four-Vertex Theorem was first proved in 1909, by Syamadus Mukhopadhyaya.
In 2005 Bjorn Dahlberg published the first proof of the converse in its full
generality. In this talk we will survey of the history of this famous theorem,
and discuss the ideas that go into the proof of its converse.
VIGRE-Algebra
2:30pm, Room 304