- You are here:
- GT Home
- Home
- News & Events

Series: Other Talks

In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.

Series: Research Horizons Seminar

(joint work with Csaba Biro, Dave Howard, Mitch Keller and Stephen Young. Biro and Young finished their Ph.D.'s at Georgia Tech in 2008. Howard and Keller will graduate in spring 2010)

Motivated by questions in algebra involving what is called "Stanley" depth, the following combinatorial question was posed to us by Herzog: Given a positive integer n, can you partition the family of all non-empty subsets of {1, 2, ..., n} into intervals, all of the form [A, B] where |B| is at least n/2. We answered this question in the affirmative by first embedding it in a stronger result and then finding two elegant proofs. In this talk, which will be entirely self-contained, I will give both proofs. The paper resulting from this research will appear in the Journal of Combinatorial Theory, Series A.

Series: ACO Student Seminar

I will describe a simple scheme for generating a valid inequality for a
stochastic integer programs from a given valid inequality for its
deterministic counterpart. Applications to stochastic lot-sizing problems
will be discussed. This is joint work with Yongpei Guan and George Nemhauser
and is based on the following two papers
(1) Y. Guan, S. Ahmed and G.L. Nemhauser. "Cutting planes for multi-stage
stochastic integer programs," Operations Research, vol.57, pp.287-298, 2009
(2)
Y. Guan, S. Ahmed and G. L. Nemhauser. "Sequential pairing of mixed integer
inequalities," Discrete Optimization, vol.4, pp.21-39, 2007
This is a joint DOS/ACO seminar.

Series: PDE Seminar

Many problems in Geometry, Physics and Biology are described by nonlinear partial differential equations of second order or four order. In this talk I shall mainly address the blow-up phenomenon in a class of fourth order equations from conformal geometry and some Liouville systems from Physics and Ecology. There are some challenging open problems related to these equations and I will report the recent progress on these problems in my joint works with Gilbert Weinstein and Chang-shou Lin.

Series: Geometry Topology Seminar

A closed hyperbolic 3-manifold $M$ determines a fundamental classin the algebraic K-group $K_3^{ind}(C)$. There is a regulator map$K_3^{ind}(C)\to C/4\Pi^2Z$, which evaluated on the fundamental classrecovers the volume and Chern-Simons invariant of $M$. The definition of theK-groups are very abstract, and one is interested in more concrete models.The extended Bloch is such a model. It is isomorphic to $K_3^{ind}(C)$ andhas several interesting properties: Elements are easy to produce; thefundamental class of a hyperbolic manifold can be constructed explicitly;the regulator is given explicitly in terms of a polylogarithm.

Series: Other Talks

In this talk Professor Tapia identifies elementary mathematical frameworks for the study of popular drag racing beliefs. In this manner some myths are validated while others are destroyed. Tapia will explain why dragster acceleration is greater than the acceleration due to gravity, an age old inconsistency. His "Fundamental Theorem of Drag Racing" will be presented. The first part of the talk will be a historical account of the development of drag racing and will include several lively videos.

Series: Geometry Topology Seminar

After reviewing a few techniques from the theory of confoliation in dimension three we will discuss some generalizations and certain obstructions in extending these techniques to higher dimensions. We also will try to discuss a few questions regarding higher dimensional confoliations.

Series: CDSNS Colloquium

We study the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain, which, roughly speaking, consists of two fixed domains joined by a thin channel. We analyze the behavior of the stationary solutions (solutions of the elliptic problem), their local unstable manifold and the attractor of the equation as the width of the connecting channel goes to zero.

Series: Combinatorics Seminar

We consider the #P complete problem of counting the number of independent
sets in a given graph. Our interest is in understanding the effectiveness of
the popular Belief Propagation (BP) heuristic. BP is a simple and iterative
algorithm that is known to have at least one fixed point. Each fixed point
corresponds to a stationary point of the Bethe free energy (introduced by
Yedidia, Freeman and Weiss (2004) in recognition of Hans Bethe's earlier
work (1935)). The evaluation of the Bethe Free Energy at such a stationary
point (or BP fixed point) leads to the Bethe approximation to the number of
independent sets of the given graph. In general BP is not known to converge
nor is an efficient, convergent procedure for finding stationary points of
the Bethe free energy known. Further, effectiveness of Bethe approximation
is not well understood.
As the first result of this paper, we propose a BP-like algorithm that
always converges to a BP fixed point for any graph. Further, it finds an \epsilon
approximate fixed point in poly(n, 2^d, 1/\epsilon) iterations for a graph of n
nodes with max-degree d. As the next step, we study the quality of this
approximation. Using the recently developed 'loop series' approach by
Chertkov and Chernyak, we establish that for any graph of n nodes with
max-degree d and girth larger than 8d log n, the multiplicative error decays
as 1 + O(n^-\gamma) for some \gamma > 0. This provides a deterministic counting
algorithm that leads to strictly different results compared to a recent
result of Weitz (2006). Finally as a consequence of our results, we prove
that the Bethe approximation is exceedingly good for a random 3-regular
graph conditioned on the Shortest Cycle Cover Conjecture of Alon and Tarsi
(1985) being true.
(Joint work with Venkat Chandrasekaran, Michael Chertkov, David Gamarnik and
Devavrat Shah)

Friday, September 11, 2009 - 15:00 ,
Location: Skiles 269 ,
John Etnyre ,
Georgia Tech ,
Organizer:

We will discuss how to put a hyperbolic structure on various
surface and 3-manifolds. We will being by discussing isometries of hyperbolic space in
dimension 2 and 3. Using our understanding of these isometries we will explicitly
construct hyperbolic structures on all close surfaces of genus greater than one and a
complete finite volume hyperbolic structure on the punctured torus. We will then consider
the three dimensional case where we will concentrate on putting hyperbolic structures on
knot complements. (Note: this is a 2 hr seminar)