Seminars and Colloquia Schedule

On the derived Witt groups of schemes

Series
Algebra Seminar
Time
Monday, December 3, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeremy Jacobson – University of Georgia
The Witt group of a scheme is a globalization to schemes of the classical Witt group of a field. It is a part of a cohomology theory for schemes called the derived Witt groups. In this talk, we introduce two problems about the derived Witt groups, the Gersten conjecture and a finite generation question for arithmetic schemes, and explain recent progress on them.

Non equilibrium steady state for a simple model of electric conduction

Series
CDSNS Colloquium
Time
Monday, December 3, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Federico Bonretto – Georgia Tech
A very simple model for electric conduction consists of N particles movingin a periodic array of scatterers under the influence of an electric field and of aGaussian thermostat that keeps their energy fixed. I will present analytic result for the behaviourof the steady state of the system at small electric field, where the velocity distribution becomesindependent of the geometry of the scatterers, and at large N, where the system can bedescribed by a linear Boltzmann type equation.

Fluctuation of the Optimal Alignment Score via Monte Carlo

Series
Research Horizons Seminar
Time
Wednesday, December 5, 2012 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Heinrich Matzinger – Georgia Tech, School of Math
The question of the asymptotic order of magnitude of the fluctuation of the Optimal Alignment Score of two random sequences of length n has been open for decades. We prove a relation between that order and the limit of the rescaled optimal alignment score considered as a function of the substitution matrix. This allows us to determine the asymptotic order of the fluctuation for many realistic situations up to a high confidence level.

Probabilities of all real zeros for random polynomials

Series
Stochastics Seminar
Time
Thursday, December 6, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Wenbo Li – University of Delaware
There is a long history on the study of zeros of random polynomials whose coefficients are independent, identically distributed, non-degenerate random variables. We will first provide an overview on zeros of random functions and then show exact and/or asymptotic bounds on probabilities that all zeros of a random polynomial are real under various distributions. The talk is accessible to undergraduate and graduate students in any areas of mathematics.

A few Ways to Destroy Entropic Chaoticity

Series
Math Physics Seminar
Time
Thursday, December 6, 2012 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Amit Einav – University of Cambridge
In this talk we will discuss the definition of chaoticity and entropic chaoticity, as well as the background that led us to define these quantities, mainly Kac's model and the Boltzmann equation. We will then proceed to investigate the fine balance required for entropic chaoticity by exploring situations where chaoticity is valid, but not entropic chaoticity. We will give a general method to construct such states as well as two explicit example, one of which is quite surprising.

Slow Mixing for the Hard-Core Model on Z^2

Series
ACO Student Seminar
Time
Friday, December 7, 2012 - 13:10 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dana Randall – College of Computing, Georgia Tech
The hard-core model has attracted much attention across several disciplines, representing lattice gases in statistical physics and independent sets in discrete mathematics and computer science. On finite graphs, we are given a parameter \lambda, and an independent set I arises with probability proportional to \lambda^{|I|}. We are interested in determining the mixing time of local Markov chains that add or remove a small number of vertices in each step. On finite regions of Z^2 it is conjectured that there is a phase transition at some critical point \lambda_c that is approximately 3.79. It is known that local chains are rapidly mixing when \lambda < 2.3882. We give complementary results showing that local chains will mix slowly when \lambda > 5.3646 on regions with periodic (toroidal) boundary conditions and when \lambda > 7.1031 with non-periodic (free) boundary conditions. The proofs use a combinatorial characterization of configurations based on the presence or absence of fault lines and an enumeration of a new class of self-avoiding walks called taxi walks. (Joint work with Antonio Blanca, David Galvin and Prasad Tetali)

The k-core thresholds in random graphs and hypergraphs

Series
Combinatorics Seminar
Time
Friday, December 7, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Omar Abuzzahab – University of Pennsylvania, Philadelphia
The k-core of a (hyper)graph is the unique subgraph where all vertices have degree at least k and which is the maximal induced subgraph with this property. It provides one measure of how dense a graph is; a sparse graph will tend to have a k-core which is smaller in size compared to a dense graph. Likewise a sparse graph will have an empty k-core for more values of k. I will survey the results on the random k-core of various random graph models. A common feature is how the size of the k-core undergoes a phase transition as the density parameter passes a critical threshold. I will also describe how these results are related to a class of related problems that initially don't appear to involve random graphs. Among these is an interesting problem arising from probabilistic number theory where the random hypergraph model has vertex degrees that are "non-homogeneous"---some vertices have larger expected degree than others.

The curve complex of a surface

Series
School of Mathematics Colloquium
Time
Friday, December 7, 2012 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joan Birman – Columbia University

Kickoff of the Tech Topology Conference from December 7-9, 2012.

This will be a Colloquium talk, aimed at a general audience. The topic is the curve complex, introduced by Harvey in 1974. It's a simplicial complex, and was introduced as a tool to study mapping class groups of surfaces. I will discuss recent joint work with Bill Menasco about new local pathology in the curve complex, namely that its geodesics can have dead ends and even double dead ends.