Seminars and Colloquia by Series

One sided bump conditions and two weight boundedness of Calderon-Zygmund operators

Series
Analysis Seminar
Time
Wednesday, February 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Reznikov – Michigan State University
We consider a so-called "One sided bump conjecture", which gives asufficient condition for two weight boundedness of a Calderon-Zygmundoperator. The proof will essentially use the Corona decomposition, which isa main tool for a first proof of $A_2$ (also, $A_p$ and $A_p-A_\infty$)conjecture. We will focus on main difficulty, that does not allow to get afull proof of our one sided bump conjecture.

From microscopic to macroscopic: some consideration on a simple model for a gas in or out of equilibrium

Series
Research Horizons Seminar
Time
Wednesday, February 6, 2013 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Federico Bonetto – Georgia Tech, School of Math
The derivation of the properties of macroscopic systems (e.g. the air in a room) from the motions and interactions of their microscopic constituents is the principal goal of Statistical Mechanics. I will introduce a simplified model of a gas (the Kac model). After discussing its relation with more realistic models, I'll present some known results and possible extension.

Fractional Ginzburg-Landau equations and harmonic maps

Series
PDE Seminar
Time
Tuesday, February 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yannick Sire – Universite Paul Cezanne d'Aix-Marseille III
I will describe a joint work with Vincent Millot (Paris 7) where we investigate the singular limit of a fractional GL equation towards the so-called boundary harmonic maps.

Limiting behaviour for the theorem of Shannon-McMillan-Breiman

Series
CDSNS Colloquium
Time
Monday, February 4, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Nicolai Haydn – USC
The theorem of Shannon-McMillan-Breiman states that for every generating partition on an ergodic system, the exponential decay rate of the measure of cylinder sets equals the metric entropy almost everywhere (provided the entropy is finite). We show that the measure of cylinder sets are lognormally distributed for strongly mixing systems and infinite partitions and show that the rate of convergence is polynomial provided the fourth moment of the information function is finite. We also show that it satisfies the almost sure invariance principle. Unlike previous results by Ibragimov and others which only apply to finite partitions, here we do not require any regularity of the conditional entropy function.

The Mathematics of Dispersion for Optical Metamaterials

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 4, 2013 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Robert Lipton – LSU
Metamaterials are a new form of structured materials used to control electromagnetic waves through localized resonances. In this talk we introduce a rigorous mathematical framework for controlling localized resonances and predicting exotic behavior inside optical metamaterials. The theory is multiscale in nature and provides a rational basis for designing microstructure using multiphase nonmagnetic materials to create backward wave behavior across prescribed frequency ranges.

The Liouville connect sum and its applications

Series
Geometry Topology Seminar
Time
Monday, February 4, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Russell Avdek – USC
We introduce a new surgery operation for contact manifolds called the Liouville connect sum. This operation -- which includes Weinstein handle attachment as a special case -- is designed to study the relationship between contact topology and symplectomorphism groups established by work of Giroux and Thurston-Winkelnkemper. The Liouville connect sum is used to generalize results of Baker-Etnyre-Van Horn-Morris and Baldwin on the existence of "monodromy multiplication cobordisms" as well as results of Seidel regarding squares of symplectic Dehn twists.

Bounds on sums of graph eigenvalues

Series
Math Physics Seminar
Time
Friday, February 1, 2013 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Evans Harrell – Georgia Tech –
I'll discuss two methods for finding bounds on sums of graph eigenvalues (variously for the Laplacian, the renormalized Laplacian, or the adjacency matrix). One of these relies on a Chebyshev-type estimate of the statistics of a subsample of an ordered sequence, and the other is an adaptation of a variational argument used by P. Kröger for Neumann Laplacians. Some of the inequalities are sharp in suitable senses. This is ongoing work with J. Stubbe of EPFL

Evolution of a Random Permutation

Series
Combinatorics Seminar
Time
Friday, February 1, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Huseyin Acan – Ohio State University
A permutation of the set {1,2,...,n} is connected if there is no k < n such that the set of the first k numbers is invariant as a set under the permutation. For each permutation, there is a corresponding graph whose vertices are the letters of the permutation and whose edges correspond to the inversions in the permutation. In this way, connected permutations correspond to connected permutation graphs. We find a growth process of a random permutation in which we start with the identity permutation on a fixed set of letters and increase the number of inversions one at a time. After the m-th step of the process, we obtain a random permutation s(n,m) that is uniformly distributed over all permutations of {1,2,...,n} with m inversions. We will discuss the evolution process, the connectedness threshold for the number of inversions of s(n,m), and the sizes of the components when m is near the threshold value. This study fits into the wider framework of random graphs since it is analogous to studying phase transitions in random graphs. It is a joint work with my adviser Boris Pittel.

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