Seminars and Colloquia by Series

Similarity results for operators of class C_0

Series
Analysis Seminar
Time
Wednesday, September 5, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Raphael Clouatre – Indiana University
The classification theorem for a C_0 operator describes its quasisimilarity class by means of its Jordan model. The purpose of this talk will be to investigate when the relation between the operator and its model can be improved to similarity. More precisely, when the minimal function of the operator T can be written as a product of inner functions satisfying the so-called (generalized) Carleson condition, we give some natural operator theoretic assumptions on T that guarantee similarity.

Circle Orders

Series
Research Horizons Seminar
Time
Wednesday, September 5, 2012 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
William Trotter – School of Mathematics, Georgia Tech
We survey research spanning more than 20 years on what starts out to be a very simple problem: Representing a poset as the inclusion order of circular disks in the plane. More generally, we can speak of spherical orders, i.e., posets which are inclusion orders of balls in R^d for some d. Surprising enough, there are finite posets which are not sphere orders. Quite recently, some elegant results have been obtained for circle orders, lending more interest to the many open problems that remain.

On the solutions of a modified two-component Camassa-Holm shallow water system

Series
PDE Seminar
Time
Tuesday, September 4, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Zhaoyang Yin – Sun Yat-sen University, China
In this talk, we consider the Cauchy problem of a modified two-component Camassa-Holm shallow water system. We first establish local well-possedness of the Cauchy problem of the system. Then we present several blow-up results of strong solutions to the system. Moreover, we show the existence of global weak solutions to the system. Finally, we address global conservative solutions to the system. This talk is based on several joint works with C. Guan, K. H. Karlsen, K. Yan and W. Tan.

Generic Chaining

Series
High-Dimensional Phenomena in Statistics and Machine Learning Seminar
Time
Tuesday, September 4, 2012 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skyles 005
Speaker
William Mantzel – School of Electrical and Computer Engineering, Georgia Tech
Recap of generic chaining from last time and more discussion about it. Then, the lower Dudley bound (Theorem 2.1.1) and the Bernoulli upper bound (4.1.2) and statement of the Bernoulli conjecture (lower bound) will be covered from The Generic Chaining book.

How to find counterfeit coins? An algorithmic version

Series
Combinatorics Seminar
Time
Friday, August 31, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeong Han Kim – Professor, Yonsei University, South Korea
In this talk, we consider a well-known combinatorial search problem. Suppose that there are n identical looking coins and some of them are counterfeit. The weights of all authentic coins are the same and known a priori. The weights of counterfeit coins vary but different from the weight of an authentic coin. Without loss of generality, we may assume the weight of authentic coins is 0. The problem is to find all counterfeit coins by weighing (queries) sets of coins on a spring scale. Finding the optimal number of queries is difficult even when there are only 2 counterfeit coins. We introduce a polynomial time randomized algorithm to find all counterfeit coins when the number of them is known to be at most m \geq 2 and the weight w(c) of each counterfeit coin c satisfies \alpha \leq |w(c)| \leq \beta for fixed constants \alpha, \beta > 0. The query complexity of the algorithm is O(\frac{m \log n }{\log m}), which is optimal up to a constant factor. The algorithm uses, in part, random walks. The algorithm may be generalized to find all edges of a hidden weighted graph using a similar type of queries. This graph finding algorithm has various applications including DNA sequencing.

Uchiyama's lemma and the John-Nirenberg inequality

Series
Analysis Seminar
Time
Wednesday, August 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg Knese – University of Alabama
Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1. Some difficulties of the method and possible future directions to take it will be suggested at the end.

Train track and automorphisms of free groups

Series
Geometry Topology Student Seminar
Time
Wednesday, August 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyunshik Shin – School of Mathematics, Georgia Tech
We will discuss the basics of automorphisms of free groups and train track structure. We will define the growth rate which is a topological entropy of the train track map.

Asymptotic Hilbert series

Series
Algebra Seminar
Time
Monday, August 27, 2012 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gregory G. Smith – Queens University
How does one study the asymptotic properties for the Hilbert series of a module? In this talk, we will examine the function which sends the numerator of the rational function representing the Hilbert series of a module to that of its r-th Veronese submodule. As r tends to infinity, the behaviour of this function depends only on the multidegree of the module and the underlying multigraded polynomial ring. More importantly, we will give a polyhedral description for the asymptotic polynomial and show that the coefficients are log-concave.

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