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Colloquium Archive

# Colloquia — Spring 2015

## Friday, April 10, 2015

Title
Speaker

Time
Place

TBA
Steve Wang
Carleton University,
3:00pm-4:00pm
CMC 130
Xiang-dong Hou

Abstract

TBA

## Friday, March 27, 2015

Title
Speaker

Time
Place

TBA
Greg Knese
Washington University
3:00pm-4:00pm
CMC 130
Dima Khavinson

Abstract

TBA

## Friday, March 20, 2015

Title
Speaker

Time
Place

TBA
Sam Nelson
Claremont McKenna College, CA
3:00pm-4:00pm
CMC 130

Abstract

TBA

## Friday, March 13, 2015

Title
Speaker

Time
Place

TBA
Carina Curto
Pennsylvania State University
3:00pm-4:00pm
CMC 130
Nataša Jonoska

Abstract

TBA

## Monday, March 9, 2015

Title
Speaker

Time
Place

TBA
Pennsylvania State University
TBA
TBA
Nataša Jonoska

Abstract

TBA

## Friday, February 27, 2015

Title

Speaker

Time
Place

Some counterexamples to long standing problems in harmonic analysis and blow up estimates in PD Inequalities.
Alexander Volberg
Michigan State University
3:00pm-4:00pm
CMC 130
Arthur Danielyan

Abstract

PDE and Partial Differential Inequalities proved to be very helpful recently in constructing counterexamples to some long-standing conjectures by Hunt, Muckenhoupt and Wheeden. We will show how these highly non-linear PDE appear and help to solve certain harmonic analysis problems.

## Friday, February 20, 2015

Title
Speaker

Time
Place

TBA
Alexander Tovbis
University of Central Florida
3:00pm-4:00pm
CMC 130
Seung-Yeop Lee

Abstract

TBA

## Friday, February 13, 2015

Title
Speaker

Time
Place

Random Matrices and Potential Theory
Thomas Bloom
University of Toronto
3:00pm-4:00pm
CMC 130
Vilmos Totik

Abstract

I will introduce the Gaussian Unitary Ensemble and other unitary ensembles of random matrices.

I will discuss aspects of these ensembles which can be studied and established via potential theory.

Specifically,I will deal with the convergence of the empirical measure of the eigenvalues and large deviation principles.

## Tuesday, February 10, 2015

Title
Speaker

Time
Place

TBA
Jozef Przytycki
George Washington University
3:30pm-4:30pm
ISA 3050

Abstract

TBA

## Friday, February 6, 2015

Title
Speaker

Time
Place

Pattern formation and bifurcations in reaction-diffusion-advection ecological models
Junping Shi
College of William and Mary
Williamsburg, VA
3:00pm-4:00pm
CMC 130
Yuncheng You

Abstract

Spatial-temporal patterns appear often in historical ecosystem data, and the cause of the patterns can be attributed to various internal or external forces. We demonstrate that in spatial ecological models, spatial-temporal patterns can arise as a result of self-organization of the ecosystem. By using bifurcation theory, we show that the spatial-temporal patterns are generated with the effect of diffusion, advection, chemotaxis or time delay.

## Friday, January 30, 2015

Title
Speaker

Time
Place

Combining Riesz bases
Shahaf Nitzan
Kent State University
4:00pm-5:00pm
CMC 130
Catherine Bénéteau

Abstract

Orthonormal bases (ONB) are used throughout mathematics and its applications. However, in many settings such bases are not easy to come by. For example, it is known that even the union of as few as two intervals may not admit an ONB of exponentials. In cases where there is no ONB, the next best option is a Riesz basis (i.e. the image of an ONB under a bounded invertible operator).

In this talk I will discuss the following question: Does every finite union of rectangles in $$R^d$$, with edges parallel to the axes, admit a Riesz basis of exponentials? In particular, does every finite union of intervals in $$R$$ admit such a basis?

This is joint work with Gady Kozma.

Title
Speaker

Time
Place

Mathematics in Cryptography: Today's Applications and Tomorrow's Foundations
Rainer Steinwandt
Florida Atlantic University
3:00pm-4:00pm
CMC 130
Brian Curtin

Abstract

The first part of the talk will show how mathematical techniques are applied in the design of modern cryptographic protocols. Taking the task of establishing a secret key among $$n\ge2$$ users over an insecure network as example, we discuss how computational assumptions enable the derivation of an efficient solution with strong provable guarantees.

Regrettably, some of the most common assumptions needed for today's cryptographic solutions are no longer justifiable in a so-called post-quantum scenario. In particular, popular constructions involving elliptic curves are not available in this setting. Post-quantum cryptography is of interest when cryptographic solutions are expected to guarantee security for many years. The cryptographic community is currently trying to identify mathematical platforms for efficient post-quantum solutions of basic cryptographic tasks like public-key encryption or digital signatures. The second part of the talk will discuss some of the current approaches, including in particular attempts that invoke tools from group theory.

## Friday, January 23, 2015

Title
Speaker

Time
Place

Self-similar groups and expanding graphs
Ievgen Bondarenko
Kyiv National University
3:00pm-4:00pm
CMC 130
Dmytro Savchuk

Abstract

Expanding graphs are highly connected sparse graphs which have numerous applications in mathematics and theoretical computer science. Reingold, Vadhan, and Wigderson (2002) discovered a simple combinatorial construction of expanding graphs. This construction was based on the new operation on regular graphs - the zig-zag product, which is closely related to the replacement product of graphs.

In this talk I will describe how to model iterated replacement product and zig-zag product of graphs by finite automata. Also I will explain a simple construction of self-similar groups whose action graphs produce a family of expanding graphs.

Title
Speaker

Time
Place