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Mathematics & Statistics
Colloquium Archive

# Colloquia — Spring 2016

Title
Speaker

Time
Place

TBA
Serguei Denisov
3:00pm-4:00pm
CMC 130
E. A. Rakhmanov

Abstract

TBA

## Friday, April 29, 2016

Title
Speaker

Time
Place

TBA
Abdenacer Makhlouf
Université de Haute Alsace
3:00pm-4:00pm
CMC 130

Abstract

TBA

## Friday, April 22, 2016

Title
Speaker

Time
Place

TBA
Yukio Matsumoto
University of Tokyo
3:00pm-4:00pm
CMC 130
Masahiko Saito

Abstract

TBA

## Friday, April 15, 2016

Title
Speaker

Time
Place

TBA
Karen Keene
North Carolina State
3:00pm-4:00pm
CMC 130
Milé Krajčevski

Abstract

TBA

## Friday, April 8, 2016

Title
Speaker

Time
Place

TBA
Michael A. Högele
Bogotá, Colombia
3:00pm-4:00pm
CMC 130
Yuncheng You

Abstract

TBA

## Friday, April 1, 2016

Title
Speaker

Time
Place

TBA
Keqin Feng
Tsinghua University
Beijing, China
3:00pm-4:00pm
CMC 130
Xiang-dong Hou

Abstract

TBA

## Friday, March 25, 2016

Title
Speaker

Time
Place

Polytopes of Stochastic Tensors
Fuzhen Zhang
Nova Southeastern University
Fort Lauderdale
3:00pm-4:00pm
CMC 130
Wen-Xiu Ma

Abstract

A square matrix is doubly stochastic if its entries are all nonnegative and each row and column sum is 1. A celebrated result known as Birkhoff's theorem about doubly stochastic matrices states that an $$n\times n$$ matrix is doubly stochastic if and only if it is a convex combination of some $$n\times n$$ permutation matrices (a.k.a. Birkhoff polytope).

We study the counterpart of the Birkhoff's theorem for higher dimensions. An $$n\times n\times n$$ stochastic tensor is a nonnegative array (hypermatrix) in which every sum over one index is 1. We study the polytope ($$O$$) of all these tensors, the convex set ($$L$$) of all tensors with some positive diagonals, and the polytope ($$T$$) generated by the permutation tensors. We show that $$L$$ is almost the same as $$O$$ except for some boundary points. We also present an upper bound for the number of vertices of $$O$$.

## Friday, March 11, 2016

Title
Speaker

Time
Place

TBA
Constanze Liaw
Baylor University
3:00pm-4:00pm
CMC 130
Alan Sola

Abstract

TBA

## Friday, February 26, 2016

Title

Speaker

Time
Place

Cavitation of spherical bubbles with surface tension and viscosity and connection with FRW cosmological equations
Stefan C. Mancas
Embry-Riddle Aeronautical University
3:00pm-4:00pm
CMC 130
Razvan Teodorescu

Abstract

In this talk an analysis of the Rayleigh-Plesset (RP) equation for a three dimensional vacuous bubble in water is presented. When the e ects of surface tension are neglected we find the radius and time of the evolution of the bubble as parametric closed-form solutions in terms of hypergeometric functions. By including capillarity we show the connection between RP equation and Abel's equation, and we present parametric rational Weierstrass periodic solutions for nonzero surface tension. When viscosity is present we present only numerical solutions. We also show the connection between the RP equation and Einstein's field equations for spatially curved FRW cosmology.

Title
Speaker

Time
Place

TBA
Thomas Banchoff
Brown University
3:00pm-4:00pm
CMC 130
Milé Krajčevski

Abstract

TBA

## Friday, February 12, 2016

Title
Speaker

Time
Place

Tiling and spectral are equivalent in $$\mathbb{Z}_p^2$$
Azita Mayeli
QCC and the Graduate Center, CUNY
3:00pm-4:00pm
CMC 130
Arthur Danielyan

Abstract

The equivalence relation between tiling and spectral property of a set has its root in the Fuglede Conjecture a.k.a. Spectral Set Conjecture in $$\Bbb R^d$$, $$d\geq 1$$. In 1974, Fuglede stated that a bounded Lebesgue measurable set $$\Omega\subset\Bbb R^d$$, with positive and finite measure, tiles $$\Bbb R^d$$ by its translations if and only if the Hilbert space $$L^2(\Omega)$$ possesses an orthogonal basis of exponentials. A variety of results were proved for establishing connection between tiling and spectral property for some special cases of $$\Omega$$. However, the conjecture is false in general for dimensions $$3$$ and higher.

In this talk, we will define the tiling and spectral sets $$E\subseteq\Bbb Z_p\times\Bbb Z_p$$, $$p$$ prime, and show that these two properties are equivalent for $$E$$. In other words, we prove that the Fuglede Conjecture holds for $$\Bbb Z_p\times \Bbb Z_p$$.

## Friday, February 5, 2016

Title
Speaker

Time
Place

The phenomena of heavy tails in physical models including random matrices
Paul Jung
University of Alabama at Birmingham
3:00pm-4:00pm
CMC 130
Seung-Yeop Lee

Abstract

We will discuss a toy model of heavy tails and show how this does not follow central limit behavior. We will then see how this relates to models in physics including random matrices. In the random matrix setting, we equate limiting spectral distributions (LSD) to spectral measures of rooted graphs. The LSD result also includes matrices with i.i.d. entries (up to self-adjointness) having infinite second moments, but following central limit behavior. In this case, the graph is the natural numbers rooted at one, so the LSD is well-known to be the semi-circle law.

## Friday, January 29, 2016

Title
Speaker

Time
Place

Graph Polynomials motivated by Gene Assembly
Hendrik Jan Hoogeboom
University of Leiden
the Netherlands
3:00pm-4:00pm
CMC 130
Nataša Jonoska

Abstract

The interlace polynomial was discovered by Arratia, Bollobas, and Sorkin by studying DNA sequencing methods. Its definition can be traced from 4-regular graphs (the Martin polynomial), to circle graphs and finally to arbitrary graphs.

Our interest in these polynomials came from the study of ciliates, an ancient group of unicellular organisms. They have the remarkable property that their DNA is stored in two vastly different types of nuclei. The two representations of the versions of the gene can be elegantly modelled using a 4-regular graph.

We give an overview of the polynomials involved, their basic properties, and their relation to the Tutte polynomial. Joint work with Robert Brijder, Hasselt Belgium.

Title
Speaker

Time
Place

Local Gaussian process approximation for large computer experiments
Robert B. Gramacy
University of Chicago
2:00pm-3:00pm
CMC 130
Lesɫaw Skrzypek

Abstract

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the support of a Gaussian process predictor based on a local subset of the data. We further derive expressions for fast sequential updating of all needed quantities as the local designs are built-up iteratively. Then we show how independent application of our local design strategy across the elements of a vast predictive grid facilitates a trivially parallel implementation. The end result is a global predictor able to take advantage of modern multicore architectures, GPUs, and cluster computing, while at the same time allowing for a non stationary modeling feature as a bonus. We demonstrate our method on examples utilizing designs sized in the tens of thousands to over a million data points. Comparisons are made to the method of compactly supported covariances, and we present applications to computer model calibration of a radiative shock and the calculation of satellite drag.

## Friday, January 22, 2016

Title
Speaker

Time
Place

Minimal Energy and Maximal Polarization
Edward B. Saff
Vanderbilt University
3:00pm-4:00pm
CMC 130
Vilmos Totik

Abstract

The work to be discussed has its origins in research conducted at USF some twenty years ago. It concerns minimal energy configurations as well as maximal polarization (Chebyshev) configurations on manifolds, which are problems that are asymptotically related to best-packing and best-covering.

In particular, we discuss how to generate $$N$$ points on a $$d$$-dimensional manifold that have the desirable qualities of well-separation and optimal order covering radius, while asymptotically having a given distribution. Even for certain small numbers of points like $$N=5$$, optimal arrangements with regard to energy and polarization can be a challenging problem.

## Friday, January 15, 2016

Title
Speaker

Time
Place

On the Complexity of Conjugacy Problem in certain Metabelian Groups
Delaram Kahrobaei
3:00pm-4:00pm
CMC 130
Dima Savchuk

Abstract

We analyze the computational complexity of the conjugacy search problem in a certain family of metabelian groups. We prove that in general the time complexity of the conjugacy search problem for these groups is at most exponential. For a subfamily of groups we prove that the conjugacy search problem is polynomial. We also show that for some of these groups the conjugacy search problem reduces to the discrete logarithm We also provide experimental evidence which illustrates our results probabilistically. This is a joint work with Conchita Martinez and Jonathan Gryak.

Polycyclic and Metabelian groups have been proposed as platform for Cryptography by Eick and Kahrobaei some years ago. The results I am presenting will have potential applications in Cryptography. The interesting question would be whether such cryptosystems are resistant against quantum algorithms.

Title
Speaker

Time
Place
Combinatorialists use the probabilistic method to construct impossibly large graphs and study their properties. For example, how does the parameter $$p$$ of an unfair coin affect simple topological questions like the number of components?