USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

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Serguei Denisov

University of Wisconsin-Madison

3:00pm-4:00pm

CMC 130

E. A. Rakhmanov

**Abstract**

TBA

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TBA

Abdenacer Makhlouf

Université de Haute Alsace

3:00pm-4:00pm

CMC 130

Mohamed Elhamdadi

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TBA

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Yukio Matsumoto

University of Tokyo

3:00pm-4:00pm

CMC 130

Masahiko Saito

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TBA

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Karen Keene

North Carolina State

3:00pm-4:00pm

CMC 130

Milé Krajčevski

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Michael A. Högele

Universidad de Los Andes

Bogotá, Colombia

3:00pm-4:00pm

CMC 130

Yuncheng You

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TBA

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Keqin Feng

Tsinghua University

Beijing, China

3:00pm-4:00pm

CMC 130

Xiang-dong Hou

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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 \(O\).

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Constanze Liaw

Baylor University

3:00pm-4:00pm

CMC 130

Alan Sola

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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 eects of surface tension are neglected wefind 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.

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Thomas Banchoff

Brown University

3:00pm-4:00pm

CMC 130

Milé Krajčevski

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TBA

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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 \(\Bbb Z_p\times \Bbb Z_p\).

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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.

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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.

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Local Gaussian process approximation for large computer experiments

Robert B. Gramacy

Booth School of Business

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.

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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.

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On the Complexity of Conjugacy Problem in certain Metabelian Groups

Delaram Kahrobaei

CUNY Graduate Center

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.

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Random Topology and Random Knots

Moshe Cohen

Technion — Israel Institute of Technology

2:00pm-3:00pm

CMC 130

Mohamed Elhamdadi

**Abstract**

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?

I will present some topological applications of the probabilistic method: random walks on the Cayley graph of a group, used for example by Nathan Dunfield and William Thurston to construct random 3-manifolds; random simplicial complexes that can be used to model large data sets; and random physical walks in three-space and the knotting phenomena that occur, with applications ranging from DNA and proteins in molecular biology to polymers in chemistry.