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Mathematics & Statistics
Colloquium Archive

# Colloquia — Spring 2020

## Friday, April 24, 2020

Title
Speaker

Time
Place

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

Abstract

TBA

Title
Speaker

Time
Place

TBA
Diego Ricciotti

3:00pm–4:00pm
CMC 130
Thomas Bieske

Abstract

TBA

## Friday, March 27, 2020

Title
Speaker

Time
Place

Object Oriented Data Analysis
J. S. Marron
Statistics and Operations Research
University of North Carolina
3:00pm–4:00pm
CMC 130
K. Ramachandran

Abstract

The rapid change in computational capabilities has made Big Data a major modern statistical challenge. Less well understood is the rise of Complex Data as a perhaps greater challenge. Object Oriented Data Analysis (OODA) is a framework for addressing this, in particular providing a general approach to the definition, representation, visualization and analysis of Complex Data. The notion of OODA generally guides data analysis, through providing a useful terminology for interdisciplinary discussion of the many choices typically needed in modern complex data analyses. The main ideas are illustrated via a survey of a number of approaches which integrate differential geometry and Bayesian statistics, yielding powerful image segmentations.

## Friday, March 13, 2020

Title
Speaker

Time
Place

TBA
Danielle Bassett
Department of Bioengineering
University of Pennsylvania
3:00pm–4:00pm
CMC 130
Nagle Lecture Series Committee

Abstract

TBA

Title
Speaker

Time
Place

A deformation for the Kadomtsev–Petviashvili (KP) hierarchy
Baofeng Feng
University of Texas Rio Grande Valley
2:00pm–3:00pm
CMC 130
Wen-Xiu Ma

Abstract

It is observed that some bilinear equations to soliton equations, such as the Camassa-Holm (CH), modified CH equations and even the nonlinear Schrödinger equation and Sasa-Satsuma equation in deriving dark soliton solutions, cannot be obtained within the framework of the KP theory developed by Kyoto school. In this talk, by introducing one or more nonzero constant in pseudo-differential operators including the dressing operator, we attempt to give a modification of the KP theory. We will give the Lax equation, the Sato equation and the corresponding tau functions. In addition, we will develop a family of bilinear equations which include the onese for the CH and mCH equations.

## Friday, February 28, 2020

Title
Speaker

Time
Place

TBA
Jozef H. Przytycki
George Washington University
3:00pm–4:00pm
CMC 130

Abstract

TBA

## Friday, February 14, 2020

Title
Speaker

Time
Place

Integrability and limit cycles in polynomial systems of ODEs
Valery Romanovsky
University of Maribor
Slovenia
3:00pm–4:00pm
CMC 130
Yuncheng You

Abstract

We discuss two problems related to the theory of polynomial plane differential systems, that is, systems of the form $\tag{1} \frac{dx}{dt}=P_{n}(x,y), \ \ \ \frac{dy}{dt}=Q_{n}(x,y),$ where $$P_{n}(x,y), Q_{n}(x,y)$$ are polynomials of degree $$n$$, $$x$$ and $$y$$ are real unknown functions.

The first one is the problem of local integrability, that is, the problem of finding local analytic integrals in a neighborhood of singular points of system (1). We present a computational approach to find integrable systems within given parametric families of systems and describe some mechanisms of integrability.

The second problem is called the cyclicity problem, or the local 16th Hilbert problem, and is related to the estimation of the number of limit cycles arising in system (1) after perturbations of integrable systems. The approach is algorithmic and is based on algorithms of computational commutative algebra relying on the Groebner bases theory.

Title
Speaker

Time
Place

TBA
3:00pm–4:00pm
CMC 130

Abstract

TBA

## Friday, January 31, 2020

Title
Speaker

Time
Place

TBA
Mihai Stoiciu
Williams College
3:00pm–4:00pm
CMC 130
Razvan Teodorescu

Abstract

TBA

## Friday, January 24, 2020

Title
Speaker

Time
Place

Images of arboreal Galois representations
Andrea Ferraguti
ICMAT
3:00pm–4:00pm
CMC 130
Giacomo Micheli

Abstract

Arboreal Galois representations are a central topic in modern arithmetic dynamics. In this talk, we will briefly review their construction, and then we will focus on arboreal representations attached to quadratic polynomials. First, we will explain a new simple but extremely powerful lemma that relates the dynamic of the polynomial to the image of the associated arboreal representation. Next, we will give an overview of several applications of this lemma: how to recover known results with one-line proofs, how to construct representations with maximal image, and how to prove that many subgroups of automorphisms of the infinite binary tree cannot arise as images of arboreal representations over global fields. This is joint work with Carlo Pagano and Daniele Casazza.

## Tuesday, January 14, 2020

Title
Speaker

Time
Place
In one complex variable, approximation theory is well developed. For example, the celebrated theorem of Mergelyan states that if $$K$$ is a compact subset of the complex plane with connected complement, then every continuous function on $$K$$ which is holomorphic on its interior can be uniformly approximated on $$K$$ by polynomials. In this talk, we will discuss what happens in several complex variables, where the situation is far from being understood. In particular, I will present some new Mergelyan-type theorems for products of planar compact sets and graphs of functions. (Joint work with J. Falco, P. Gauthier and V. Nestoridis.