# Colloquia

## Steve Butler

An introduction to the normalized Laplacian matrix

Date: 4/18/2018

Time: 2:30PM-3:30PM

Place: 315 Armstrong Hall

**Abstract:** Spectral graph theory looks at the interplay between the structure of graphs and the eigenvalues associated with some particular matrix. Different matrices give different information, so it is important to understand how the different matrices behave, and which matrix to use for which types of problems. We will give an introduction to one of the lesser known matrices, the normalized Laplacian matrix, which has ties to the probability transition matrix of a random walk. This matrix is useful in many settings, particularly for graphs which are not regular, but also has some strange quirks.

All are welcome.

## Ilie Ugarcovici

The structure and spectrum of odometer systems

Date: 3/2/2018

Time: 3:00PM-4:00PM

Place: 315 Armstrong Hall

**Abstract:** Odometer systems (or adding machines) are a well studied class of examples in the classical theory of measurable and topological dynamical systems. They can be viewed measure theoretically as cutting and stacking transformations of the unit interval. Alternatively, they can be viewed algebraically as a Z-action on an inverse limit space of increasing quotient groups of Z. Recently, there have been attempts to understand odometer systems over an arbitrary finitely generated and residually finite group. In this talk I will discuss some classification results for odometer systems defined over semidirect product groups, in particular the Heisenberg group. This is joint work with S. Orfanos (DePaul) and A. Sahin (Wright State).

All are welcome.

## Henrik Holm

Prime ideals in commutative and non-commutative rings

Date: 3/9/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

Abstract:Prime ideals are important in commutative algebra (e.g. localization and Krull dimension), in algebraic geometry (e.g. affine schemes),

and in number theory (e.g factorization in Dedekind domains). This talk --which is about prime ideals, their generalizations, and their

uses -- has three parts: In the first part, I will talk about certain aspects of prime ideals in commutative rings. In the second part, I will explain

elements of Kanda's recently developed theory of (so-called) atoms. The notion of atoms is a useful and interesting generalization of prime ideals

to non-commutative rings (and to abelian categories). In the third part, I will explain work in progress, joint with R. H. Bak, on how to actually

compute/determine the atoms for certain types of non-commutative rings.

All are welcome.

## Naoki Taniguchi

Almost Gorenstein rings

Date: 3/6/2018

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

All are welcome.

## Ihsan Topaloglu

Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion

Date: 2/23/2018

Time: 3:00PM-4:00PM

Place: 422 Armstrong Hall

**Abstract:** In this talk I will consider an aggregation model with nonlinear diffusion in domains with boundaries and present on the zero diffusion limit of its solutions. This model is used in describing phenomena related swarming and social aggregations, such as biological swarms and pattern formation, granular media, and self-assembly of nanoparticles. Using the formulation of the aggregation model as a gradient flow on spaces of probability measures equipped with the Wasserstein metric, I will present the convergence of weak solutions for fixed times, as well as the convergence of energy minimizers in this limit. I will also present numerical simulations that support the analytical results and demonstrates that adding small nonlinear diffusion approximates, as well as regularizes, the plain aggregation model. This is a joint project with Razvan Fetacau and Mitchell Kovacic.

All are welcome.

## Jai Laxmi Talks

We have a special guest this week from the Indian Institute of Technology,Bombay.

**Talk #1:**

Date: 11/14/2017

Time: 4:00PM-5:00PM

Place: 313 Armstrong Hall

**Talk #2:**

Date: 11/15/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Talk #3:**

Date: 11/16/2017

Time: 4:00PM-5:00PM

Place: 313 Armstrong Hall

Abstract: View

All are welcome.

## Matt Insall

By Renaming If Necessary

Date: 11/10/2017

Time: 3:00PM-4:00PM

Place: 422 Armstrong Hall

**Abstract:**We explain here how renaming can be insufficient. In particular, we

show that in many rings, there exists a function that is not a conjugate

of some polynomial function. The only tools needed are from typical

undergraduate Mathematics courses, such as Linear Algebra. If time

permits, we will show some relevant computations in MathCAD, and in

the Universal Algebra Calculator. This talk is intended to be accessible

to undergraduate students.

All are welcome.

## Thomas Polstra

When are two rings similar?

Date: 11/7/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract:** Inspired by results of Samuel, Hironaka, Cutkosky and Srinivasan, and others which give criteria for rings which are quotients of a common power series ring to be isomorphic, it is natural to investigate when two rings, which are the quotient of a common power series ring, are ”similar.” In this talk we will discuss recent collaboration between the speaker and Ilya Smirnov which investigates this problem in rings of prime characteristic.

All are welcome.

## Roger Wiegand

Rigid Ideals in Complete Intersection Domains

Date: 10/24/2017

Time: 4:00PM-5:00PM

Place: 315 Armstrong Hall

**Abstract:** View

All are welcome.

## Misha Feldman

Short-time existence of smooth solutions for semigeostrophic system with variable Coriolis parameter.

Date: 10/12/2017

Time: 3:45PM-4:45PM

Place: 315 Armstrong Hall

**Abstract:** The semigeostrophic (SG) system is a model of large scale atmosphere/ocean flows. Previous results were obtained for the SG system with constant Coriolis parameter, by rewriting the problem in the "dual variables" and using Monge-Kantorovich mass transport techniques. A more physically realistic SG model has variable Coriolis parameter. Dual space is not available in this case. We work directly in the original "physical" coordinates, and show existence of smooth solutions for short time. This is a joint work with J. Cheng and M. Cullen.

All are welcome.

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