# Colloquia

## 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.

## WVU-China Graph Theory and Combinatorics Workshop

Every year, the Department of Mathematics at WVU hosts about 10 long term visitors sponsored by Chinese Scholar Council to conduct research in graph theory and combinatorics. To strengthen our collaboration with Chinese Graph Theory and Combinatorics Society, the Department of Mathematics will host a WVU-China Workshop on Graph Theory and Combinatorics on Thursday, September 14, 2017.

All are welcome and are invited to attend the workshop.

## Workshop Schedule

#### Location: Mountainlair Shenandoah Room

Time |
Speaker |
Title |
||||
---|---|---|---|---|---|---|

8:30am - 9:00am | Dr. Eddie Fuller, Chair of Mathematics, West Virginia University | Opening Remarks | ||||

9:00am - 9:50am | Xueliang Li, Nankai University | Conflict-free connections of graphs | ||||

10:00am - 10:50am | Kevin Milans, West Virginia University | First-Fit chain partitions in partially ordered sets | ||||

11:00am - 11:50am | Guanghui Wang, Shangdong University | Splitting graphs and digraphs | ||||

12:00pm - 1:30pm |
Lunch Break |
Lunch Break |
||||

1:30pm - 2:20pm | John Goldwasser, West Virginia University | Polychromatic colorings of complete graphs with respect to 1-regular and 2-regular subgraphs | ||||

2:30pm - 3:20pm | Mike Schroeder, Marshall University | Adding To and Removing From the Structure of Graph Decompositions | ||||

3:30pm - 4:20pm | Jerzy Wojciechowski, West Virginia University | General Matroids and the Almost Intersection Property | ||||

4:30pm - 5:20pm | Jiaao Li, West Virginia University | Nowhere-zero Flow Problems |

## Other Participants from China

- Professor Lingqi Zhao, College of Computer Science and Technology, Inner Mongolia University for Nationalities
- Bofeng Huo, Qinghai Normal University
- Liqiong Xu, Jimei University
- Yingzhi Tian, Xinjiang University

## Brief Introduction to the Speakers from China

#### Dr. Xueliang Li, Nankai University

- President for the Chinese Society of Combinatorics and Graph Theory
- Director of the Center for Combinatorics at Nankai University
- Dean of the School of Mathematics and Statistics, Qinghai Normal University
- Vice President of the International Academy of Mathematical Chemistry (IAMC)
- A member of editorial boards of many journals including Discrete Applied Mathematics, Graphs and Combinatorics, et al.
- President of Tianjin Society for Industrial and Applied Mathematics (TJSIAM)
- Council Member of the Chinese Mathematical Society (CMS)
- Executive Council Member of the Chinese Society for Industrial and Applied Mathematics (CSIAM)

#### Dr. Guiying Yan, Academy of Mathematics and Systems Science, Chinese Academy of Sciences(CAS)

- Vice Director of National Center for Mathematics and Interdisciplinary Sciences at CAS
- Secretary-General of China Society for Industrial and Applied Mathematics (CSIAM)

#### Dr. Guanghui Wang: School of Mathematics, Shandong University

- Assistant Dean of School of Mathematics, Shandong University
- Deputy General Secretary of Graph Theory and Combinatorics Branch of Operations Research Society of China
- Director of Young Crew Management Board of the Society

## Pages