The Department of Mathematics at Western Michigan University presents colloquiums.

**Time: 4 p.m. (time may vary)**

**Place: 6625 Everett Tower**

### Spring 2017

## thursday, apr. 20

**Trees, trees, so many trees! **presented by Allen Schwenk, Ph.D., Western Michigan University

Refreshments served at 3:50 p.m.

Abstract: How can we count the number of spanning trees of a particular graph? There are direct counting methods, the Matrix Tree Theorem, Prufer Codes and eigenvalue methods. We shall examine several approaches as time permits.

## Thursday, mar. 30

**College student's perception of mathematics **presented by Katrina Piatek-Jimenez, Ph.D., Central Michigan University

Refreshments served at 3:50 p.m.

Abstract: This talk will focus on a recent study in which we asked 179 college students to "Draw a Mathematician" and list five characteristics and careers for mathematicians. We then conducted four focus group interviews with a total of 12 participants during which we asked the participants to view 16 photos of individuals and asked them to determine whether they believed each person was a mathematician or not and to explain their reasoning. Through our analysis of the data, we found that many college students do have specific beliefs about mathematicians, and that some of their perceptions are different than those found in previous studies with younger children.

## Thursday, mar. 2

**Money management from a mathematical point of view **presented by Stanislaus Maier-Paape, Ph.D., Aachen University

Refreshments served at 3:50 p.m.

Abstract: In this talk I will present some recent results of money management and portfolio theory which confirm and generalize the money management ansatz of Ralph Vince who used as goal function the so called"terminal wealth relative". Particular emphasis will be given to risk aspects of that ansatz. Furthermore I will consider how these results are related to the well known "modern portfolio theory" of Markowitz of 1952.

## Thursday, jan. 26

**Greatest common divisors and Diophantine approximation **presented by Aaron Levin, Ph.D., Assistant Professor, Michigan State University

Refreshments served at 3:50 p.m.

Abstract: In 2003, Bugeaud, Corvaja and Zannier gave an (essentially sharp) upper bound for the greatest common divisor

gcd(a^{n}-1, b^{n}-1)

where a and b are fixed integers and n varies over the positive integers. In contrast to the elementary statement of their result, the proof required deep results from Diophantine approximation. I will discuss their result, subsequent generalizations and related problems, and recent work of my own, all centered around greatest common divisors.

### Fall 2016

## Thursday, Nov. 3

**Teaching calculus now - current trends and best practices** presented by David Bressoud, Ph.D., Professor, Macalaster College

Refreshments served at 3:50 p.m.

Abstract: Since 2009, the Mathematical Association of America has conducted national studies of mainstream calculus. For the first five years, Characteristics of Successful Programs in College Calculus undertook a large-scale national survey of students and instructors in calculus I with follow-up case study visits to 20 of the colleges and universities that had interesting and promising programs. We are now embarked on an expanded study begun in 2015, Progress through Calculus. This project broadens our study to the entire precalculus through calculus II sequence while focusing on cataloging the efforts currently underway to improve student success through this sequence and documenting what does and does not work in the actual implementation of these efforts. This talk will provide an overview of what has been learned.

## Friday, Oct. 14

**The first function **presented by Carl Pomerance, Ph.D., John G. Kemeny Parents Professor Emeritus, Dartmouth College

1104 Rood Hall

Refreshments served at 3:50 p.m.

Abstract: Let s(n) denote the sum of the positive divisors of n that are smaller than n. Introduced by Pythagoras 2500 years ago, it is perhaps the first function ever studied in mathematics. Steeped in numerology and colorful metaphors, the ancient problems related to s(n) have helped to spur the development of much of number theory. This talk will present a gentle historical perspective, leading up to some very recent new results.

About: Dr. Carl Pomerance received his B.A. from Brown University in 1966 and his Ph.D. from Harvard University in 1972 under the direction of John Tate. Currently he is the John G. Kemeny Parents Professor Emeritus at Dartmouth College, after previous positions at the University of Georgia and Bell Labs. A number theorist, Pomerance specializes in analytic, combinatorial and computational number theory, with application in the field of cryptology. He considers the late Paul Erdos as his greatest influence.

## Thursday, Sept. 15

**On primal regularity estimates for single-valued and set-valued mappings **presented by Radek Cibulka, Ph.D., University of West Bohemia, Pilsen, Czech Republic

Refreshments served at 3:50 p.m.

Abstract: We survey some regularity statements in variational analysis. We focus on theorems guaranteeing the openness at a linear rate of a mapping around the reference point, which is known to be equivalent to metric regularity. In particular, we are going to discuss techniques used in the proofs of such statements. We start with regularity criterion by A.D. loffe which can be traced back to the work of M. Fabian and D. Preiss, that substitutes complicated iterative procedures. When time permits we intend to present some applications of theoretical results. The lecture is based on two papers co-authored with M. Fabian and A.D. loffe.

**Thursday, Sept. 1**

**Colloquium session-differential games, control and optimization**

Refreshments served at 2:15 p.m.

**Schedule**

2:30 p.m.

**On solution of control problems on a finite time interval **presented by Vladimir Ushakov, Ph.D., Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

3:10 p.m.

**Convex duality in math finance** presented by Jim Zhu, Ph.D, Department of Mathematics, Western Michigan University

3:50 p.m.

**Optimal control problems and dynamic games on infinite horizon **presented by Alexander Tarasyev, Ph.D, Krasovskii Institute of Mathematics and Mechanics, Ekaterinburg, Russia

4:35 p.m.

**Harmonic analysis and Matrix Riccati Equations **presented by Yuri Ledyaev, Ph.D, Department of Mathematics, Western Michigan University