**Welcome to the Mathematics Department!**

Our research specialties are in algebra, analysis, geometry, probability and topology.

There are about thirty-five research faculty members and almost seventy graduate students in the department.

The American Mathematical Society has ranked us in the top group of U.S. research departments in Mathematics.

Six members of the department were named Fellows of the American Mathematical Society in 2013. Three members of the department spoke in the Lie Theory Section of the 2014 International Congress of Mathematics.

We also take great pride in the quality of our outstanding undergraduate teaching as well as our thriving graduate program.

The EUGENE MATH CIRCLE is continuing in the department. It is aimed at elementary, middle and high school students who enjoy math and want to be stretched by challenging problems.

## News and Events

## Distinguished Lecture Series for Students

Ken Ono – Associate Producer of The Man Who Knew Infinity (starring Jeremy Irons and Dev Patel, currently playing in theaters), former professional cyclist (for the Pepsi Miyata team), former member of Team USA in the world age-group triathlon championships, and distinguished mathematics professor at Emory University – will visit and give a broadly accessible talk (as part of the Distinguished Lectures for Students series) at 5:15 pm on Wednesday, May 25, in Lillis 282.

A poster with more details is available here:

Poster

Ono says the talk will be broadly accessible, “even by 6th graders.”

## Moursund Lectures

# Moursund Lectures

### 17-19 May 2016

## Peter Ozsváth

### Princeton University

Professor Ozsváth will give three lectures on the general theme of

### Floer homology and 3-manifolds

- Lecture 1: Holomorphic disks and low-dimensional topology
**Abstract:**Heegaard Floer homology is a closed three-manifold invariant, defined in joint work with Zoltan Szabo, using methods from symplectic geometry (specifically, the theory of pseudo-holomorphic disks). The inspiration for this invariant comes from gauge theory. I will describe Heegaard Floer homology, motivate its construction, list some of its key properties, and give some of its topological applications.4pm, Tuesday, 17 May 2016, 145 Straub Hall

- Lecture 2: A knot invariant from grid diagrams
**Abstract:**Knot Floer homology is an invariant for knots in three-space, which arises naturally when one attempts to understand how Heegaard Floer homology transforms under certain three-dimensional operations. Knot Floer homology has the form of a bigraded vector space, encoding information about the complexity of the knot. The invariant was

originally defined in collaboration with Zoltan Szabo, and indepedently by Jacob Rasmussen. I will describe a combinatorial algorithm for computing this invariant, discovered in joint work with Ciprian Manolescu and Sucharit Sarkar, and further elaborated in joint work with Manolescu, Szabo, and Dylan Thurston. I will also sketch some of the applications of this invariant to knot theory, and some of its connection with other knot invariants.4pm, Wednesday, 18 May 2016, 110 Fenton Hall

- Lecture 3: Bordered Floer homology
**Abstract:**I will describe “bordered Floer homology”, an invariant for three-manifolds with boundary that generalizes Heegaard Floer homology. The bordered theory associates a differential graded algebra to a parameterized surface; it also assocates a graded module to a three-manifold with boundary. This construction leads to a better conceptual understanding of Heegaard Floer homology, and it also gives a method for computation. Bordered Floer homology was introduced in joint work with Robert Lipshitz and Dylan Thurston. Time permitting, I will also describe a bordered approach to knot invariants, which is joint work with Zoltan Szabo.4pm, Thursday, 19 May 2016, 145 Straub Hall

## Leanne Merrill receives Teaching Excellence Award

Congratulations to Leanne Merrill for receiving the Graduate Student Teaching Excellence Award from the UO Graduate School!

## Hayden Harker receives Williams Fund

Congratulations to Hayden Harker for receiving the Williams Fund for his proposal to create Mathematical Thinking Labs.

## Mike Prices wins Thomas F. Herman Award

Congratulations to Mike Price for winning the Thomas F. Herman Faculty Achievement Award for Distinguished Teaching, the highest teaching honors at the University of Oregon.

## Distinguished Lecture Series for Undergraduates

Farshid Hajir (University of Massachusetts) will present a lecture on May 10, 2016 in 145 Straub Hall at 5:15-6:15 pm as part of Distinguished Lecture Series for Undergraduates.

Title: The Jacobi-Legendre Correspondence: A Vignette in the History of Mathematics

Abstract: Once upon a time, a recent math PhD (in Germany) got up the courage to write to one of the world’s greatest mathematicians (in France) about the problems he was working on regarding elliptic functions. The Master wrote back a few days later at length and with much praise for the youngster’s work. Thus began the correspondence between Carl Gustav Jacob von Jacobi (the youngster) and Adrien-Marie Legendre (the Master). The correspondence is filled with lessons about the process of mathematical discovery, about how mathematicians inspire and compete with each other, as well as wonderful math. This lecture – largely a talk in the history of math – will tour highlights in the Jacobi-Legendre correspondence, famous for richness in mathematical gems. Naturally, the ulterior motive is to introduce the audience to elliptic functions and other mathematical objects that fascinated Jacobi and Legendre.

## Niven Lectures

Cameron Gordon, a Professor at the University of Texas at Austin, will visit campus April 6-7, 2016. Professor Gordon will present two lectures as part of the Niven Lectures.

Undergraduate lecture:

Wednesday, April 6 at 4pm in Fenton Hall 110

Title: Knots

Abstract: A knot is just a closed loop in 3-dimensional euclidean space, embedded in some possibly highly tangled fashion. The mathematical study of knots began in the second half of the nineteenth century, motivated by problems in physics, and continues to be an active area of research. Probably the most basic question in knot theory is: is it possible to tell if a knot is really knotted (and if so, how)? It was also recognized early on that any knot becomes unknotted in four dimensions. This leads to the question of how many “jumps” into the 4th dimension are needed to untie a given knot, a question that is still very mysterious. We will describe some of the history of the subject and discuss these questions.

Colloquium lecture:

Thursday, April 7 at 4pm in Straub Hall 145

Title: Left-orderability of 3-manifold groups

Abstract: The fundamental group is a more or less complete invariant of a 3-dimensional manifold. We will discuss how the purely algebraic property of this group being left-orderable is related to two other aspects of 3-dimensional topology, one geometric and the other essentially analytic.

## Ben Elias receives Sloan Fellow

Congratulations to Ben Elias for his Sloan Research Fellowship! Read more about it at Around the O.

## Frank W. Anderson, Professor Emeritus

Frank W. Anderson, Professor Emeritus, passed away February 5, 2016, in Eugene. Frank joined the Math Department in 1957, became Professor in 1968, and retired in 2003. He was the department head from 1987 to 1994 and supervised 20 doctoral students.

Frank and his wife, Dorothy, donated two funds for the Math Department: the Frank W. Anderson Graduate Teaching Fund and the Frank W. and Dorothy D. Anderson Mathematics Ph.D. Student Research Award Fund.

## NSF Career Award for Ben Elias

The Department congratulates Ben Elias for his new NSF Career Award on “Categorical Representation Theory of Hecke Algebras.”

## AWM Distinguished Speaker

AWM Distinguished Lecture Series

Cristina Ballantine, Professor of Mathematics at College of the Holy Cross, will visit campus January 21 – 22, 2016.

Undergraduate Talk:

Thursday, Jan. 21st at 4pm in Deady 102

Title: Rolle’s Theorem for Polynomials over Finite Fields

Abstract: Rolle’s Theorem from calculus states that a differentiable function f that takes the same value at two different points must have a horizontal tangent line between them. As a consequence, between any two zeros of f there must be a zero of its derivative function f’.

Is this still true if f is a polynomial and the coefficients of f live in a world different from the real numbers? We will investigate what happens if this new world is a finite field (a finite set in which you can still perform operations similar to addition, subtraction, multiplication, and division).

No background beyond linear algebra is needed for this talk.

Colloquium Talk

Friday, Jan. 22nd at 4pm in Deady 208

Title: Graphs and Number Theory

Abstract: Graphs are the mathematical models for networks. Expander graphs are well-connected yet sparse graphs. The expansion property of a regular or bi-regular graph is governed by the second largest eigenvalue of its adjacency matrix. Optimal expanders are called Ramanujan graphs. We will introduce the notion of primes for graphs and define the Ihara-Zeta function and the Riemann Hypothesis in the context of graphs. Graphs satisfying the Riemann Hypothesis are Ramanujan. We will use methods from the representation theory of p-adic groups to construct infinite families of (regular and bi-regular) Ramanujan graphs.

## Distinguished Lecture Series for Undergraduates

Tim Chartier (Davidson College) will present a lecture on January 11, 2016 in 207 Chapman Hall at 5:15-6:15 pm as part of the Distinguished Lecture Series for Undergraduates.

Title: Playing from a Laptop: Sports Analytics

Abstract: Sports analytics is a growing field. The larger field of data analytics is exploding as a field requiring skills in mathematics and computer science. What sports projects can be tackled as an undergraduate? This talk will discuss a variety of projects Dr. Tim Chartier of Davidson College has directed with his students, who have ranged from first years to seniors and include math and non-math majors. His projects have varied from helping the German National Basketball Team to his own college teams. He’s also aided the NBA, NASCAR, and ESPN. Learn how to play a sport — as a sports analyst!

## AWM Distinguished Speaker

Angélica Osorno, an Assistant Professor at Reed College, will visit campus on November 12 – 13, 2015. She will present two lectures, one suitable for undergraduates and the second a colloquium for faculty and graduate students.

Undergraduate Lecture on November 12th at 4 p.m. in Condon 301

Title: Why Should We Care About Category Theory

Abstract: One of the first mathematical concepts we learn as children is counting, and when we do so, we think of counting the number of elements in a specific set. Soon after, we forget about sets and we just consider the abstract numbers themselves. This abstraction simplifies many things, but it also makes us forget about some structure that we had when we were thinking about sets. That structure can be encoded by a category. In this talk we will describe certain concepts in category theory, and you will realize that in most of your mathematics classes you have been working with categories, you just didn’t know about it. There will be plenty of examples that will show that category theory provides a unifying language for mathematics, and that many constructions are more naturally understood when they are seen through the categorical lens.

Colloquium on November 13th at 4 p.m. in Deady 208

Title: Why Do Algebraic Topologists Care About Categories

Abstract: The study of category theory was started by Eilenberg and MacLane, in their effort to codify the axioms for homology. Category theory provides a language to express the different structures that we see in topology, and in most of mathematics. Categories also play another role in algebraic topology. Via the classifying space construction, topologists use categories to build spaces whose topology encodes the algebraic structure of the category. This construction is a fruitful way of producing important examples of spaces used in algebraic topology. In this talk we will describe how this process works, starting from classic examples and ending with some recent work.

## Kleshchev elected AMS Fellow

Congratulations to Sasha Kleshchev, who has been elected an AMS Fellow in the class of 2016.

The citation reads “For contributions to the representation theory of finite groups, Hecke algebras, and Kac-Moody algebras, and for exposition.”

See http://www.ams.org/profession/ams-fellows/new-fellows for the complete list of new fellows.

## Mike Price wins Tykeson Teaching Award

Congratulations to Mike Price for winning the College of Arts & Sciences Tykeson Teaching Award.