**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

## Graduate Student Cathy Hsu Wins Poster Award at JMM

At the Joint Math Meetings in Atlanta this month, doctoral candidate Cathy Hsu won the Most Outstanding Graduate Student Research Poster award from the Association for Women in Mathematics. The Department congratulates her on her success!

## Ben Elias wins New Horizon Prize

Congratulations to Assistant Professor Benjamin Elias. He and his collaborator, Geordie Williamson of Kyoto University and University of Sydney, were awarded a $100,000 New Horizon Prize in Mathematics on Sunday, December 4th. There are three of these awards given each year in recognition of the achievements of early-career mathematicians.

For more details, visit https://breakthroughprize.org/News/34

This story was also featured in AroundtheO. See the spotlight article at http://around.uoregon.edu/content/math-professor-ben-elias-brings-new-horizons-prize-uo?atm_source=ato12-14-16

## AWM Student Chapter Distinguished Speaker

Monica Vazirani, Professor of Mathematics at University of California, Davis will visit campus on November 10th and 11th to deliver the fall 2016 AWM Student Chapter Distinguished Speaker Lectures.

Professor Vazirani will give a broadly accessible talk on Thursday, November 10th in Deady 106.

The title of this talk, which is suitable for undergraduates, is *Applications of symmetry via the lemma that is not Burnside’s*.

Professor Vazirani will give a colloquium talk on Friday, November 11th, at 4:00 pm in Deady 208. The title of this research-level talk, is *Representations of the affine BMW algebra*.

## Distinguished Lecture Series for Students – November 14th

Jayadev Athreya – Director the Washington Experimental Mathematics Lab, Associate Professor of Mathematics at the University of Washington, and co-creator of the project Axiomatic that blends math and art – will visit and give a broadly accessible talk (as part of the Mathematics Department’s Distinguished Lectures for Students series) at 5:15 pm on Monday, November 14 in Straub 245. All are welcome, and undergraduates are especially encouraged to attend.

A poster with more details is available here:

Poster

## Vitulli Receives AWM Service Award

Congratulations to Marie Vitulli, Professor Emerita, for receiving an Association for Women in Mathematics Service Award.

## Vaintrobfest – November 5th & 6th

A conference to honor Arkady Vaintrob’s 60th birthday will be held at the Department of Mathematics on November 5-6, 2016. Talks will be given in several areas, reflecting Professor Vaintrob’s diverse interests.

More details can be found at http://www-math.mit.edu/~etingof/vaintrobfest.html

## UO Math Alumna Appointed Director of AMS D.C. Office

Karen Saxe, DeWitt Wallace Professor of Mathematics at Macalester College, has been named Director of the Washington, D.C. Office of the American Mathematical Society.

Professor Saxe received her doctoral degree from the University of Oregon Department of Mathematics in 1988.

Read the full announcement at http://www.ams.org/news?news_id=3136.

## Funds for Faculty Excellence

Congratulations to Huaxin Lin and Victor Ostrik for receiving the Fund for Faculty Excellence Award this year.

## 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.

Read more about Mike’s achievement **here.**

## 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.