17-19 May 2016
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
Congratulations to Leanne Merrill for receiving the Graduate Student Teaching Excellence Award from the UO Graduate School!
Congratulations to Hayden Harker for receiving the Williams Fund for his proposal to create Mathematical Thinking Labs.
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.
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.
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.
Wednesday, April 6 at 4pm in Fenton Hall 110
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.
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.
Congratulations to Ben Elias for his Sloan Research Fellowship! Read more about it at Around the O.
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.
The Department congratulates Ben Elias for his new NSF Career Award on “Categorical Representation Theory of Hecke Algebras.”
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.