# Moursund Lectures

### 5-7 May 2014

## Jacob Lurie

### Harvard

Professor Lurie will give three lectures over the course of his week in Eugene (Monday, Tuesday, Wednesday) on the general theme of

### Theory of “Spectral” Algebraic Geometry.

- Lecture 1: Cohomology Theories and Commutative Rings

4pm, Monday, 5 May 2014, 100 Willamette - Lecture 2: Ambidexterity

4pm, Tuesday, 6 May 2014, 100 Willamette - Lecture 3: Roots of Unity in Stable Homotopy Theory

4pm, Wednesday, 7 May 2014, 100 Willamette

All three lectures will be preceded by Tea in Fenton 219 at 3:15pm. Here is the poster including a detailed abstract of the talks.

### 21-23 May 2013

## Raphael Rouquier

### UCLA

Professor Rouquier will give three lectures over the course of his week in Eugene (Tuesday, Wednesday, Thursday) on the general theme of

### Higher Representation Theory.

- Lecture 1: Quiver Hecke algebras

4pm, Tuesday, 21 May 2013, 240C McKenzie - Lecture 2: Representations and geometry

4pm, Wednesday, 22 May 2013, 240C McKenzie - Lecture 3: Topology in dimensions 3 and 4

4pm, Thursday, 23 May 2013, 240A McKenzie

All three lectures will be preceded by Tea in Fenton 319 at 3:15pm. Here is the poster including detailed abstracts of each talk.

### 21-25 May 2012

## Andrei Okounkov

### Columbia University

Professor Okounkov will give three lectures over the course of his week in Eugene.

### Quantum Groups and Quantum Cohomology.

Quantum cohomology is a deformation of the classical cohomology algebra of an algebraic variety X that takes into account enumerative geometry of rational curves in X. A great deal is know about its structure for special X. For example, Givental and Kim described the quantum cohomology of flag manifolds in terms of certain quantum integrable systems, namely Toda lattices. A general vision for a connection between quantum cohomology and quantum integrable systems recently emerged in supersymmetric gauge theories, in particular in the work of Nekrasov and Shatashvili. Mathematically, the relevant class of varieties X to consider appears to be the so-called equivariant symplectic resolutions. These include, for example, cotangent bundles to compact homogeneous varieties, as well as Hilbert schemes of points and more general instanton moduli spaces. In my lectures, which will be based on joint work with Davesh Maulik, I will construct certain solutions of the Yang-Baxter equation associated to symplectic resolutions as above. The associated quantum integrable system will be identified with the quantum cohomology of X. If time permits, we will also explore K-theoretic generalization of this theory.

### 20-22 April 2010

## Anatoly Libgober

### University of Illinois at Chicago

Professor Libgober will present three lectures on the following topics:

- Lecture 1: Topology of quasi-projective varieties. Abstract.

4pm, Tuesday, 20 April 2010, 100 Willamette - Lecture 2: Lefschetz methods in topology of algebraic varieties and theory of Alexander invariants. Abstract.

4pm, Wednesday, 21 April 2010, 125 McKenzie - Lecture 3: Hodge theoretical methods for the study of Alexander invariants. Abstract.

4pm, Thursday, 22 April 2010, 282 Lillis

### 10-12 November 2009

## Terence Tao

### University of California, Los Angeles

Professor Tao will present three lectures on the following topics:

- Lecture 1: Recent Progress in Additive Prime Number Theory. Abstract.

4pm, Tuesday, 10 November 2009, 129 McKenzie - Lecture 2: Compressed Sensing. Abstract.

4pm, Wednesday, 11 November 2009, 221 McKenzie - Lecture 3: Discrete Random Matrices. Abstract.

4pm, Thursday, 12 November 2009, 221 McKenzie

Recordings of the lectures (audio and video) are available here. The audio is good (Tao was wearing a microphone). One can’t see Tao very well, but one can see the slides for the presentation.

### 7-9 May 2008

## William Fulton

### University of Michigan

Professor Fulton will present three lectures on “Equivariant cohomology of homogeneous varieties”:

- Lecture 1: 4pm, Wednesday, 7 May 2008, 115 Lawrence.
- Lecture 2: 4pm, Thursday, 8 May 2008, 115 Lawrence.
- Lecture 3: 4pm, Friday, 9 May 2008, 115 Lawrence.

The abstract is on the poster.

### 23-25 May 2007

## Gerhard Huisken

### Max Planck Institute of Gravitational Physics

Professor Huisken will present three lectures on the following topics:

- Lecture 1: The heat equation and uniformisation in geometry.

4pm, Wednesday, 23 May 2007, 221 McKenzie - Lecture 2: Isoperimetric inequalities and the concept of mass in General Relativity.

4pm, Thursday, 24 May 2007, 204 Villard - Lecture 3: Isoperimetric inequalities via geometric evolution equations.

4pm, Friday, 25 May 2007, 205 Deady

Click here for the abstracts (pdf).

### 15-17 March 2006

## Victor Ginzburg

### University of Chicago

Professor Ginzburg will present three lectures on “Noncommutative geometry and quiver algebras”:

- Lecture 1: Symplectic resolutions, their deformations and quantizations.

4pm, Wednesday, 15 March 2006, 106 Deady - Lecture 2: Noncommutative symplectic geometry, quivers, and matrix integrals.

4pm, Thursday, 16 March 2006, 106 Deady - Lecture 3: Calabi-Yau algebras.

4pm, Friday, 17 March 2006, 110 Willamette

The abstract is on the poster.

### 25-27 April 2005

## Richard Schoen

### Stanford University

Professor Schoen will present three lectures:

- Lecture 1: The Yamabe problem revisited

4:00 p.m., Monday, 25 April 2005, 106 Deady Hall - Lecture 2: Global compactness theorems for constant scalar curvature metrics

4:00 p.m., Tuesday, 26 April 2005, 106 Deady Hall - Lecture 3: Sharp isoperimetric inequalities for minimal surfaces in Euclidean space

4:00 p.m., Wednesday, 27 April 2005, 110 Willamette Hall

The abstracts are on the poster.

### 12-16 April 2004

## Maxim Kontsevich

### IHES, Bures-sur-Yvette, France

Professor Kontsevich will present three lectures on Integral Affine Structures:

- Lecture 1: Definitions and basic examples

4:00 p.m., Monday, 12 April 2004, 100 Willamette Hall - Lecture 2: Non-Archimedean and tropical viewpoints

4:00 p.m., Wednesday, 14 April 2004, 100 Willamette Hall - Lecture 3: Collapsing in mirror symmetry

4:00 p.m., Friday, 16 April 2004, 110 Fenton Hall

### 14-18 January 2002

## Victor Guillemin

### Massachusetts Institute of Technology

Professor Guillemin will present the following three lectures:

- Lecture 1: Betti numbers of polytopes and graphs

4:00 p.m., Monday, 14 January 2002, 110 Fenton Hall - Lecture 2: The GKM theorem

4:00 p.m., Wednesday, 16 January 2002, 110 Fenton Hall - Lecture 3: Multiplicative Morse theory for symplectic G-manifolds

4:00 p.m., Friday, 18 January 2002, 110 Fenton Hall

### 25-27 October 2000

## Dennis Sullivan

### CUNY at Stony Brook

Professor Sullivan will present the following three lectures on Fluids, quantum theory and algebraic topology:

- Lecture 1: Discrete modules

4:00 p.m., Wednesday, 25 October 2000, 123 Pacific Hall - Lecture 2: Algebraic quantization

4:00 p.m., Thursday, 26 October 2000, 110 Fenton Hall - Lecture 3: String topology

4:00 p.m., Friday, 27 October 2000, 110 Fenton Hall

### 11-15 October 1999

## Alexander Varchenko

### University of North Carolina in Chapel Hill

Professor Varchenko will present the following three lectures on multidimensional hypergeometric functions and representation theory:

- Lecture 1: The KZ differential equations and hypergeometric functions

4:00 p.m., Monday, 11 October 1999, 110 Fenton Hall - Lecture 2: Statistical mechanics, R-matrices and qKZ difference equations

4:00 p.m., Wednesday, 13 October 1999, 110 Fenton Hall - Lecture 3: The qKZ equations, q-hypergeometric functions, and quantization of geometry

4:00 p.m., Friday, 15 October 1999, 110 Fenton Hall

### 11-15 October 1998

## Jean-Pierre Serre

### College de France, Paris

Professor Serre will present two lecture series on the following topics:

- Lecture series 1: Finite subgroups of Lie groups
- Lecture series 2: The notion of complete reducibility in group theory

Lecture notes are available for both series here.

### March 1997

## Efim Zelmanov

### UC San Diego

### March 1998

## Philip Griffiths

### October 1995

## Clifford Taubes

### Harvard University

### January 1993

## Yu I Manin

### Max Planck Institut für Mathematik

### January 1989

## Michael Atiyah

### Cambridge University, UK