Moursund Lectures

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2023-2024 | 2016-2019 | 2010-2015 | all by 2009

Contents

6-7 February 2024

Dr. Chris Hacon
University of Utah

  • Lecture 1: Classification of algebraic varieties, part 1, 4pm, Tuesday, February 6, 128 Chiles Hall
  • Lecture 2: Classification of algebraic varieties, part 2, 4pm, Wednesday, February 7, 128 Chiles Hall

Abstract : Algebraic geometry is the study of geometric objects defined by the solution of polynomial equations. One of the most natural and ambitious goals of the subject is to classify all such objects. For one dimensional complex projective varieties (i.e. Riemann Surfaces), the answer is given by the Deligne-Mumford moduli spaces M_g. For any g at least 2, there is an algebraic variety of dimension 3g-3 whose points parametrize uniquely all Riemann Surfaces of genus g. Moreover, these spaces admit a geometrically meaningful compactification of great importance. In these lectures we will discuss the recent generalization of this results to arbitrary dimension. The first talk will be focused on old and new techniques of the minimal model program and the second talk will be focused on the construction of the moduli spaces themselves.

7-10 March 2023

Dr. Soren Galatius
Department of Mathematical Sciences KU

  • Lecture 1: Topological Pontryagin Classes
    March 7th at 4:00 PM
  • Lecture 2: Cohomology of Moduli Spaces of Graphs and Surfaces
    March 8th at 4:00 PM
  • Lecture 3: On the Homology of General Linear Groups of Infinite Fields
    March 10th at 4:00 PM

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8-10 April 2019

Amie Wilkinson
University of Chicago

Professor Wilkinson will present three lectures:

There will be a reception at 5pm on Monday in the Fenton Lounge, room 219. All three lectures will be preceded by Tea in the Fenton Lounge at 3:30pm.

 

3-5 April 2018

Dusa McDuff
Columbia University

Professor McDuff will present three lectures:
Embedding questions in symplectic Topology

  • Lecture 1: Introduction to Symplectic Topology
    4pm, Tuesday, April 3, 2018, Deady Hall 208
  • Lecture 2: Embeddings of 4-dimensional ellipsoids
    4pm, Wednesday, April 4, 2018, McKenzie Hall 229
  • Lecture 3: Beyond 4-dimensions
    4pm, Thursday, April 5, 2018, Deady Hall 208

 

16-18 May 2017

Mikhail Khovanov
Columbia University

Professor Khovanov will present three lectures:

  • Lecture 1: The Jones polynomial of links and tangles and its categorification
    4pm, Tuesday, May 16, 2017, Pacific Hall 123
  • Lecture 2: Categorification of the Kuperberg bracket
    4pm, Wednesday, May 17, 2017, Willamette Hall 100
  • Lecture 3: How to categorify the ring of integers localized at two
    4pm, Thursday, May 18, 2017, NEW LOCATION: McKenzie Hall 125

 

17-19 May 2016

Peter Ozsváth
Princeton University

Professor Ozsváth will give three lectures on the general theme of

Floer homology and 3-manifolds

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11-13 May 2015

Gang Tian
Beijing University and Princeton University

Professor Tian will give three lectures on the general theme of

Curvature Flows

  • Lecture 1: Curvature Flows
    4pm, Monday, 11 May 2015, 229 McKenzie
  • Lecture 2: Analytic Minimal Model Program through Ricci Flow
    4pm, Tuesday, 12 May 2015, 229 McKenzie
  • Lecture 3: New Curvature Flows
    4pm, Wednesday, 13 May 2015, 229 Willamette

All three lectures will be preceded by Tea in Fenton 219 at 3:15pm.

 

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.

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

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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

 

November 1986

Victor Kac

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