University of Oxford
Dates and topic TBA
8-10 April 2019
University of Chicago
Professor Wilkinson will present three lectures:
- Lecture 1 : The general case
Abstract: The celebrated Ergodic Theorems of George Birkhoff and von Neumann in the 1930’s gave rise to a mathematical formulation of Boltzmann’s Ergodic Hypothesis in thermodynamics. This reformulated hypothesis has been described by a variety of authors as theconjecture that ergodicity — a form of randomness of orbit distributions — should be“the general case” in conservative dynamics. I will discuss remarkable discoveries in the intervening century that show why such a hypothesis must be false in its most restrictive formulation but still survives in some contexts. In the end, I will begin to tackle the question, “When is ergodicity and other chaotic behavior the generalcase?”
4pm, Monday, April 8, 2019, Deady Hall 208
- Lecture 2 : Robust mechanisms for chaos, I: Geometry and the birth of stable ergodicity
Abstract: The first general, robust mechanism for ergodicity was developed by E. Hopf in the 1930’s in the context of Riemannian geometry. Loosely put, Hopf showed that for a negatively curved, compact surface, the “typical” infinite geodesic fills the manifold in a very uniform way, a property called equidistribution. I will discuss Hopf’s basic idea in both topological and measure-theoretic settings and how it has developed into a widely applicable mechanism for chaotic behavior in smooth dynamics.
4pm, Tuesday, April 9, 2019, Deady Hall 208
- Lecture 3 : Robust mechanisms for chaos, II: Stable ergodicity and partial hyperbolicity
Abstract: Kolmogorov introduced in the 1950’s a robust mechanism for non-ergodicity, which is now known as the KAM phenomenon (named for Kologorov, Arnol’d and Moser). A current, pressing problem in smooth dynamics is to understand the interplay between KAM and Hopf phenomena in specific classes of dynamical systems. I will describe a class of dynamical systems, called the partially hyperbolic systems, in which the two phenomena can in some sense be combined. I’ll also explain recent results that give strong evidence for the truth of a modified ergodic hypothesis in this setting, known as the Pugh-Shub stable ergodicity conjecture.
4pm, Wednesday, April 10, 2019, Gerlinger Hall 242
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
Professor McDuff will present three lectures:
Embedding questions in symplectic Topology
These lectures will provide an introduction to the area, with special emphasis on problems of symplectic embeddings.
- 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
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
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
11-13 May 2015
Beijing University and Princeton University
Professor Tian will give three lectures on the general theme of
- 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
UC San Diego
Yu I Manin
Max Planck Institut für Mathematik
Cambridge University, UK