Fall 2022

Andras Vasy, Stanford University (poster)

Abstract: In the first lecture I will explain the black hole stability problem in classical general relativity and some of the recent results on it — these involve a fascinating combination of geometry and the analysis of partial differential equations. I will also give at least some indication of some of the tools that went into proving this. In the second lecture, I will discuss in more detail the analytic and geometric tools that lead to the understanding of black hole stability with a positive cosmological constant (Kerr-de Sitter spacetimes) and their extensions for making progress on the vanishing cosmological constant case (Kerr). This is based on joint works with Dietrich Haefner, Peter Hintz and Oliver Lindblad Petersen

• Thursday, October 13, 2022, 4:00–5:00pm, Latrobe Hall 120: The black hole stability problem — an introduction and results
• Friday, October 14, 2022, 4:00–5:00pm, Krieger Hall 300: Analysis and geometry in the black hole stability problem

Spring 2019

Bhargav Bhatt, University of Michigan (poster)

• Thursday, April 4, 4:00–5:00pm, Latrobe 120: Interpolating p-adic cohomology theories
• Friday, April 5, 3:00–4:00pm, Krieger 304: The direct summand conjecture

Fall 2018

Mihalis Dafermos, Princeton University and University of Cambridge  (poster)

• Monday, October 22, 4:00–5:00pm, Shaffer 304: On falling into black holes I    Video for first talk
• Tuesday, October 23, 4:30–5:30pm, Shaffer 304: On falling into black holes II   Video for second talk 

Fall 2017

Richard Melrose, MIT  (poster)

• Tuesday, October 24, 5:00–6:00pm, Hodson 316: Resolution, metrics and harmonic forms
• Wednesday, October 25, 3:00–4:00pm, Bloomberg 168: Hodge theory for the Weil-Petersson metric on Riemann moduli spaces

Spring 2017

Luis Caffarelli, University of Texas

• Wednesday, March 29, 4:00–5:00pm, Krieger 205: Sets boundaries minimizing local and non local interactions I
• Thursday, March 30, 4:00–5:00pm, Gilman 50: Sets boundaries minimizing local and non local interactions II

Spring 2016

Joaquim Ortega-Cerdà, Universitat de Barcelona (Poster)

• Tuesday, March 29, 4:30–5:45, Shaffer 304: Sampling polynomials in algebraic varieties
• Thursday, March 31, 4:00–5:00, Krieger 205: Equidistributing points in a sphere

Spring 2015

Elias Stein, Princeton

• Monday, April 13: How to think about the Cauchy-Szego projection
• Tuesday, April 14: Singular integrals: the product theory and its outgrowth

Spring 2014

Christopher Hacon, University of Utah

• Thursday, March 13: Birational classification of algebraic varieties
• Friday, March 14: On Shokurov’s conjectures on log canonical thresholds

Fall 2013

Pierre Cartier, IHES and University Paris-Diderot

• Thursday, November 21: About the Cosmic Galois group, a tale of geometry, number theory, and physics
• Friday, November 22: A quantum group as Galois group for some difference equations: one more instance of noncommutative geometry

Spring 2013

Maciej Zworski, Berkeley

Decay rates in quantum and classical dynamics

Spring 2012

Tobias Colding, MIT

• Mean curvature flow
• Ricci curvature

Fall 2011

Bernd Sturmfels, University of California Berkeley

• Multiview Geometry
• Mustafin Varieties

Spring 2011

Fedor Bogomolov, Courant Institute

• Kummer theorem and projective geometry
• The Arf-Kervaire problem in algebraic topology

Fall 2010

Kazuya Kato, University of Chicago

• Classifying spaces of degenerating Hodge structures
• Degeneration of Hodge and p-adic Hodge structures

Spring 2010

Dan Freed, University of Texas

• Dirac operators and differential K-theory
• Loop groups and twisted K-theory

Fall 2009

Eric Bedford, Indiana University

• Dynamics of Complex Surface Automorphisms
• Dynamics of Rational Surface Automorphisms

Spring 2009

Ken Ono, University of Wisconsin-Madison

• Unearthing the Visions of a Master: Harmonic Maass Forms
• Heegner Divisors, L-functions and Maass Forms

Victor Guillemin, MIT

• Spectral Measures

Fall 2008

James McKernan, MIT

• Finite generation of the canonical ring
• The cone theorem revisited

Spring 2008

János Kollár, Princeton

• Which Powers of Holomorphic Functions are Integrable
• Diophantine Subsets of Function Fields of Curves

Fall 2007

Valery Alexeev, UGA

• Canonical limits of varieties
• Tropical geometry versus classical geometry

D.H. Phong, Columbia

• Stability and constant scalar curvature

Lars Hesselholt, MIT

• Homeomorphisms of Manifolds and Algebraic K-theory
• The absolute de Rham-Witt Complex and the Fundamental Theorem
• Introduction to algebraic K-theory

Spring 2007

Kazuhiro Fujiwara

• Counting the number of solutions in finite fields
• Galois representations and arithmetic geometry of shimura varieties

Ravi Vakil

• A geometric Littlewood-Richardson rule
• Murphy’s Law in algebraic geometry: Badly behaved moduli spaces

Fall 2006

Yves André

• Ambiguity theory, old and new
• Periods and motives

Wilhelm Schlag

• On the Schroedinger flow on surfaces of revolution
• Dispersive estimates for wave equations and applications to stability of solitons

Spring 2006

Robert Bryant

• Aufwiedersehen surfaces, revisited
• Gradient Kahler-Ricci solitons

Fall 2005

Ezra Getzler

• Lie theory for differential graded lie algebras
• Open/closed modular operads
• Open/closed deligne-mumford moduli spaces and topological field theory

Yuri Tschinkel

• Geometry over finite fields
• Arithmetic over function fields

Spring 2005

Michael Douglas

• String theory and geometry

Matilde Marcolli

• Quantum statistical mechanics of Q-lattices
• Renormalization and motivic Galois theory