Past DLS Lecturers

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

2017
Roman Bezrukavnikov
Igor Rodnianski
Claire Voisin
Geordie Williamson
2016
Donald Goldfarb
Benedict Gross
Akshay Venkatesh
2015
Manjul Bhargava
Andrei Okounkov
2014
Robert Bryant
Peter Markowich
Yuval Peres
2013
Michael Aizenman
Ursula Hamenstädt
László Lovász
Gilles Pisier
Richard Taylor
Jean-Pierre Wintenberger
2012
Paul Seidel
2011
Noga Alon
Michael Brenner
Pierre Colmez
Ehud Hrushovski
2010
Michael Harris
Pierre-Louis Lions
Barry Mazur
Ken Ono
Leonid Polterovich
Horng-Tzer Yau
2009
Gregory Margulis
2008
Mario Bonk
John Coates
Elias Stein
Avi Wigderson
2007
Charles Fefferman
C. David Levermore
Shing-Tung Yau
Shouwu Zhang
2006
Peter Sarnak
Peter Schneider
2005
Jean Bellissard
Etienne Ghys
Goro Shimura
Andrei Suslin
Zhengan Weng
2004
Pierre Deligne
Michael Harris
Alexander Lubotzky
2003
Hillel Furstenberg
Robert Langlands
Peter Lax
Nikolai Reshetikhin
Clifford Taubes
Shing-Tung Yau
2002
Raoul Bott
L.H. Eliasson
Dennis Gaitsgory
Jesper Lutzen
Louis Nirenberg
Oded Schramm
I.M. Singer
2001
Michael Atiyah
Jean-Michel Bismut
Alain Connes
Jöran Friberg
David Mumford
Gilles Pisier
Jean-Pierre Serre
Freydoon Shahidi
Gregg Zuckerman
2000
Christophe Deninger
Nessim Sibony
Gang Tian

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Algebraic geometry session at AMS Fall Sectional Meeting @ UC Riverside, 4–5 November 2017

I’ll be speaking (on rationality) at the AMS Fall Sectional Meeting at Riverside. Other speakers in the algebraic geometry session are Aravind Asok, Emily Clader, Omprokash Das, Humberto Diaz, Matthias Flach, Martin Gallauer, James McKernan, Wenhao Ou, Dustin Ross, and Alexander Soibelman. The session is organized by Humberto Diaz, Jose Gonzalez, and Ziv Ran.

The invited addresses are by Paul Balmer, Pavel Etingof, and Monica Vazirani.

Photo: NO YOU CAN’T HAVE MY LEAVES STOP ASKING, from reddit.

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New paper: The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay

I’ve posted a new paper on the arXiv. Most of the results premiered at Oberwolfach, but since then I’ve added an interesting new example inspired by related work of Takehiko Yasuda, whom I met there. (Oberwolfach at work!)

The paper shows that the Kodaira vanishing theorem can fail on smooth Fano varieties of any characteristic p > 0. Taking cones over some of these varieties, we give the first examples of terminal singularities which are not Cohen-Macaulay. By a different method, we construct a terminal singularity of dimension 3 (the lowest possible) in characteristic 2 which is not Cohen-Macaulay.

Image: Palmerston, Foreign Office cat, sneaks up on cheese; from his DiploMog twitter feed

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WAGS @ UCLA, 14–15 October 2017

WAGS returns to UCLA.

The Fall 2017 edition of the Western Algebraic Geometry Symposium (WAGS) will take place the weekend of 14–15 October 2017 at IPAM on the UCLA campus, hosted by the UCLA Mathematics Department. Details are now on the conference website.

If you plan to attend but haven’t yet registered, please register. It’s free, and knowing who’s coming will allow us to ensure that:

  • We have enough space.
  • We have enough coffee.
  • We have enough food.
  • We have a name tag ready for you, so that the conference is successful in helping you meet fellow mathematicians and helping other mathematicians meet you.
  • We can help our funder to demonstrate — with evidence — that they’re supporting a thriving enterprise.

Send questions to fall2017@wagsymposium.org. [UPDATE: I previously gave the wrong email address (starting fall17).]

Photo of the Powell Cat from the Daily Bruin. More about the Powell Cat on twitter.

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New (review) paper: Recent progress on the Tate conjecture

My paper about the Tate conjecture for Bull. AMS is now available to view.

In it I survey the history of the Tate conjecture on algebraic cycles. The conjecture is closely intertwined with other big problems in arithmetic and algebraic geometry, including the Hodge and Birch–Swinnerton-Dyer conjectures. I conclude by discussing the recent proof of the Tate conjecture for K3 surfaces over finite fields.

After returning the proofs to the AMS, it occurred to me that it could be helpful to readers if I recommended some available related videos. I was too slow for the AMS’s speedy production, however, so I make the recommendations here.

Videos

F. Charles. K3 surfaces over finite fields: insights from complex geometry (2015).

K. Madapusi Pera. Regular integral models for orthogonal Shimura varieties and the Tate conjecture for K3 surfaces in finite characteristic (2012).

D. Maulik. Finiteness of K3 surfaces and the Tate conjecture (2012).

Photo is from foldedspace.org.

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March for Science

The March for Science will be on Earth Day, Saturday, April 22, 2017, in 605 cities across the U.S. and beyond. Come out and march for truth against lies! Check out the web site for details of the march in your city. I’ll be marching in Houston.

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Now it’s about stacks (new paper)

I’ve posted an updated version of a paper on the arXiv, Hodge theory of classifying stacks (initial version posted 10 March 2017). We compute the Hodge and de Rham cohomology of the classifying space BG (defined as sheaf cohomology on the algebraic stack BG) for reductive groups G over many fields, including fields of small characteristic. These calculations have a direct relation with representation theory, yielding new results there. The calculations are closely analogous to, but not always the same as, the cohomology of classifying spaces in topology. This is part of the grand theme of bringing topological ideas into algebraic geometry to build analogous organizing structures and machines.

In the first version of the paper, I defined Hodge and de Rham cohomology of classifying spaces by thinking of BG as a simplicial scheme. In the current version, I followed Bhargav Bhatt‘s suggestion to make the definitions in terms of the stack BG, with simplicial schemes as just a computational tool. Although I sometimes resist the language of algebraic stacks as being too abstract, it is powerful, especially now that so much cohomological machinery has been developed for stacks (notably in the Stacks Project). (In short, stacks are a flexible language for talking about quotients in algebraic geometry. There is a “quotient stack” [X/G] for any action of an algebraic group G on a scheme X.)

Using the language of stacks led to several improvements in the paper. For one thing, my earlier definition gave what should be considered wrong answers for non-smooth groups, such as the group scheme μp of pth roots of unity in characteristic p. Also, the paper now includes a description of equivariant Hodge cohomology for group actions on affine schemes, generalizing work of Simpson and Teleman in characteristic zero. There is a lot of room here for further generalizations (and calculations).

Photo: Susie the cat in Cambridge, November 2000.

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