IAS: getting settled

Using the study in Institute housing

As we start the second week of the fall term at the Institute, the backbone for the Topology of Algebraic Varieties program has been settled. (This forms a small subset of all the relevant mathematical activities at the Institute and the university.)

The regular weekly round of program activities is:
11:00 am Preprint seminar, organized by János Kollár
2:00 pm Talk 1 of the double seminar joint with Princeton
3:30 pm Talk 2 of the double seminar joint with Princeton

11:15 am Program seminar

Some specific events of interest are:
Workshop on Fundamental Groups and Periods, IAS, October 13–17
Barry Mazur: Minerva Lectures, Princeton University, October 14, 15, 17
AGNES, University of Pennsylvania, October 31–November 2

Details and more information on program activities are available on the Institute website and on the informal program website.

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IAS Workshop 13-17 October 2014: Fundamental Groups and Periods

This workshop is part of the topical program “The Topology of Algebraic Varieties” which will take place during the 2014–2015 academic year at the Institute for Advanced Study. One theme of the workshop is to present the latest work on the possible fundamental groups of algebraic varieties. The other theme is periods of integrals, such as multiple zeta values, which are related to fundamental groups via Hodge theory, and also mixed Tate motives.

Registration for this workshop is now open at the IAS site: http://www.math.ias.edu/wfgp.

There is also an unofficial website that aims to give information about activities surrounding the Institute special year: http://www.topalg2014.org/.

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Save the date: October 25-26, 2014

What: AMS Fall Western Section (official site: here)
Where: San Francisco State University, San Francisco
Who: Invited addresses by Kai Behrend, Kiran Kedlaya, Julia Pevtsova,
Burt Totaro

The meeting includes the following special sessions (among others — sessions continue to be added):

Algebraic Geometry
Renzo Cavalieri, Colorado State University renzo@math.colostate.edu
Noah Giansiracusa, University of California, Berkeley
Burt Totaro, University of California, Los Angeles

Categorical Methods in Representation Theory
Eric Friedlander, University of Southern California
Srikanth Iyengar, University of Nebraska, Lincoln
Julia Pevtsova, University of Washington julia@math.washington.edu

Polyhedral Number Theory
Matthias Beck, San Francisco State University mattbeck@sfsu.edu
Martin Henk, Universität Magdeburg
Joseph Gubeladze, San Francisco State University

And James H. Simons will give the 2014 Einstein Public Lecture at this meeting on October 25, 2014.

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WAGS @ Boulder, 12-13 April 2014


The next edition of WAGS (Western Algebraic Geometry Symposium) is coming up: 12-13 April at the University of Colorado at Boulder. See you there.

Speakers are:
Daniel Erman, Wisconsin
Brendan Hassett, Rice
Elham Izadi, UC San Diego
Martijn Kool, UBC
James McKernan, UC San Diego
Martin Olsson, Berkeley

Image from lowjumpingfrog on flickr via pet360.

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The Chow ring of a finite group (AGNES talk)

Chow rings

I’m speaking at the AGNES workshop on the last weekend in April, at Stony Brook (click here for more workshop information).

Title: The Chow ring of a finite group

Abstract: A natural class of singular varieties consists of the quotients of vector spaces by linear actions of a finite group G. We can ask what the Chow group of algebraic cycles is, for such a quotient. By taking larger and larger representations of G, we can package these Chow groups into a ring, called the Chow ring of the classifying space of G, or (for short) the Chow ring of G. It maps to the cohomology ring of G, usually not by an isomorphism.

We present the latest tools for computing Chow rings of finite groups. These tools give complete calculations for all “small” groups and many other finite groups. A surprising point is that Chow rings become “wild,” in a precise sense, for some slightly larger finite groups.

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AGNES @ Stony Brook, April 25-27


The Spring 2014 workshop of AGNES (Algebraic Geometry Northeastern Series) is the weekend of Friday-Sunday, April 25-27, in the Simons Center at Stony Brook University. There are funds to support participants. The registration deadline is March 15th.

The list of confirmed and tentative speakers is as follows.

Ron Donagi (Pennsylvania)
Eugene Gorsky (Columbia)
Sandor Kovacs (Washington)
James McKernan (UC San Diego)
Zsolt Patakfalvi (Princeton)
Michael Thaddeus (Columbia)
Burt Totaro (UCLA)
Cynthia Vinzant (Michigan)

The webpage for the workshop is at the following URL.


There is a registration form on the webpage. The deadline is March 15th, but particularly for funding purposes, participants are encouraged to register as soon as possible.

Additional details will be announced on the workshop webpage. We hope to see you at AGNES Spring 2014.

Organizers: Samuel Grushevsky, Radu Laza, Robert Lazarsfeld, Jason Starr

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Hodge structures of type (n, 0, …, 0, n)

innesUPDATE (5/3/2014): Now published.
The citation is:

B. Totaro (2014) “Hodge Structures of Type
(n, 0, … , 0, n),” International Mathematics Research Notices, rnu063, 24 pages.

ORIGINAL POST: I’ve posted a new paper on the arXiv:
Hodge structures of type (n,0,…,0,n)
The abstract: This paper determines all the possible endomorphism algebras for polarizable Q-Hodge structures of type (n,0,…,0,n). This generalizes the classification of the possible endomorphism algebras of abelian varieties by Albert and Shimura. As with abelian varieties, the most interesting feature of the classification is that in certain cases, every Hodge structure on which a given algebra acts must have extra endomorphisms.

(“In the crook of his free arm nestled the dignified Hodge.”)

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