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We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown). | We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown). | ||
+ | |||
+ | ===Sep 25: Jim Demmel (Berkeley) === | ||
+ | ''Communication Avoiding Algorithms for Linear Algebra and Beyond'' | ||
+ | |||
+ | Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices. | ||
+ | |||
===March 28: Michael Lacey (GA Tech) === | ===March 28: Michael Lacey (GA Tech) === |
Revision as of 11:02, 30 August 2013
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Fall 2013
date | speaker | title | host(s) | ||
---|---|---|---|---|---|
Sept 6 | Matt Baker (Georgia Institute of Technology) | Riemann-Roch for Graphs and Applications | Ellenberg | ||
Sept 13 | Uri Andrews (University of Wisconsin) | ||||
Sept 20 | Valerio Toledano Laredo (Northeastern) | Gurevich | |||
Wed, Sept 25, 2:30PM | Ayelet Lindenstrauss | Meyer | |||
Wed, Sept 25 (LAA lecture) | Jim Demmel (Berkeley) | Communication Avoiding Algorithms for Linear Algebra and Beyond | Gurevich | ||
Thurs, Sept 26 (LAA lecture) | Jim Demmel (Berkeley) | Implementing Communication Avoiding Algorithms | Gurevich | ||
Sept 27 (LAA lecture) | Jim Demmel (Berkeley) | Communication Lower Bounds and Optimal Algorithms for Programs
that Reference Arrays |
Gurevich | ||
Oct 4 | Frank Sottile (Texas A&M) | Caldararu | |||
Oct 11 | Amie Wilkinson (Chicago) | WIMAW (Cladek) | |||
Tues, Oct 15, 4PM (Distinguished Lecture) | Alexei Borodin (MIT) | Integrable probability I | Valko | ||
Wed, Oct 16, 2:30PM (Distinguished Lecture) | Alexei Borodin (MIT) | Integrable probability II | Valko | ||
No colloquium due to the distinguished lecture | |||||
Oct 25 | Paul Garrett (Minnesota) | Gurevich | |||
Nov 1 | Allison Lewko (Microsoft Research New England) | Stovall | |||
Nov 8 | Tim Riley (Cornell) | Dymarz | |||
Nov 15 and later | Reserved | Street |
Spring 2014
date | speaker | title | host(s) |
---|---|---|---|
Jan 24 | |||
Jan 31 | Urbashi Mitra (USC) | Gurevich | |
Feb 7 | David Treumann (Boston College) | Street | |
Feb 14 | |||
Feb 21 | |||
Feb 28 | |||
March 7 | |||
March 14 | |||
Spring Break | No Colloquium | ||
March 28 | Michael Lacey (GA Tech) | The Two Weight Inequality for the Hilbert Transform | Street |
April 4 | Kate Jushchenko (Northwestern) | Dymarz | |
April 11 | Risi Kondor (Chicago) | Gurevich | |
April 18 (Wasow Lecture) | Christopher Sogge (Johns Hopkins) | A. Seeger | |
April 25 | Charles Doran(University of Alberta) | Song | |
May 2 | Lek-Heng Lim (Chicago) | Boston | |
May 9 | Rachel Ward (UT Austin) | WIMAW |
Abstracts
Sep 6: Matt Baker (GA Tech)
Riemann-Roch for Graphs and Applications
We will begin by formulating the Riemann-Roch theorem for graphs due to the speaker and Norine. We will then describe some refinements and applications. Refinements include a Riemann-Roch theorem for tropical curves, proved by Gathmann-Kerber and Mikhalkin-Zharkov, and a Riemann-Roch theorem for metrized complexes of curves, proved by Amini and the speaker. Applications include a new proof of the Brill-Noether theorem in algebraic geometry (work of by Cools-Draisma-Payne-Robeva), a "volume-theoretic proof" of Kirchhoff's Matrix-Tree Theorem (work of An, Kuperberg, Shokrieh, and the speaker), and a new Chabauty-Coleman style bound for the number of rational points on an algebraic curve over the rationals (work of Katz and Zureick-Brown).
Sep 25: Jim Demmel (Berkeley)
Communication Avoiding Algorithms for Linear Algebra and Beyond
Algorithm have two costs: arithmetic and communication, i.e. moving data between levels of a memory hierarchy or processors over a network. Communication costs (measured in time or energy per operation) already greatly exceed arithmetic costs, and the gap is growing over time following technological trends. Thus our goal is to design algorithms that minimize communication. We present algorithms that attain provable lower bounds on communication, and show large speedups compared to their conventional counterparts. These algorithms are for direct and iterative linear algebra, for dense and sparse matrices, as well as direct n-body simulations. Several of these algorithms exhibit perfect strong scaling, in both time and energy: run time (resp. energy) for a fixed problem size drops proportionally to the number of processors p (resp. is independent of p). Finally, we describe extensions to algorithms involving arbitrary loop nests and array accesses, assuming only that array subscripts are affine functions of the loop indices.
March 28: Michael Lacey (GA Tech)
The Two Weight Inequality for the Hilbert Transform
The individual two weight inequality for the Hilbert transform asks for a real variable characterization of those pairs of weights (u,v) for which the Hilbert transform H maps L^2(u) to L^2(v). This question arises naturally in different settings, most famously in work of Sarason. Answering in the positive a deep conjecture of Nazarov-Treil-Volberg, the mapping property of the Hilbert transform is characterized by a triple of conditions, the first being a two-weight Poisson A2 on the pair of weights, with a pair of so-called testing inequalities, uniform over all intervals. This is the first result of this type for a singular integral operator. (Joint work with Sawyer, C.-Y. Shen and Uriate-Tuero)
Past talks
Last year's schedule: Colloquia 2012-2013