Rocky Mountain Algebraic Combinatorics Seminar

Topological generation of algebraic groups (and applications)

Spencer Gerhardt
Colorado State University

Class generation problems arise in a number of different contexts, often as a tool for solving a seemingly unrelated problem. In this talk we consider a particular generation problem for algebraic groups which has applications to random generation of finite simple groups and linear representations of algebraic groups.

Let G be a simple algebraic group defined over a sufficiently large field. Let C1,..., Ce be some conjugacy classes of G. We consider the following question: what are necessary and sufficient conditions for the existence of a tuple (x1,...,xe) ∈ C1×...×Ce such that 〈x1,...,xe〉 is Zariski dense in G? The solution yields new results on generic stabilizers in linear representation of algebraic groups, and can be used to strengthen existing results on random (r,s)-generation of finite groups of Lie type. Some work in this talk is joint with Tim Burness and Robert Guralnick.


Representation theory and additive combinatorics in algorithms for matrix multiplication

Joshua Grochow
University of Colorado, Boulder

How hard it is to multiply matrices is a central open question in computational complexity, with ties to algebraic geometry and representation theory. In this talk I'll survey some recent work on matrix multiplication which brings together algorithms, representation theory, and additive combinatorics. Highlights include a transparent proof (joint with C. Moore) of Strassen's original 1969 algorithm for matrix multiplication - which was the first to beat O(n3) steps - and using ideas from the resolution of the Cap Set Conjecture to deepen our understanding of the Cohn-Umans group-theoretic approach to matrix multiplication (joint with J. Blasiak, T. Church, H. Cohn, E. Naslund, W. F. Sawin, and C. Umans).


Weber 223
4–6 pm
Friday, October 6, 2017
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University

This is a joint Denver U / UC Boulder / UC Denver / U of Wyoming / CSU seminar that meets biweekly. Anyone interested is welcome to join us at a local restaurant for dinner after the talks.

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Previous Seminars:

September 22, 2017
Amanda Schaeffer Fry, Henry Kvinge
September 8, 2017
Peter Mayr, James B. Wilson
May 5, 2017
Ferdinand Ihringer, Gavin King
April 21, 2017
Vladimir D. Tonchev, Morgan Rodgers
April 7, 2017
Jason Williford, Anton Betten
March 24, 2017
Isabella Novik, Peter Brooksbank
March 3, 2017
Jintai Ding, Curtis Bennett
February 17, 2017
Fatma Karaoglu, Eric Moorhouse
February 3, 2017
Tim Penttila, James B. Wilson
December 2, 2016
Jim Fowler, Andrew Kelley
November 11, 2016
Joseph Gersch, Joshua Maglione
October 28, 2016
John MacLaren Walsh, Henry Adams
October 14, 2016
JM Landsberg, James B. Wilson
September 30, 2016
Alexander Hulpke, Oscar Levin
September 16, 2016
Delaram Kahrobaei, Amit Patel
June 23, 2016
Jason Cantarella, Michal Adamaszek
April 29, 2016
Nick Loehr, Jason Williford
April 15, 2016
Alexander Hulpke, Klaus Lux
April 1, 2016
Eamonn O'Brien, Izabella Stuhl
February 19, 2015
James Wilson, Anton Betten
December 4, 2015
Maria Monks Gillespie, Dane Flannery
November 13, 2015
Richard Green, Tim Penttila
October 23, 2015
Christina Boucher, Sylvia Hobart
October 9, 2015
Josh Maglione, Ghodratollah Aalipour
September 25, 2015
Ross McConnell, Henry Adams
September 11, 2015
James B. Wilson, Tim Penttila
May 8, 2015
Amanda Schaeffer Fry, Peter Brooksbank
April 24, 2015
Heide Gluesing-Luerssen, Phil DeOrsey
March 6, 2015
Felice Manganiello, Eric Moorhouse
February 20, 2015
Anton Dzhamay, Anton Betten
February 6, 2015
Alexander Hulpke, Morgan Rodgers
December 5, 2014
Stefaan De Winter, Gretchen Matthews
November 14, 2014
Greg Coxson, Tom Dorsey
October 31, 2014
Octavio Paez Osuna, Sylvia Hobart
October 10, 2014
Takunari Miyazaki, Eric Moorhouse
September 26, 2014
Elissa Ross, Anton Betten
September 12, 2014
Petr Vojtěchovský, Alexander Hulpke
May 9, 2014
Philip DeOrsey, Tim Penttila
April 25, 2014
William J Martin, Jason Williford
April 11, 2014
Victor Pambuccian, George Shakan
March 7, 2014
Nathan Lindzey, Jens Harlander
February 21, 2014
Ross McConnell, Anton Betten
November 22, 2013
Justin Hughes, Josh Maglione

Department of Mathematics
Fort Collins, Colorado 80523