Rocky Mountain Algebraic Combinatorics Seminar

Optimality v. Symmetry

JM Landsberg
Texas A\&M

Given a polynomial or tensor with symmetry, does an optimal expression for it also have symmetry? A classical example is Fischer's expression for the monomial x1x2...xn as a sum of 2n−1 n-th powers of linear forms. (Ranestad and Schreyer showed his expression is optimal.) The monomial is invariant under permutations of the basis vectors, the permutation group on n elements. Fischer's expression also has symmetry, but under the permutation group on n−1 elements! I will discuss how to exploit such symmetry in two central problems in theoretical computer science: Valiant's algebraic analog of P v. NP and the problem of determining the number of arithmetic operations needed to multiply two nxn matrices. The first is a comparison of the permanent and determinant polynomials. The second became a question in 1969 when Strassen discovered the standard algorithm for multiplying matrices is not the optimal one, which, after much work, has led computer scientists to conjecture that as n grows, it becomes almost as easy to multiply nxn matrices as it is to add them!

The first project is joint work with N. Ressayre, the second is joint work with G. Ballard, L. Chiantini, C. Ikenmeyer, G. Ottaviani and N. Ryder.


Tensor products should be over Lie algebras

James B. Wilson

In 1938 Whitney cleaned up multilinear analysis and gave us tensors as universal products. He made one misstep - tensoring over rings. I will demonstrate the error, and prove that tensors over Lie algebras are in fact universal. Illustrating the power of the right perspective I will characterize simple rings, simple modules, Azumaya rings, simple Lie algebras, Octonions and other exceptional tensors completely by their Lie tensor product. Jointly with U. First and J. Maglione.


Weber 223
4–6 pm
Friday, October 14, 2016
(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 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