Rocky Mountain Algebraic Combinatorics Seminar

Monodromy and K-theory of Schubert Curves via Generalized Jeu de Taquin

Maria Monks Gillespie
University Of California, Berkeley

Schubert curves are the spaces of solutions to certain one-dimensional Schubert problems involving flags osculating the rational normal curve. The real locus of a Schubert curve is known to be a natural covering space of RP1, so its real geometry is fully characterized by the monodromy of the cover. It is also possible, using K-theoretic Schubert calculus, to relate the real locus to the overall (complex) Riemann surface.

The monodromy operator turns out to be the commutator of jeu de taquin rectification and promotion on certain skew Young tableaux. We give a new local algorithm for computing this commutator, and use it to provide purely combinatorial proofs of some of the connections to K-theory. If time permits, we will also describe some of the geometric consequences of our combinatorial results. This is joint work with Jake Levinson.


Automorphisms of generalized Sylvester Hadamard matrices

Dane Flannery
National University of Ireland, Galway

Cocyclic development of pairwise combinatorial designs was discovered by Warwick de Launey and Kathy Horadam in the early 1990s. We first recount some algebraic essentials of the theory. Building on this, we proceed to discuss recent new results about the cocyclic development of a certain infinite family of generalized Hadamard matrices (which contain the Sylvester Hadamard matrix family as a special case). Specifically, we characterise the `indexing groups' of the matrices considered as cocyclic designs. Many open questions remain; we mention some of these. This is joint work with Ronan Egan (also at National University of Ireland, Galway).


Weber 223
4–6 pm
Friday, December 4, 2015
(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:

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