Mathematics Seminar

Rocky Mountain Algebraic Combinatorics Seminar

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On Galois Automorphisms Acting on Characters and Navarro's Sylow 2-Normalizer Conjectures

Amanda Schaeffer Fry
Metropolitan State

Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalizing Sylow 2-subgroup, which is given in terms of the behavior of the ordinary irreducible characters of G under a specific Galois automorphism. Navarro-Tiep-Vallejo have conjectured a similar statement regarding groups whose Sylow 2-normalizers contain a single irreducible 2-Brauer character. Thanks to reduction theorems proved by myself and Navarro-Vallejo, respectively, a large part of the proofs of these conjectures is to understand the action of this Galois automorphism on characters of groups of Lie type. I will discuss the recent proof of these conjectures, including a description of the action of Galois automorphisms on characters of groups of Lie type. (Some portions of these results are joint work with J. Taylor.)

 

Khovanov's Heisenberg category, moments in free probability, and shifted symmetric functions

Henry Kvinge
Colorado State University

Khovanov introduced a remarkable monoidal category H, known as the Heisenberg category. H is defined via a calculus of planar diagrams and conjecturally categorifies the Heisenberg algebra. In this talk we will explore some of the combinatorics associated with H, showing in particular how the graphical calculus for closed diagrams in H encodes both the algebra of shifted symmetric functions of Okounkov-Olshanski and moments of Kerov's transition measure on Young diagrams.

 

Weber 223
4–6 pm
Friday, September 22, 2017
(Refreshments in Weber 117, 3:30–4 pm)
Colorado State University

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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.

PDF version Previous Seminars: 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