Mathematics
Seminar



Rocky Mountain Algebraic Combinatorics Seminar
Normal supercharacter theories and Hopf structures
Farid Aliniaeifard
University of Colorado, Boulder
The concept of Hopf algebras originated from the theory of
algebraic groups and algebraic topology in the mid 20th century and now it has many application in algebraic combinatorics. Also, the notion of a Hopf monoid in the monoidal category of linear spec ies was introduced by Aguiar and Mahajan, and they show the great importance of this concept in algebraic combinatorics with examples that shows many combinatorial objets have Hopf monoid structures . Hopf structures have numerous applications in many other mathematical branches, and now it is a familiar concept in representation theory as the class functions or superclass functions of some tower of groups have Hopf structures where representation theoritic functors give the product and coproduct. In this talk, we give a brief introduction to normal supercharacter theories and Galois c haracter theories, and then we construct several Hopf structure by using these supercharacter theories. (With Nat Thiem and Shawn Burkett)
Subgroups of simple groups of Lie type are maximally diverse
Brady Tyburski
Colorado State University
Highly symmetric geometries over vector spaces over fields are the source of
all but one infinite family of simple groups. These groups of Lie type have
rigid properties labeled by the delicate geometries organized by Dynkin
diagrams and Chevalley’s commutator formulas which govern their products.
Being simple, these groups have enormous conjugacy classes forcing many
subgroups to be isomorphic and allowing for several classification projects
of these subgroups.
In this talk, we demonstrate this rigidity is an illusion. Simple groups of
Lie type and order n have n
^{Θ(logn)} pairwise nonisomorphic
subgroups – the most possible for any group of order n. Similar counts
for the number of conjugacy classes apply, too.
Weber 223
4–6 pm
Friday, Sep 28, 2018
(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.
PDF version
Previous Seminars:
 Sep 7, 2018
 James Wilson,
Alexander Hulpke
 Apr 20, 2018
 Maria Monks Gillespie,
Alistair Savage
 Apr 6, 2018
 Susan Hermiller,
Nathaniel Thiem
 March 23, 2018
 Henry Tucker,
Richard Green
 March 2, 2018
 Nik Ruskuc,
Joshua Grochow
 February 16, 2018
 Hamidreza Chitsaz,
Mark Lewis
 February 2, 2018
 James B. Wilson,
Anton Betten
 November 10, 2017
 Michael Kinyon,
Petr Vojt\v{e}chovsk\'y
 October 20, 2017
 Eric Moorhouse,
William DeMeo
 October 6, 2017
 Spencer Gerhardt,
Joshua Grochow
 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 GluesingLuerssen,
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
