Rocky Mountain Algebraic Combinatorics Seminar

Upcoming Seminars Schedule

A Potpourri of Projective 2-Designs

Emily King
Colorado State University

Zauner conjectured that for all d there exists a set of d2 equiangular vectors in Cd (SICs or Gabor equiangular tight frames). Another important open problem concerns the existence of d+1 so-called mutually unbiased bases (MUBs) in Cd (maximal sets of MUBs) for any d not equal to a prime power. Both classes of objects are complex projective 2-designs. In this talk, the basics of (weighted) projective 2-designs will be discussed, including their recent generalization to finite fields. A collection of new results will be presented.

Pandey, Paulsen, Prakash, and Rahaman recently proposed an approach to make quantitative progress on Zauner's Conjecture in terms of the entanglement breaking rank of a certain quantum channel. This quantity is equal to the size of the smallest weighted projective 2-design. A construction of an infinite class of projective 2-designs over finite fields will also be presented, time permitting. This construction makes use of difference sets. Finally, in the quaternionic setting, every tight projective 2-design for Hd determines an equi-isoclinic tight fusion frame of d(2d−1) subspaces of Rd(2d+1) of dimension 3. This is joint work with Joey Iverson and Dustin Mixon.


Representation theoretic Hopf algebras and q-chromatic symmetric functions

Lucas Gagnon
UC Boulder

Hopf algebras are a nice way to incorporate algebraic tools into the study of combinatorial objects with recursive structure, and in some cases these combinatorial Hopf structures also encode representation theoretic information. This talk will use a new example to explain this general idea. On the combinatorial side is the chromatic quasisymmetric function, a q-analogue of Stanley’s chromatic symmetric function of a graph; this function can be realized as the image of a homomorphism between Hopf algebra structures on graphs and (quasi-)symmetric functions. On the representation theory side is a collection of GLn(Fq)-modules that arise in the study of the maximal unipotent upper triangular subgroup of GLn(Fq). I will show that the GLn(Fq)-modules are, up to a canonical equivalence, a representation-theoretic realization of some chromatic quasisymmetric functions. Along the way I will define a new Hopf algebra of class functions on the unipotent upper triangular groups and use lots of pictures and examples.


Weber 223
4–6 pm
Friday, May 6, 2022
(Refreshments 3:30–4 pm)
Colorado State University

This is a joint Denver U / UC Boulder / 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:

Apr 8, 2022
Michael Levet,
Apr 7, 2022
Willen De Graaf,
Dec 2, 2021
Leonard Soicher,
Dec 3, 2021
Foster Tom,
Oct 28, 2021
Simon Blackburn,
Oct 15, 2021
Khanh Nguyen,
Oct 15, 2021
Khanh Nguyen,
Oct 1, 2021
Mikl\'os B\'ona, Mei Yin
Sep 17, 2021
Nathan Lindzey, James Wilson
Sep 3, 2021
Sean Griffin, Maria Gillespie
May 7, 2021
Harley Meade,
April 23, 2021
Jonah Blasiak,
April 9, 2021
Kenneth McLaughlin,
March 12, 2021
Marni Mishna,
February 26, 2020
Justin Lynd,
February 12, 2020
Michael Epstein,
December 4, 2020
Fatma Karaoglu,
November 13, 2020
James Wilson, James Wilson
October 30, 2020
Shawn Burkett, Wencin Poh
October 16, 2020
Edinah K. Gnang, Alexander Hulpke
September 18, 2020
Aram Dermenjian,
September 18, 2020
Aram Dermenjian,
August 14 2020
Federico Castillo,
July 24 2020
James Wilson,
July 10 2020
Nathan Lindsey,
June 12, 2020
Maria Gillespie,
May 29, 2020
Henry Adams,
May 8, 2020
Dustin Mixon,
Apr 24, 2020
Peter Cameron,
Apr 3, 2020
Alexander Hulpke,
Feb 28, 2019
Joseph Iverson, John Jasper
Jan 24, 2019
Jonathan Novak,
Dec 6, 2019
Brendon Rhoades, James Wilson
Nov 15, 2019
Joshua Grochow, Maria Gillespie
Nov 1, 2019
Eilidh McKemmie, Michael Epstein
Oct 11, 2019
Martin Kassabov, Eric Moorhouse
Sep 27, 2019
Alexander Hulpke, Tianjuan Xu
Sep 13, 2019
Laura Scull, Emily King
Sep 28, 2018
Farid Aliniaeifard, Brady Tyburski
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 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