Rocky Mountain Algebraic Combinatorics Seminar

Upcoming Seminars Schedule

Homotopy theory for graphs

Laura Scull
Fort Lewis College, Durango, CO

Homotopy theory studies deformations of space, an inherently continuous concept. In this talk, we will explore how to translate this concept to the discrete category of graphs. We will see how to define homotopy for graphs by using categorical concepts, and then show how to analyze what these translate to concretely, and how we can break down a deformation of graph maps into moves of one vertex at a time. We also discuss how to recognize when two graphs are the same up to deformation ("homotopy equivalent"), and look at developing homotopy invariants for graphs. No prior knowledge of either homotopy theory or graph theory will be needed, and many examples will be given. Parts of this work are joint with Dr. Tien Chih at MSU Billings, and parts were developed in collaboration with Fort Lewis College undergraduate students Coleman Kane, Diego Novoa and Jonathon Thompson.


Combinatorics and Group Symmetry in [Hilbert Space] Frame

Emily King
Colorado State University

Frames are collections of vectors in Hilbert spaces which have reconstruction properties akin to orthonormal bases. In order for such a representation system to be robust in applications, one often asks that the vectors be geometrically spread apart; that is, the pairwise angles between the lines they span should be as large as possible. It ends up that structures in algebraic combinatorics, like difference sets and balanced incomplete block designs (BIBDs), can be used in different ways to construct optimal configurations. Furthermore, the linear dependencies of the vectors are often encoded as BIBDs. The orbit of a vector under a group actions sometimes also yields optimal configurations. There is at least one infinite class of frames, the so-called Gabor-Steiner ETFs which have both group symmetry and a combinatorial construction. In this talk, these and other connections between frames and algebraic combinatorics, combinatorial design theory, algebraic graph theory, and more will be presented. A couple of open conjectures in frame theory and quantum information theory will also be discussed, with one in particular possibly being amenable to combinatorial methods. Frames, difference sets, BIBDs, and affine geometry will be defined and explained, making at least part of the talk accessible to a more general audience.


Weber 223
4–6 pm
Friday, Sep 13, 2019
(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:

Sep 28, 2018
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