Rocky Mountain Algebraic Combinatorics Seminar

Upcoming Seminars Schedule

Automorphic Loops: A Survey and Recent Progress

Michael Kinyon
University of Denver

The multiplication group Mlt(G) of a group G is just the permutation group generated by all left and right translations, which is essentially what you get when you think of both the left and right regular representations simultaneously. The inner automorphism group Inn(G) can then be characterized as the stabilizer in Mlt(G) of the identity element of G.

In the nonassociative world, if Q is a loop, then the same definitions give the multiplication group Mlt(Q) and the inner mapping group Inn(Q), but the latter does not necessarily act as automorphisms of Q. A loop is said to be automorphic if every inner mapping is an automorphism. Thus automorphic loops include groups but much more that.
This talk will start with a survey of automorphic loops, including a potted history and ending with the current state of the art. The main open problem is the existence or nonexistence of a finite, simple, nonassociative, automorphic loop, and I will talk about results both published and unpublished regarding them.


On the classification of involutory latin quandles

Petr Vojt\v{e}chovsk\'y
University of Denver

Quandles are binary algebras designed for colorings of arcs in knot diagrams that are invariant under Reidemeister moves. Quandles also solve the quantum Yang-Baxter equation. It is therefore of considerable interest to construct well-structured families of quandles. In this talk I will present a classification of involutory latin quandles of order p*q (using group actions on periodic sequences over finite fields) and also a computer enumeration of involutory latin quandles of odd prime power order (using central extensions).


Weber 223
4–6 pm
Friday, November 10, 2017
(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:

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