Mathematics
Seminar



Rocky Mountain Algebraic Combinatorics Seminar
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unpublished regarding them.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
YangBaxter equation. It is therefore of considerable interest to construct
wellstructured 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.
PDF version
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 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
