Mathematics
Seminar



Rocky Mountain Algebraic Combinatorics Seminar
Tensor Isomorphism
Joshua Grochow
University of Colorado, Boulder
Full title: Tensor Isomorphism: completeness, graphtheoretic methods, and consequences
for Group Isomorphism
We consider the problems of testing isomorphism of tensors,
pgroups,
cubic forms, algebras, and more, which arise from a variety of areas,
including machine learning, group theory, computational complexity, and
cryptography. Despite a perhaps seeming similarity with Graph Isomorphism,
the currentbest algorithms for these problems (when given by bases) are
still exponential  for most of them,
q^{n2} over GF(
q). Similarly,
while efficient practical software exists for Graph Isomorphism, for these
problems even the best current software can only handle very small instances
(e.g., 10 x 10 x 10 over GF(13)). We will discuss what is known (some of it
very recent) about algorithms and complexity for these problems. A small
spoiler: They are all equivalent! Even isomorphism of dtensors and
isomorphism of 3tensors. Various parts based on joint works with V. Futorny
& V. V. Sergeichuk (Lin. Alg. Appl. , 2019; preprint arXiv:1810.09219), Y.
Qiao (arXiv:1907.00309), and P. Brooksbank, Y. Li, J. B. Wilson, & Y. Qiao
(arXiv:1905.02518).
Enumerating Anchored Permutations with Bounded Gaps
Maria Gillespie
CSU
Suppose you start on the bottom stair of a staircase with n stairs and climb
to the top stair, using up or down steps of no more than k stairs at a time, such that every stair is stepped on exactly once. In how many different ways can you climb the stairs?
We will show that there always exists a finitedepth homogeneous linear
recurrence relation to enumerate such stair climbing patterns, which may be
expressed as permutations with bounded differences of consecutive entires.
We provide explicit recursions for k=2 and k=3, resolving a conjecture
that was previously listed on OEIS A249665. We then use techniques from
spectral graph theory to give asymptotic bounds for the sequences for all
k.
This is joint work with Ken G. Monks and Ken M. Monks.
Weber 223
4–6 pm
Friday, Nov 15, 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.
PDF version
Previous Seminars:
 Nov 1, 2019
 Eilidh McKemmie,
Michael Epstein
 Oct 11, 2019
 Martin Kassabov,
Eric Moorhouse
 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 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
