Mathematics
Seminar



Rocky Mountain Algebraic Combinatorics Seminar
Polynomialtime isomorphism tests for groups of most finite orders
James B. Wilson
Colorado State University
Using statistics of prime factorizations of integers and structures of
finite groups we demonstrate that the complexity of group isomorphism is
polynomial time for almost all orders of groups. Reports on joint work
with H. Dietrich, Monash University.
The Clebsch Map from a Combinatorial Perspective
Anton Betten
Colorado State University
Cubic surfaces with 27 lines are all birational. What this means is that
we can always find a polynomial map which takes one surface to another.
This key observation was made by Alfred Clebsch (1833  1872) in the
mid 18hundereds. The map that Clebsch found takes a cubic surface and
maps it to a projective plane. Six lines on the surface are special.
They collapse to points under this map. Knowing the configuration of
these six points is equivalent to knowing the surface up to projective
equivalence. Clebsch may have taken his motivation from earlier work of
Chasles (1793  1880), who considered a similar map from the
hyperboloid to the plane. Today, anybody can create these polynomial
maps with a few lines of Maple code, for instance (Noam Elkies has an
example on his website, for instance).
In the talk, we will consider cubic surfaces over a finite field
(those fields did not really exist at the time of Clebsch and Chasles,
hence were not considered in their work). We are interested in classifying
cubic surfaces with 27 lines over \mathbb F
_{q} up to projective
equivalence. A closer look at the Clebsch map leads to a classification
algorithm. As a byproduct, a counting formula can be derived which
counts the number of distinct cubic surfaces with 27 lines in PG(3,q).
This is joint work with Fatma Karaoglu from the University of Sussex
in the UK.
Weber 223
4–6 pm
Friday, February 2, 2018
(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:
 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
