Rocky Mountain Algebraic Combinatorics Seminar

Upcoming Seminars Schedule

Polynomial-time 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 Fq up to projective equivalence. A closer look at the Clebsch map leads to a classification algorithm. As a by-product, 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.

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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 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