Mathematics
Seminar
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Rocky Mountain Algebraic Combinatorics Seminar
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 F
q 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.
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 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
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Department of Mathematics
Fort Collins, Colorado 80523
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