Rocky Mountain Algebraic Combinatorics Seminar

$Q$-polynomial association schemes with at most 5 classes.

Jason Williford
University of Wyoming

An association scheme can be thought of as a combinatorial generalization of a finite transitive permutation group, where the notion of global symmetry is replaced by certain local symmetry conditions. The definition of association scheme is due to Bose and Shimamoto in 1939, in the context of the design of experiments. Since then it has found connections to coding theory, group theory, and finite geometry.

In the 1973 thesis of Philippe Delsarte, the author identified two special classes of association schemes: the so-called P-polynomial and Q-polynomial schemes. The schemes that are P-polynomial are precisely those generated by a distance-regular graph, in which Delsarte gave natural analogues to coding theory. Similarly, Delsarte gave a natural analogue to design theory in Q-polynomial schemes.
However, Q-polynomial schemes have no analogous combinatorial definition. Consequently, much less is known about them then their P-polynomial counterparts. In this talk, we will discuss what is known about primitive 3-class Q-polynomial schemes, and imprimitive Q-polynomial schemes with at most 5 classes. We will also present new tables of parameter sets summarizing known constructions, non-existence results and open cases.


Cubic Surfaces over a Finite Field

Anton Betten

Classifying cubic surfaces over the complex numbers was one of the highlights of nineteenth century mathematics. The geometry is beautiful, with 27 lines contained in each surface. In this talk, we will consider the problem of classifying cubic surfaces over small finite fields. There seems to be strong opinions about how this should be done. Manin in 1974 asks the rhetorical question: "What use is it to know, for instance, the number of coplanar triples of lines or the number of double Schlaefli sixfolds?" We will discuss practical algorithms to classify cubic surfaces via their Schlaefli double sixes and via their tritangent planes.


Weber 223
4–6 pm
Friday, April 7, 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.

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Previous Seminars:

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