Rocky Mountain Algebraic Combinatorics Seminar

Cubic surfaces over $\mathbb{F}_{13}$

Fatma Karaoglu
University of Sussex (UK)

Given five skew lines a1, a2, a3 , a4, a5 with a single transversal b6 such that each set of four ai omitting aj (j = 1, …, 5) has a unique further transversal bj, then the five lines b1, b2, b3, b4, b5 also have a transversal a6. These twelve lines form a double-six. The double six lies on a unique cubic surface with 15 further lines cij given by [ai,bj] ∩[aj, bi].

Hirschfeld in 1964 discussed the existence and the properties of the cubic surfaces over the finite fields of odd and even order and classified over \mathbbF4, \mathbbF7, \mathbbF8, and \mathbbF9. Sadeh in 1985 classified the cubic surfaces in PG(3,11). In this talk, we classify cubic surfaces with twenty-seven lines over the finite field of thirteen elements by classifying 6-arcs not lying on a conic in the plane, although projectively distinct arcs do not necessarily represent projectively distinct surfaces.


Covers of Symplectic Dual Polar Spaces

Eric Moorhouse
University of Wyoming

For q ≡ 1 mod 4, the symplectic dual polar graph of type G=Sp(2n,q) admits a double cover admitting 2×G as a group of automorphisms (M. and Williford, 2015). I will describe how this construction works over the field of real numbers (and possibly also mentioning more general fields). Here the group 2×G is replaced by the relevant metaplectic group, an extension of Sp(2n,F) which is not necessarily split. Here, as in our original finite case, the Maslov index plays a crucial role.


Weber 223
4–6 pm
Friday, February 17, 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:

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