Mathematics
Seminar



Rocky Mountain Algebraic Combinatorics Seminar
Large Erd\H{o}sKoRado Sets in Polar Spaces
Ferdinand Ihringer
University of Regina
An ErdösKoRado set (EKR set) Y of { 1, …, n} is a family of ksets, which
pairwise
intersect nontrivially. A nontrivial problem is to provide tight upper bounds on Y and classify all
examples, which obtain that bound.
Erdös, Ko and Rado proved Y ≤ \binomn−1k−1 for n ≥ 2k. Equality holds for n ≥ 2k+1 if and only if Y is the
family of all ksets, which contain one fixed element.
If we equip the vector space \mathbb
F_{q}^{n} with a reflexive, nondegenerate sesquilinear form,
then the subspaces that vanish on that form are a polar space, socalled
isotropic subspaces.
The largest isotropic subspaces of a polar space are called generators. We say
that two generators intersect trivially if the dimension of their intersection is 0.
An
EKR set of a polar space is a set of pairwise nontrivially intersecting generators.
We present various results on EKR sets for polar spaces, in particular we will discuss
some recent socalled weak HiltonMilner type results.
Searching for Balanced Sets
Gavin King
University of Wyoming
Let X be a finite set of unit vectors in some Euclidean space.
Define R_{α, β}(x,y) for α, β ∈ \mathbb R and x, y ∈ X as
R_{α, β}(x, y) = {z ∈ X: 〈z,x〉 = α,〈z,y〉 = β} satisfying:
 For each x,y, R_{α, β}(x,y)=R_{α, β}(y,x).
 For any α, there is a constant p_{α} such that for all
x, ∑R_{α, α}(x,x)=p_{α} x.
 For each α, β, γ there exists a constant m_{β,γ}^{α} such that for any pair of vectors v_{i}, v_{j} with 〈v_{i}, v_{j} 〉 = α, we have
∑R_{β, γ}(v_{i},v_{j})−∑R_{γ, β}(v_{i}, v_{j}) = m_{β, γ}^{α} (v_{i}−v_{j}),
regardless of our choice of v_{i} and v_{j}.
Balanced sets are a notion intricately tied to the concept of association
schemes, and especially to the association schemes with the Qpolynomial
property. I will be discussing the existing work on balanced sets as well as
my own, such as a classification of balanced sets with small numbers of
inner products, and ways to search for balanced sets connected to
permutation groups.
Weber 223
4–6 pm
Friday, May 5, 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.
PDF version
Previous Seminars:
 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
