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Lethbridge Number Theory and Combinatorics Seminar
Date: November 23, 2015
Time: 12:00-12:50pm
Lecturer(s): Mohammad Bardestani (University of Ottawa)
Location: University of Lethbridge
Topic: Isotropic quadratic forms and the Borel chromatic number of quadratic graphs
Description (in plain text format):
For a field F and a quadratic form Q defined on an n-dimensional vector space V over F, let G_Q, called the quadratic graph associated to Q, be the graph with the vertex set V where vertices u, w in V form an edge if and only if Q(v − w) = 1. Quadratic graphs can be viewed as natural generalizations of the unit-distance graph featuring in the famous Hadwiger-Nelson problem. In the present talk, we will prove that for a local field F of characteristic zero, the Borel chromatic number of G_Q is infinite if and only if Q represents zero non-trivially over F.
The proof employs a recent spectral bound for the Borel chromatic number of Cayley graphs, combined with an analysis of certain oscillatory integrals over local fields. As an application, we will also answer a variant of question 525 proposed in the 22nd British Combinatorics Conference 2009.
Other Information:
Location: C630 University Hall
Contact:
Barb Hodgson | hodgsonb@uleth.ca | (403) 329-2470 | uleth.ca/artsci/math-computer-science
