[Theory] UC Theory Seminar

Alexander Razborov razborov at uchicago.edu
Tue Feb 15 10:32:40 CST 2022


Departments of Mathematics & Computer Science
Combinatorics & Theory Seminar

Tuesday, February 252, 3:30pm
John Crerar Library 298

Chris Jones (U of C)

TITLE: Almost-Orthogonal Bases for Inner Product Polynomials

ABSTRACT: We consider low-degree polynomials of inner products between a 
collection of random vectors. We give an explicit, almost-orthogonal 
basis for this vector space of polynomials when the random vectors are 
Gaussian, spherical, or Boolean. In all three cases, our basis admits an 
interesting combinatorial description based on the topology of the 
underlying graph of inner products. In the spherical case, interesting 
examples suggest a connection to graph planarity.

Based on joint work with Aaron Potechin.

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Legal:

This convening is open to all invitees who are compliant with UChicago 
vaccination requirements and, because of ongoing health risks, 
particularly to the unvaccinated, participants are expected to adopt the 
risk mitigation measures (masking and social distancing, etc.) 
appropriate to their vaccination status as advised by public health 
officials or to their individual vulnerabilities as advised by a medical 
professional. Public convening may not be safe for all and carries a 
risk for contracting COVID-19, particularly for those unvaccinated. 
Participants will not know the vaccination status of others and should 
follow appropriate risk mitigation measures.



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