[Theory] Announcing First Theory Lunch

[Antares Chen]

Hi everyone,

Before the end of Fall quarter, we sent out a scheduling poll for a weekly
theory lunch. Thank you all for your interest! Based on these responses,
we'll be holding theory lunch each week on *Wednesday 12.30pm to 1.30pm* in
the *John Crerar Library Room 390* (auditorium at the center of the third
floor).

Our first meeting will be held on *Wednesday 1/26/22* with Chris Jones
speaking about "An Almost Orthogonal Basis for Inner Product Polynomials"
(abstract below). The talk is currently planned to be given both *in-person*,
and *online through Zoom*; more information about this, with relevant links
and logistics will be sent out next week.

Unfortunately, the first theory lunch will likely be held without food due
to current covid restrictions at UChicago. We're working with the PSD to
determine the earliest date where we can safely hold in-person events with
catering.

Finally, an important note from the UChicago PSD. 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.

Thank you and hope you're staying safe!
Antares

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*Date:* January 26, Wednesday
*Time: *12:30pm CT
*Location: *JCL 390

*Speaker:  Chris Jones (University of Chicago)*

*Title: An Almost Orthogonal Basis of Inner Product Polynomials*

*Abstract:* Consider drawing i.i.d. n-dimensional standard Gaussian vectors
d_i. We study functions of the d_i which are rotationally invariant, i.e.
they only depend on the pairwise angles and norms of the d_i. For example,
computing E <d_1,d_2><d_2,d_3><d_3,d_4><d_4,d_1>, some beautiful
combinatorics arises based on the topology of the underlying graph. With
the intent of doing Fourier analysis, we give an (almost) orthogonal basis
for this space. We also study the cases of Boolean and spherical d_i; when
the d_i are spherical instead of Gaussian, interesting examples suggest a
connection to graph planarity. Based on joint work with Aaron Potechin.
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