[Theory] [Theory Lunch] Chris Jones (U. of Chicago), Wednesday 1/26, 12:30pm-1:30pm, JCL 390.

[Antares Chen]

Hi everyone,

This will be the *last logistics announcement* before the start of theory
lunch this week. A few updates:

   - We now have a calendar
   <https://calendar.google.com/calendar/u/0/embed?src=c_osgf1c1qemdras8mu7l7pdhjrs@group.calendar.google.com&ctz=America/Chicago>
   for theory lunch events. Event listings will include speaker information +
   zoom links to attend the presentation online.
   - We have a web page <https://orecchia.net/event/theory-lunch/> where we
   will post theory lunch logistics, announcements, speaker schedule and any
   additional speaker material.
   - Subsequent posts to the UChicago theory email list will only include a
   weekly announcement for the current week's presentation with an email
   subject formatted similar to that above. The talk announcement will follow
   below.

Thank you and hope to see you on Wednesday,
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*

*Zoom: *[link
<https://uchicago.zoom.us/j/95725383918?pwd=OHl5WHVIL3RORVRWQ2RBdk43R1pQdz09>
]

*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.

*Note*: In line with current departmental guidance, lunch will not be
served at the talk.

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