[Theory] FW: Theory Lunch 2023-03-22T17:30:00.000Z

[Christopher Kang]

________________________________
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Sent: Wednesday, March 22, 2023 12:43:18 AM (UTC-06:00) Central Time (US & Canada)
To: Antares Chen <antaresc at uchicago.edu>
Cc: Christopher Kang <ctkang at uchicago.edu>
Subject: Theory Lunch 2023-03-22T17:30:00.000Z


Today's Theory Lunch talk:

Tushant Mittal (University of Chicago): Meeting Ramanujan, well almost!

https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09<https://urldefense.com/v3/__https://uchicago.zoom.us/j/91616319229?pwd=dDdXQnFXeGNubFRkZy9hTDQrcWlXdz09__;!!BpyFHLRN4TMTrA!7RDk1m844JpCxiHNrCPuSz0m2FJkOUHJTaaQp2LKhAIklpP1eZZ0rXTt8OslMUaSjjat2w6D8fAH1oS2S_FzChI1lu1l_-PQzHE$>

Description: A Ramanujan graph is a “spectrally optimal” expander, i.e., a sparse yet very-well connected graph. Optimality here, is with respect to the tug of war between the graph’s sparsity (degree) and its “well-connectedness” (spectral expansion).

The problem at hand is that of amplifying a graph’s quality while preserving its structure. That is, starting from a given (poor-quality) expander, can we deterministically improve it all the way to a Ramanujan one? We show that we can almost get there using Ta-Shma’s breakthrough technique, originally used to construct error-correcting codes.

In this talk, we will introduce the notion of expanders, and, sketch out the wonderful connections between pseudorandomness, error-correction and representation theory. Based on joint work with Fernando Granha Jeronimo, Sourya Roy and Avi Wigderson.

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