[Colloquium] Tushant Mittal’s Candidacy Exam/ May 3, 2024

[Devin Davis]

This is an announcement of Tushant Mittal’s Candidacy Exam. =================================================

Candidate: Tushant Mittal

Date: May 3, 2024.

Time: 3 PM.

Location: TTIC 529, Fifth Floor

Remote location: https://uchicago.zoom.us/j/99961926847?pwd=V1lTY1lQTk9xV2QyTDROS1F2V1VPZz09<https://urldefense.com/v3/__https:/uchicago.zoom.us/j/99961926847?pwd=V1lTY1lQTk9xV2QyTDROS1F2V1VPZz09__;!!BpyFHLRN4TMTrA!7MsNkC6oS1tvwx24WRwpmiKA3lr72GwJITf1Y60lcjdw5ZDQnENi6HFqzcbJ_v7NPZHU6Irht5J8jZHxCsWNEic$>

Meeting ID: 999 6192 6847 Passcode: 146080


Title: Expanders with Abelian symmetries and Quantum LDPC Codes

Abstract:
One method to construct expander graphs with abelian symmetries is via the technique of graph lifts introduced by Bilu and Linial. For an abelian group G acting on the set [𝓁], an (G,𝓁)-lift of a graph X is a graph obtained by replacing each vertex by 𝓁 copies, and each edge by a matching corresponding to the action of an element of G.

In this talk, we will see how to analyze the expansion of lifted graphs and give explicit constructions of expanders via this approach. As a corollary, we obtain explicit quantum lifted product codes with almost linear distance and explicit classical quasi-cyclic LDPC codes with a wide range of circulant sizes.

This is based on joint work with Fernando Granha Jeronimo, Ryan O'Donnell, Pedro Paredes, and Madhur Tulsiani.

Advisors: Janos Simon, Madhur Tulsiani

Committee: Janos Simon, Madhur Tulsiani, Ryan O'Donnell, and Bill Fefferman.


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