I am a postdoc in Prof. Avi Wigderson group at the Institute for Advanced Study. Before, I was a PhD student at UChicago, where I was very fortunate to have Prof. Madhur Tulsiani as my advisor. I received a B.Sc. and M.Sc. degrees from Unicamp Brazil (my home country) and also received an engineering degree from Telecom Paris (France) as part of a double degree program.
I have been investigating problems involving coding theory, the sum-of-squares hierarchy, high-dimensional expanders and representation theory of the symmetric group. I am particularly intrigued by the (many) intersection(s) of CS theory and mathematics.
Exact Completeness of LP Hierarchies for Linear Codes
(with Leonardo Nagami Coregliano and Chris Jones) - Preprint
Almost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification
(with Tushant Mittal, Sourya Roy and Avi Wigderson) - FOCS 2022 (invited to special issue)
A Complete Linear Programming Hierarchy for Linear Codes
(with Leonardo Nagami Coregliano and Chris Jones) - ITCS 2022
Near-linear Time Decoding of Ta-Shma's Codes via Splittable Regularity
(with Shashank Srivastava and Madhur Tulsiani) - STOC 2021
[video @STOC'21] [slides @STOC'21] [video @JTW'20] [slides @Junior Theorists Workshop'20]
Unique Decoding of Explicit \(\epsilon\)-balanced Codes Near the Gilbert-Varshamov Bound
(with Dylan Quintana, Shashank Srivastava and Madhur Tulsiani) - FOCS 2020 (invited to special issue)
[longer video @FOCS20] [longer slides @FOCS20] [slides general CS audience]
Sum-of-Squares Lower Bounds for Sherrington-Kirkpatrick via Planted Affine Planes
(with Mrinalkanti Ghosh, Chris Jones, Aaron Potechin and Goutham Rajendran) - FOCS 2020
Tighter Bounds on the Independence Number of the Birkhoff Graph
(with Leonardo Nagami Coregliano) - European J. of Combinatorics
Approximating Constraint Satisfaction Problems on High-Dimensional Expanders
(with Vedat Levi Alev and Madhur Tulsiani) - FOCS 2019
A Constrained Random Walk Through Coding Theory
(Fernando Granha Jeronimo) - Dissertation
I was a TA 14 times for various courses during my PhD.