About me

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.

Please, feel free to reach out to me if you are interested in working together.


Papers

Exact Completeness of LP Hierarchies for Linear Codes
(with Leonardo Nagami Coregliano and Chris Jones) - Preprint


Fast Decoding of Explicit almost Optimal \(\epsilon\)-balanced \(q\)-ary Codes
              and Fast Approximation of Expanding \(k\)-CSPs
- 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
[video @IAS]


Explicit Abelian Lifts and Quantum LDPC Codes
(with Tushant Mittal, Ryan O’Donnell, Pedro Paredes and Madhur Tulsiani) - ITCS 2022
[video @IAS]


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


List Decoding of Direct Sum Codes
(with Vedat Levi Alev, Dylan Quintana, Shashank Srivastava and Madhur Tulsiani) - SODA 2020
[slides @SODA20]


Approximating Constraint Satisfaction Problems on High-Dimensional Expanders
(with Vedat Levi Alev and Madhur Tulsiani) - FOCS 2019

Other Writings

A Constrained Random Walk Through Coding Theory
(Fernando Granha Jeronimo) - Dissertation

Teaching Activities

I was a TA 14 times for various courses during my PhD.

Contact

Email: granha[at]ias[dot]edu

2022 Fernando Granha Jeronimo
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