Fernando Granha Jeronimo

About me

I am a postdoc in Avi Wigderson's group at the Institute for Advanced Study (IAS). I obtained my PhD from UChicago, where I was very fortunate to have 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, expanders and high-dimensional expanders, optimization such as the sum-of-squares hierarchy, representation theory of the symmetric group and quantum. Interactions among these areas are very present in my research. I am also particularly intrigued by the many connections between CS theory and mathematics. Glimpses on some of my interests in coding theory and expanders can be found in short talks at IAS here and here.

Papers

The Power of Unentangled Quantum Proofs with Non-negative Amplitudes
(with Pei Wu) - STOC 2023

Fast Decoding of Explicit almost Optimal \(\epsilon\)-balanced \(q\)-ary Codes
              and Fast Approximation of Expanding \(k\)-CSPs - Preprint

Exact Completeness of LP Hierarchies for Linear Codes
(with Leonardo Nagami Coregliano and Chris Jones) - ITCS 2023
[video @ITCS]

Almost Ramanujan Expanders from Arbitrary Expanders via Operator Amplification
(with Tushant Mittal, Sourya Roy and Avi Wigderson) - FOCS 2022 (invited to special issue)
[video @IAS] [video @Princeton]

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

Research Courses

Code Bounds: A (Crude) Course

Reading Groups in Theory

Expansion and Coding Theory (IAS+Princeton University)

Previous External Speaker Series.

Previous Reading Group on Coding Theory

Previous Reading Group on High-dimensional Expanders

Teaching Activities

I was a TA 14 times for various courses during my PhD receiving two (annual) TA prizes from the CS department.

Contact

Email: granha[at]ias[dot]edu