Fernando Granha Jeronimo

About me

I am an assistant professor of CS in the Siebel School of Computing and Data Science at the University of Illinois Urbana-Champaign.

My research is in theoretical computer science (TCS). I have been investigating problems mainly involving the following areas:

• - Coding Theory,
• - Expanders and High-dimensional Expanders,
• - Optimization such as the Sum-of-Squares hierarchy, and
• - Quantum Computing.

Interactions among these areas are very present in my research. In particular, I love expansion (broadly defined) since it provides an amazing lens to explore and understand phenomena in all the above areas. 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.

Email: granha[at]illinois[dot]edu

Teaching

CS 598: Expansion, Codes, and Optimization both Classical and Quantum (Fall 2024)

Papers

Explicit Codes approaching Generalized Singleton Bound using Expanders
(with Tushant Mittal, Shashank Srivastava and Madhur Tulsiani)

List Decoding Explicit Binary Codes Near Capacity at (semi-)Structured Centroids
(Fernando Granha Jeronimo)

Coherence in Property Testing: Quantum-Classical Collapses and Separations
(with Nir Magrafta, Joseph Slote and Pei Wu) - QIP 2025

Higher-order Delsarte Dual LPs: Lifting, Constructions and Completeness
(with Leonardo Nagami Coregliano, Chris Jones, Nati Linial and Elyassaf Loyfer)

List Decodable Quantum LDPC Codes
(with Thiago Bergamaschi, Tushant Mittal, Shashank Srivastava and Madhur Tulsiani)

Pseudorandom and Pseudoentangled States from Subset States
(with Nir Magrafta and Pei Wu) - TQC 2024 (poster)

Dimension Independent Disentanglers from Unentanglement and Applications
(with Pei Wu) - CCC 2024

List Decoding of Tanner and Expander Amplified Codes from Distance Certificates
(with Shashank Srivastava and Madhur Tulsiani) - FOCS 2023

The Power of Unentangled Quantum Proofs with Non-negative Amplitudes
(with Pei Wu) - STOC 2023 (QIP 2024)
[video @STOC'23]

Fast Decoding of Explicit almost Optimal \(\epsilon\)-balanced \(q\)-ary Codes and
              Fast Approximation of Expanding \(k\)-CSPs
(Fernando Granha Jeronimo) - RANDOM 2023

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

Short Bio

Prior to UIUC, I was a Simons-Berkeley fellow kindly hosted in Venkatesan Guruswami's group, and thankfully supported in part as a Google Research Fellow. I had a wonderful experience as a postdoc in Avi Wigderson's group at the Institute for Advanced Study (IAS). I obtained my PhD from UChicago. 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.

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

Past Teaching Activities

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