Farzan Byramji

I am a third year PhD student in the UCSD theory group, where I am fortunate to be advised by Shachar Lovett and Russell Impagliazzo. Previously, I was a student in the CSE department of IIT Kanpur, where I worked with Rajat Mittal and got a BT-MT dual degree.

My research interests lie broadly in complexity theory and combinatorics. I am particularly interested in questions about propositional proof systems, Boolean circuits, decision trees and communication protocols.

Email: fbyramji at ucsd dot edu

Research

• Lower Bounds for Bit Pigeonhole Principles in Bounded-Depth Resolution over Parities
  with Russell Impagliazzo
  Manuscript, 2025
  [arXiv | ECCC]

• Lifting to Randomized Parity Decision Trees
  with Russell Impagliazzo
  RANDOM 2025
  [ECCC]

• Relations between monotone complexity measures based on decision tree complexity
  with Vatsal Jha, Chandrima Kayal, and Rajat Mittal
  COCOON 2024
  [arXiv | ECCC]

• Query complexity of Boolean functions on slices
  Discrete Mathematics, 2024
  [arXiv]

• A bijection between symmetric valleys in Dyck paths and even degree internal vertices in ordered trees
  INTEGERS, 2022