Research Works and Talks

Talks

  1. Hensel and Newton Methods in Valuation Rings by J von zur Gathen

    Course-work presentation (Algebra and Computation), CMI

  2. Algebraic Geometric Codes

    Course-work presentation (Algorithmic Coding Theory II), CMI

    Report

  3. Iterated Mod Problem

    Course-work presentation (Parallel Algorithms and Complexity), CMI

    Slides

Research Internships

  1. Polyhedral Combinatorics and Derandomization of Isolation Lemma

    Supervisor: Rohit Gurjar, IIT Mumbai

    Duration: May - Jul, 2024

    • I read the papers:
      • Bipartite Perfect Matching is in Quasi-NC by Fenner, Gurjar and Thierauf
      • Linear Matroid Intersection Is in Quasi-NC by Gurjar and Thierauf
      • Fractional Linear Matroid Matching is in Quasi-NC by Gurjar, Oki, Raj
      and learned how the idea of giving every cycle a nonzero circulations is generalized from bipartite graphs to matroid intersection polytopes to allowing half intergral vertices in matroid matching polytopes
    • Additionally I read about isolating a path connecting the source vertex and sink vertex in a black-box layered graph from the paper 'Derandomizing Isolation in Space-Bounded Settings' by Melkebeek and Prakriya.

  2. Quantum Property Testing of Junta Functions and Partially Symmetric Functions

    Supervisor: Arijit Ghosh, Indian Statistical Institute, Kolkata

    Duration: Dec, 2023

    • I read the survey 'Quantum boolean functions' by Ashley Montanaro, Tobias J. Osborne and learned about Fourier analysis of boolean functions in Quantum setting and Testing and Learning algorithms for Stabilizer states
    • I learned about Classical Junta Testing from Eric Blais' paper Testing Juntas Nearly Optimally and then read about Quantum Junta Testing Algorithm from 'Testing and Learning Quantum Juntas Nearly Optimally' by Thomas Chen, Shivam Nadimpalli, Henry Yuen
    • Also learned about Partially Symmetric Boolean Functions and it's classical algorthm of testing partially symmetric functions from the paper 'Partially Symmetric Functions are Efficiently Isomorphism-Testable' by Eric Blais, Amit Weinstein, Yuichi Yoshida

  3. Factorization of Arithmetic Circuits in Algebraic Complexity Theory

    Supervisor: Nitin Saxena, IIT Kanpur

    Duration: May - Jul, 2023

    • I read 'Discovering the roots: Uniform closure results for algebraic classes under factoring' by Pranjal Dutta, Nitin Saxena and Amit Sinhababu where I learned how to factorize arithmetic circuits and why VP is closed under factorization. Also leanred how Polynomial Identity Testing and Multivariate Factorizations are equivalent from 'Equivalence of Polynomial Identity Testing and Deterministic Multivariate Polynomial Factorization' by Swastik Kopparty, Shubhangi Saraf, Amir Shpilka
    • Also read the Kaltofen's proof of VP closed under factorization.
    • I also read how VBP is closed under factorization from Amit Sinhababu and Thomas Tierauf's paper 'Factorization of Polynomials given by Arithmetic Branching Programs'
    • I also learned about the difficulties about proving factor closure for VF from the above mentioned two papers
    • I read about factorization of formulas with individual degree bounded form the paper 'Factors of low individual degree polynomials' by Rafael Oliveira and we were trying to remove the condition for formulas

  4. Computational Number Theroy and Algebra for Algebraic Comlexity Theory

    Supervisor: Nitin Saxena, IIT Kanpur

    Duration: Dec, 2023

    • I learned about Computational Number Theory and Algebra from Nitin Saxena's Course and read the book 'Modern Computer Algebra' by Von Zur Gathen and Jurgen Gerhard
    • Also I learned about Arithmetic Circuits from Amir Shpilka's Survey and Ramprasad Saptharishi's Survey on Arithmetic Circuits.