Research Works and Talks
Talks
Hensel and Newton Methods in Valuation Rings by J von zur Gathen
Course-work presentation (Algebra and Computation), CMI
Algebraic Geometric Codes
Course-work presentation (Algorithmic Coding Theory II), CMI
Iterated Mod Problem
Course-work presentation (Parallel Algorithms and Complexity), CMI
Research Internships
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
- 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.
- I read the papers:
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
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
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.