In this project I tried to extend the idea of bounding the number of vectors in the integer lattice which has $L_1$ norm less than twice the shortest vector for 0-1 matrices with $k$-column sum to derandomize isolation lemma over more general polytopes. Additionally I read about isolating a path connecting in a black-box layered graph.

In this project I learned about Quantum Boolean Functions and some basics of Quantum algorithms for property testing from the Survey by Montanaro-Osborne, 2008. I learned about Classical and Quantum Junta Function testing. We worked on finding a more efficient Quantum Algorithm for testing Paritally symmetric boolean functions by improving the classical algorithm in Blais-Weinstein-Yoshida's Paper.

In the project I learned factorization techniques and closure of of VP and VBP under factorization. I also read closure of VF with bounded individual degree from Oliviera, 2016 paper and we worked on removing the bounded individual degree condition

I did a basic study of Computational Number Theory and Algebra from Nitin Saxena's course and about Arithmetic Circuits from Amir Shpilka's Survey and Ramprasad Saptharishi's Survey on Arithmetic Circuits.