# Computer Science and Discrete Mathematics (CSDM)

## Uniform words are primitive (cont'd)

What is the distribution of the element obtained by a fixed word in the letters \(a\), \(b\), \(c\),..., such as \(ab\), \(a^2\), or \(aba^{-2}b^{-1}\)? More concretely, do these new random elements have uniform distribution?

In general, a word \(w\) in the free group \(F_k\) is called uniform if it induces the uniform distribution on every finite group \(G\). So which words are uniform?

## Breaking \(e^n\) barrier for deterministic poly-time approximation of the permanent and settling Friedland's conjecture on the Monomer-Dimer Entropy

## Uniform words are primitive

What is the distribution of the element obtained by a fixed word in the letters \(a\), \(b\), \(c\),..., such as \(ab\), \(a^2\), or \(aba^{-2}b^{-1}\)? More concretely, do these new random elements have uniform distribution?

In general, a word \(w\) in the free group \(F_k\) is called uniform if it induces the uniform distribution on every finite group \(G\). So which words are uniform?

## Colouring graphs with no odd holes

## A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions

## A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions

The focus of the talk will be towards achieving the following goal:

Given a degree-d polynomial threshold function, deterministically approximating the fraction of satisfying assignments up to o(1) error in polynomial time. Along the way, we'll first survey some important existing results in this area.

## Search games and Optimal Kakeya Sets

## Results and open problems in theory of quantum complexity

1. Quantum vs. classical query complexity

2. Quantum vs. classical query complexity for almost all inputs

3. Quantum counterparts of Valiant-Vazirani theorem (reducing NP to unique-NP)