
# Pravesh K. Kothari's homepage

Research Instructor
Department of Computer Science, Princeton University

## Brief Bio

Before moving to Princeton, I received my PhD from UT Austin advised by Adam Klivans, where I was partially supported by the Simons Award for Graduate Students in Theoretical Computer Science, and Bachelor's degree from IIT Kanpur advised by Surender Baswana.

## Contact

Email: "lastname" at cs dot princeton dot edu
Offices: Simonyi 007 (IAS, Default) and 413 (35, Olden Street, Princeton)

## Research

I am broadly interested in theoretical computer science. Currently, a major focus in my research is to understand the power of the sum-of-squares method in the context of 1) algorithm design - in order to obtain fast approximation algorithms for problems in Machine Learning, Combinatorial Optimization and beyond and 2) average case complexity - in order to gather evidence of hardness and computational vs statistical complexity tradeoffs for solving random/typical instances of hard optimization problems.

## Selected Recent Papers (for all papers, see here)

Approximating Rectangles by Juntas and a Weakly Exponential Lower Bound for LP Relaxations of CSPs
With Raghu Meka and Prasad Raghavendra
STOC, 2017
Invited to SICOMP Special Issue for STOC 2017 Show Abstract

A Nearly Tight Sum-of-Squares Lower Bound for Planted Clique
With Boaz Barak , Sam Hopkins , Jon Kelner , Ankur Moitra and Aaron Potechin
FOCS 2016. [Video- IAS CS/DM Seminar] [Boaz's WOT post]
Invited to SICOMP Special Issue for FOCS 2016 Show Abstract

SoS and Planted Clique: Tight Analysis of MPW Moments
at all Degrees and an Optimal Lower Bound at Degree Four

With Samuel B. Hopkins and Aaron Potechin
SODA 2016
Invited to the ACM Transactions on Algorithms, Special Issue for SODA 2016
(Conference version to be merged with Tight Lower Bounds for Planted Clique in the Degree-4 SOS Program by Tselil Schramm and Prasad Raghavendra .) Show Abstract

Provable Submodular Minimization Using Wolfe's Algorithm
With Deeparnab Chakrabarty and Prateek Jain
NIPS 2014 (Oral Presentation) Show Abstract