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Pravesh K. Kothari's homepage

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Research Instructor
Department of Computer Science, Princeton University
Institute for Advanced Study, Princeton

Brief Bio

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.

I will join the Computer Science Department (and the diverse theory group) at CMU in Fall 2019.

Recent/Upcoming Events/Talks

TTI-Chicago Summer Workshop on High-Dimensional Robust Statistics [Aug 2018]
Oberwolfach Workshop on Complexity Theory, Oberwolfach, Germany [Nov 2018]
ICERM Workshop on Real Algebraic Geometry and Optimization, Providence, RI [Oct'18]
IAS Computer Science and Discrete Mathematics Seminar, Princeton [Feb 6]
ITCS 2018, Cambridge, MA [Jan 11-14]
ICTS Workshop on Algorithms and Optimization, Bangalore, India [Jan'18]
MIT Theory of Computation Colloquium [Dec 5 2017]
Simons Workshop on Hierarchies, Extended Formulations and Matrix-Analytic Techniques, Berkeley, CA [Nov 2017]
Columbia Theory Seminar [Oct 27]
Guest Lecture: Seminar on New Directions in Theoretical Machine Learning, Princeton CS [Oct 2017]
Oberwolfach Workshop on Proof Complexity and Beyond, Oberwolfach, Germany [Aug 2017]

Service

PC Member APPROX/RANDOM 2018 , SODA 2019

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. My recent research has focused on investigating meta-algorithms such as the Sum of Squares method and Extended Formulations. Specifically, I have worked on
1) obtaining fast algorithms for problems arising in unsupervised machine learning, combinatorial optimization, quantum information and cryptography and, on the flip side,
2) obtaining general lower-bound techniques to gather evidence for tight computational vs statistical complexity trade-offs for some basic problems arising in average-case complexity.

Selected Recent Papers (for all papers, see here)

Small-Set Expansion in Shortcode Graph and the 2-to-1 Conjecture
With Boaz Barak and David Steurer
A generally accessible article on the recent proof of the 2-to-2 games conjecture that partly relies on this work.
Show Abstract

Efficient Algorithms for Outlier-Robust Regression
With Adam Klivans and Raghu Meka
COLT 2018 (to appear). Show Abstract

An Analysis of t-SNE Algorithm for Data Visualization
With Sanjeev Arora and Wei Hu
COLT 2018 (to appear). Show Abstract

Outlier-Robust Moment Estimation Via Sum-of-Squares
With David Steurer Show Abstract

STOC 2018 (to appear) (conference version to be merged with the paper below)

Better Agnostic Clustering Via Relaxed Tensor Norms
With Jacob Steinhardt Show Abstract

STOC 2018 (to appear) (conference version to be merged with the paper above)

Sum-of-Squares Meets Nash: Lower Bounds for finding any equilibrium
With Ruta Mehta Show Abstract

STOC 2018 (to appear)

Limits on Low-Degree Pseudorandom Generators (Or: Sum-of-Squares Meets Program Obfuscation)
With Boaz Barak , Zvika Brakerski and Ilan Komargodski
EUROCRYPT 2018 (to appear) Show Abstract

The power of sum-of-squares for detecting hidden structures
With Samuel B. Hopkins , Aaron Potechin , Prasad Raghavendra , Tselil Schramm and David Steurer
FOCS 2017 Show Abstract

Quantum Entanglement, Sum-of-Squares and the Log-Rank Conjecture
With Boaz Barak and David Steurer
STOC, 2017 Show Abstract

Sum-of-Squares Lower Bounds for Refuting any CSP
With Ryuhei Mori , Ryan O'Donnell and David Witmer
STOC, 2017 Show Abstract

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