# Algorithms and Geometry Collaboration: Collaboration Scientists

### Zeyuan Allen-Zhu, Sc.D.

Zeyuan Allen-Zhu is a postdoctoral researcher jointly hosted by Princeton University and the Institute for Advanced Study. He obtained his B.S. with highest honors in math and physics from Tsinghua University, and he earned his S.M. and Sc.D. in computer science from the Massachusetts Institute of Technology, under the supervision of Jonathan Kelner and Silvio Micali.

He has received several international awards for his algorithms, including gold medals in the International Olympiad in Informatics, second place in the ACM International Collegiate Programming Contest, and the world championship in the USA Computing Olympiad. His doctoral thesis introduced new frameworks for modeling uncertainty in games and designed new optimization tools for building faster algorithms in computer science. His current research interests lie in algorithm design in its broadest sense and in mathematical modeling for physical, social, economic and biological systems.

### Eshan Chattopadhyay, Ph.D.

Eshan Chattopadhyay is a postdoctoral researcher at the Institute for Advanced Study. He received his Ph.D. from the University of Texas at Austin in 2016, under the supervision of David Zuckerman.

His research focuses on pseudorandomness and its interconnections and applications to other areas of theoretical computer science. For his doctoral thesis, titled “Explicit Two-Source Extractors and More,” he worked on constructing extractors, which are algorithms that convert weak sources of randomness into truly random bits.

### Gil Cohen, Ph.D.

Gil Cohen is a postdoctoral researcher at Princeton University. He obtained his Ph.D. in 2015 from the Weizmann Institute of Science in Israel under the guidance of Ran Raz. In 2015-16 he was a postdoctoral fellow in the theory group at the California Institute of Technology, hosted by Leonard Schulman and Thomas Vidick.

His research is mainly in complexity theory and related mathematics, with a recent focus on explicit constructions of pseudorandom objects such as various types of extractors, Ramsey graphs and pseudorandom generators. He also studies algebraic-geometric codes, lower bounds in various models, cryptography, quantum computation and other topics.

### Pravesh Kothari, Ph.D.

Pravesh Kothari started as a research instructor with a joint appointment at the department of computer science at Princeton University and the Institute of Advanced Study, Princeton, in September 2016. He obtained his Ph.D. in computer science in summer 2016 from the University of Texas at Austin advised by Professor Adam Klivans.

Recently, he has been interested in understanding the sum of squares method, a general algorithmic scheme based on semidefinite programming that has been remarkably successful in algorithm design.

His doctoral dissertation showed strong lower bounds on generic algorithmic schemes based on linear and semidefinite programming. A highlight of this work was establishing strong intractability for fundamental problems in average case complexity on the sum of squares method. In addition, his past research also focused on pseudorandomness and theoretical machine learning.

### William Leeb, Ph.D.

William Leeb is a postdoctoral research associate in the Program in Applied and Computational Mathematics at Princeton University. He received his Ph.D. in mathematics from Yale University in 2015, under the supervision of Ronald Coifman.

His research interests are primarily in metric approximation and computational harmonic analysis, with applications to problems in machine learning and statistical estimation. He is particularly interested in adapting tools from classical signal processing for use in analyzing data sampled from more general domains.

### Piotr Nayar, Ph.D.

Piotr Nayar is a postdoctoral researcher at the Wharton School of the University of Pennsylvania. He obtained his Ph.D. in mathematics from the University of Warsaw in 2014, working under the supervision of Krzysztof Oleszkiewicz.

His research interests include probability, concentration of measure, convex geometry, analysis on the discrete cube, and inequalities in Markov chain theory and information theory.

### Aaron Potechin, Ph.D.

Aaron Potechin is a postdoctoral researcher with a joint appointment with the Simons Collaboration on Algorithms and Geometry at Cornell University and the Institute for Advanced Study. He obtained his Ph.D. in mathematics from the Massachusetts Institute of Technology in 2015, under the supervision of Jonathan Kelner.

His research focuses on computational complexity theory and combinatorics. For his doctorate, he analyzed monotone space complexity via the switching network model. He is currently working to prove lower bounds for the sum-of-squares hierarchy in the planted clique problem.

### Orit Raz, Ph.D.

Orit Raz is a postdoctoral researcher hosted jointly by the Institute for Advanced Study and the Center for Discrete Mathematics and Theoretical Computer Science at Rutgers University. She obtained her Ph.D. from Tel Aviv University in 2016, under the supervision of Micha Sharir.

Her research interests are discrete geometry and combinatorics. She is particularly interested in the interaction of combinatorics with other areas of mathematics.

### Brandon Seward, Ph.D.

Brandon Seward is an assistant professor at the Courant Institute of Mathematical Sciences at New York University. Prior to NYU, he was a postdoc at the Hebrew University of Jerusalem. He received his Ph.D. from the University of Michigan in 2015, under the supervision of Ralf Spatzier.

His research falls into the areas of group theory, dynamics and descriptive set theory. Seward’s work finds inspiration in the connection between groups and the structure of their actions. He studies countable groups from a geometric and combinatorial perspective, as well as group actions from the perspectives of ergodic theory, topological dynamics and Borel dynamics.

### Avishay Tal, Ph.D.

Avishay Tal is a postdoctoral researcher in the Theoretical Computer Science and Discrete Mathematics group at the Institute for Advanced Study. He obtained his Ph.D. in 2015 from the Weizmann Institute of Science, under the guidance of Ran Raz. His thesis title was “Analysis of Boolean Functions in Theoretical Computer Science.”

His research interests include complexity theory, analysis of Boolean functions, circuit and formula lower bounds, decision-tree complexity, pseudorandomness, and the relationship between algorithms and complexity.

### Konstantin Tikhomirov, Ph.D.

Konstantin Tikhomirov is an instructor in the department of mathematics at Princeton University.

He obtained his candidate of sciences degree in Russia in 2011, under the supervision of Sergey Astashkin, and his Ph.D. from the University of Alberta in 2016, supervised by Nicole Tomczak-Jaegermann and Vlad Yaskin. His research interests include probability and combinatorics, as well as discrete and convex geometry.

### Tomasz Tkocz, Ph.D.

Tomasz Tkocz is a postdoctoral research associate in the department of mathematics at Princeton University. He obtained his Ph.D. from the University of Warwick in 2015, working under the supervision of Keith Ball.

His research interests include analysis, probability and convex geometry, with an emphasis on high-dimensional phenomena as well as inequalities in information theory.