Guy Moshkovitz

About Me

I am an Assistant Professor in the Department of Mathematics at the City University of New York (Baruch College). Previously, I was a postdoctoral researcher at the Institute for Advanced Study in Princeton and DIMACS. In 2018 I was a postdoctoral researcher at Harvard University in the Special Year on Combinatorics and Complexity.

I completed my Ph.D. studies at the School of Mathematics at Tel Aviv University, advised by Prof. Asaf Shapira, and my M.Sc. studies at the School of Computer Science under the supervision of Prof. Oded Regev.


I have a broad interest in: Extremal Combinatorics, Graph/Hypergraph Theory, Algebraic Geometry, probabilistic and algebraic methods in Combinatorics, and their applications to Theoretical Computer Science.

I also mentor at the NYC Discrete Math REU.

Email: guymoshkov at gmail.com

Research Highlights

Additive Combinatorics:

  • A first step towards the Polynomial Gowers Inverse conjecture.

  • A proof, using tools from algebraic geometry, that several notions of rank for 3-tensors are equivalent --- and applications to computer science.

Quanta Magazine covered these works: Mathematicians Find Structure in Biased Polynomials.

Extremal Combinatorics:

  • A proof that the hypergraph regularity lemma cannot have a primitive recursive bound, settling a long-standing open question & confirming prediction of Tao [JCTA '06]

  • A variant of the famous Sauer-Shelah Lemma for a wide range of parameters (and a new variant of the famous Kruskal-Katona Theorem)

  • A near-resolution of the Erdos-Szekeres Ramsey problems

  • A short and simple proof of the celebrated lower bound for the graph regularity lemma due to Gowers [GAFA '97]

Theoretical Computer Science:

  • Lower bounds for multiple results on graph decompositions, nearly matching bounds by Arora-Barak-Steurer [J. ACM '15] and many others

  • A new, combinatorial approach to arithmetic circuit lower bounds, via the polynomial method

Papers

For a simplified version of this result for 3-uniform hypergraphs, see: A Tight Bound for Hypergraph Regularity I

A full version of this paper: (arXiv)

Teaching

Courses:

  • Vector Calculus (2022)

  • Linear Algebra & Matrix Methods (2021)

  • Analytic Geometry (2021)

  • Calculus III (2020)

  • Introduction to Discrete Structures I (2019)

  • Introduction to Discrete Mathematics (2016)

  • Calculus B2 (2014, 2015, 2016)

  • Linear Algebra A1 (2013, 2014, 2015)

  • Differential and Integral Calculus (2012, 2013)

  • Linear Algebra (2012)

Teaching awards: 2014, 2016 (Rector's list for excellence in teaching)