Additive Combinatorics:

• The partition-vs-analytic rank conjecture is true up to a logarithmic factor

• A first step towards the Polynomial Gowers Inverse conjecture over large fields

• 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  some of 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

• Nearly-polynomial inverse theorem for the U^d norm in degree d+1 (with T. Milo), submitted. *

• Schur complements for tensors and multilinear commutative rank (with D. Zhu), submitted. *

• A weak regularity lemma for polynomials (with D. Woodruff), to appear in the Proceedings of the 41st Computational Complexity Conference (CCC '26). *

• Slice rank and partition rank of the determinant (with A. Lampert), Proceedings of the 17th Innovations in Theoretical Computer Science conference (ITCS '26).

• Uniform stability of Ranks (with D. Zhu). *

• Quasi-linear Relation between Partition and Analytic Rank (with D. Zhu), submitted. *
  For a previous version of this result with a poly-logarithmic factor, see: Quasi-linear Relation between Partition and Analytic Rank.

• Partition and Analytic Rank are Equivalent over Large Fields (with A. Cohen), Duke Mathematical Journal 172 (2023), 2433-2470. *

• Sharp Effective Finite-Field Nullstellensatz (with J. Yu), The American Mathematical Monthly 130 (2023), 720-727. *

• Structure vs. Randomness for Bilinear Maps (with A. Cohen), Discrete Analysis 12 (2022).  *
  A conference version appeared in the Proc. of the 53rd ACM Symposium on Theory of Computing (STOC 2021), 800-808.

• Geometric Rank of Tensors and Subrank of Matrix Multiplication (with S. Kopparty and J. Zuiddam), Discrete Analysis 1 (2023). 
  A conference version appeared in the Proc. of the 35th Computational Complexity Conference (CCC 2020), 1-21.

• Limitations on Regularity Lemmas for Clustering Graphs (with N. Alon), Advances in Applied Mathematics 124 (2021).

• Traces of Hypergraphs (with N. Alon and N. Solomon), Journal of the London Mathematical Society 100 (2019), 498-517.

• A Tight Bound for Hypergraph Regularity (with A. Shapira), Geometric and Functional Analysis 29 (2019), 1531-1578.

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

• A Sparse Regular Approximation Lemma (with A. Shapira), Transactions of the American Mathematical Society 371 (2019), 6779-6814.

• Decomposing a Graph Into Expanding Subgraphs (with A. Shapira), Random Structures and Algorithms 52 (2018), 158-178.

• Constructing Near Spanning Trees with Few Local Inspections (with R. Levi, D. Ron, R. Rubinfeld and A. Shapira), Random Structures and Algorithms 50 (2017), 183-200.

• An Improved Lower Bound for Arithmetic Regularity (with K. Hosseini, S. Lovett and A. Shapira), Mathematical Proceedings of the Cambridge Philosophical Society 161 (2016), 193-197.

• A Short Proof of Gowers' Lower Bound for the Regularity Lemma (with A. Shapira), Combinatorica, 36 (2016), 187-194.

• Exact Bounds for Some Hypergraph Saturation Problems (with A. Shapira), Journal of Combinatorial Theory Series B 111 (2015), 242-248.

A full version of this paper: (arXiv)

• Ramsey Theory, Integer Partitions and a New Proof of the Erdos-Szekeres Theorem (with A. Shapira), Advances in Mathematics 262 (2014), 1107-1129.

• Complexity Lower Bounds through Balanced Graph Properties, Proc. of the 27th IEEE Conference on Computational Complexity (CCC 2012), 159-169.

Courses:

• Complexity & Computational Models (2024, 2025)

• Linear Algebra & Matrix Methods (2021, 2023)

• Vector Calculus (2022)

• Calculus III (2020, 2022)

• Analytic Geometry (2021)

• 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)

• arXiv: Combinatorics section, Computational Complexity section

• ECCC

• Advances in Mathematics

• Combinatorica

• Combinatorics, Probability and Computing

• Discrete Analysis

• Duke Mathematical Journal

• Geometric and Functional Analysis

• Journal of Combinatorial Theory, Series B

• Journal of the London Mathematical Society

• Random Structures & Algorithms

• Theory of Computing

• The American Mathematical Monthly