Dmitrii Zakharov

Hello. I'm a fourth year graduate student at MIT working with Prof. Larry Guth. I am interested in various topics around extremal and additive combinatorics, discrete geometry, harmonic analysis and connections between them.

Email: zakhdm@mit.edu

CV: file link 

Publications and Preprints: 

Heilbronn's triangle problem:

1. Lower bounds for incidences with A. Cohen and C. Pohoata Inventiones Mathematicae (2025)

2. Upper bounds for Heilbronn’s triangle problem in higher dimensions, BLMS (2024)

3. A new upper bound for the Heilbronn triangle problem with A. Cohen and C. Pohoata 

Additive combinatorics:

1. Generalized Arithmetic Kakeya with C. Pohoata

2. Sharp bound for the Erdős-Straus non-averaging set problem with H.T. Pham

3. Ruzsa's problem on Bi-Sidon sets with J. Pach, Combinatorica (2025)

4. An explicit economical additive basis with V. Jain, H.T. Pham and M. Sawhney, accepted to CPC

5. Most integers are not a sum of two palindromes, Cambridge Phil. Soc. Math. Proc. (2024)

6. On skew corner-free sets with C. Pohoata

7. On the Erdős-Ginzburg-Ziv Problem in large dimension with L. Sauermann, accepted to AJM

8. Zero subsums in vector spaces over finite fields with C. Pohoata, Algebra & Number Theory (2022)

9. Convex geometry and the Erdos–Ginzburg–Ziv problem, accepted to Discrete Analysis

Erdos-Szekeres type problems:

1. Color avoidance for monotone paths with E. Mulrenin and C. Pohoata, accepted to Discrete Analysis

2. A sharp Ramsey theorem for ordered hypergraph matchings with L. Sauermann, Advances in Combinatorics (2025)

3. Convex polytopes from fewer points with C. Pohoata, Duke (2025)

4. On the number of high-dimensional partitions with C. Pohoata, PLMS (2024)

Various problems in discrete geometry and combinatorics:

1. On the minimal period of integer tilings with I. Laba, BLMS (2025)

2. On sets of orthogonal exponentials on the disk

3. Spherical sets avoiding orthonormal bases, accepted to Comptes Rendus Mathématique

4. On the trifference problem for linear codes with C. Pohoata, IEEE Trans. on Information Theory (2022)

Turan-type problems:

1. Essentially tight bounds for rainbow cycles in proper edge-colourings with N. Alon, M. Bucic, L. Sauermann and O. Zamir, PLMS (2025)

2. The Extremal Number of Surfaces with A. Kupavskii, A. Polyanskii, I. Tomon, IMRN (2021)

3. Random multilinear maps and the Erdos box problem with D. Conlon and C. Pohoata, Discrete Analysis (2022)

4. Norm hypergraphs with C. Pohoata 

5. Turan-type results for intersection graphs of boxes with I. Tomon, CPC (2020)

Extremal set theory, intersecting families etc:

1. Sharp bounds for rainbow matchings in hypergraphs with C. Pohoata and L. Sauermann, JLMS (2025)

2. Cutting corners with A. Kupavskii and A. Sagdeev

3. Spread approximations for forbidden intersections problems with A. Kupavskii, Adv. in Math. (2024)

4. On the size of maximal intersecting families, CPC (2024)

5. Regular bipartite graphs and intersecting families with A. Kupavskii, JCTA (2018)

Acute sets:

1. Acute sets, DCG (2019)

2. The right acute angles problem? with A. Kupavskii, Eur. J. Comb. (2020)

Colorings of distance graphs:

1. Chromatic numbers of Kneser-type graphs, JCTA (2020)

2. Chromatic Numbers of Some Distance Graphs, Math. Notes (2020)

3. Clique-chromatic numbers of graphs of intersections with A. Raigorodskii, Math. Notes (2019)