Dmitrii Zakharov

Hello. I'm a third 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

Publications and Preprints (sorted by topic): 

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, accepted to Combinatorica

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

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

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 

Erdos-Szekeres type problems:

1. Color avoidance for monotone paths with E. Mulrenin and C. Pohoata

2. A sharp Ramsey theorem for ordered hypergraph matchings with L. Sauermann, accepted to Advances in Combinatorics

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 orthogonal bases

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, accepted to PLMS 

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, accepted to JLMS 

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)