2 citations · 3 across the 22 of their papers we have counts for
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Generalized Arithmetic Kakeya
Cosmin Pohoata, Dmitrii Zakharov
Around the early 2000-s, Bourgain, Katz and Tao introduced an arithmetic approach to study Kakeya-type problems. They showed that the Euclidean Kakeya conjecture follows from a nat…
Color avoidance for monotone paths
Eion Mulrenin, Cosmin Pohoata, Dmitrii Zakharov
In 2014, Moshkovitz and Shapira determined the tower height for hypergraph Ramsey numbers of tight monotone paths. We address the color-avoiding version of this problem in which on…
Expanding polynomials for sets with additive structure
Sanjana Das, Cosmin Pohoata, Adam Sheffer
The expansion of bivariate polynomials is well-understood for sets with a linear-sized product set. In contrast, not much is known for sets with small sumset. In this work, we prov…
Lower bounds for incidences
Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov
Let be a set of points in the unit square and let be a set of -tubes such that passes through . We prove a lower bound for the numbe…