4 papers · 1 filter
On off-diagonal Ramsey numbers for vector spaces over
Zach Hunter, Cosmin Pohoata
For every positive integer , we show that there must exist an absolute constant such that the following holds: for any integer and any red-blue coloring…
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…
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…
Sharp bounds for rainbow matchings in hypergraphs
Cosmin Pohoata, Lisa Sauermann, Dmitrii Zakharov
Suppose we are given matchings of size in some -uniform hypergraph, and let us think of each matching having a different color. How large does need to be…