Research

MIT PRIMES — Research 2025 · Conference talk · 10/19/2025

MIT PRIMES Research Conference slides (PDF)

Talk abstract. We will begin by exploring the Szemerédi-Trotter theorem in its various equivalent formulations and discussing its significance in incidence geometry. The focus will then shift to sharp constructions for the Szemerédi-Trotter theorem, tracing their development from the earliest examples to recent ones based on generalized arithmetic progressions, including constructions I created through my original research.

MIT PRIMES — Research 2024 · 12/8/2024

MIT PRIMES Research Conference slides (PDF)

Paper abstract. We explore analogs of Erdős's 1946 distinct distance and unit distance problems in d-dimensional p-adic spaces using the Chebyshev distance metric. For these problems, we determine explicit bounds and demonstrate their tightness with simple constructions. Additionally, we study a variation of the distinct distance problem, focusing on maximizing rather than minimizing the number of distinct distances in vector spaces with a non-Archimedean translation-invariant metric. We show that pairwise distinct points in such spaces determine at most N-1 distinct distances.