Current Appointments & Affiliations
Assistant Professor of Mathematics
·
2023 - Present
Mathematics,
Trinity College of Arts & Sciences
Assistant Professor of Computer Science
·
2023 - Present
Computer Science,
Trinity College of Arts & Sciences
Recent Publications
Common graphs with arbitrary chromatic number
Journal Article Compositio Mathematica · July 3, 2025 Ramsey’s theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdős conjectured that the random 2-edge-coloring minimizes the number of monochromatic copies of K Full text CiteUndecidability of Polynomial Inequalities in Tournaments
Journal Article International Mathematics Research Notices · June 1, 2025 Many fundamental problems in extremal combinatorics are equivalent to proving certain polynomial inequalities in graph homomorphism densities. In 2011, a breakthrough result by Hatami and Norine showed that it is undecidable to verify polynomial inequaliti ... Full text CiteUndecidability of polynomial inequalities in weighted graph homomorphism densities
Journal Article Forum of Mathematics Sigma · March 18, 2024 Many problems and conjectures in extremal combinatorics concern polynomial inequalities between homomorphism densities of graphs where we allow edges to have real weights. Using the theory of graph limits, we can equivalently evaluate polynomial expression ... Full text CiteRecent Grants
Extremal Combinatorics: Themes and Challenging Problems
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2023 - 2028On Regularity Methods and Applications in Graph Theory
ResearchPrincipal Investigator · Awarded by National Science Foundation · 2020 - 2024View All Grants
Education, Training & Certifications
Stanford University ·
2023
Ph.D.
Princeton University ·
2019
Ph.D.