Prof. Tristan C Collins

Professor Collins conducts research at the intersection of geometric analysis, partial differential equations, and algebraic geometry. In joint work with Valentino Tosatti, Collins described the singularity formation of the Ricci flow on Kahler manifolds in terms of algebraic data. In work with Gabor Szekelyhidi, he gave a necessary and sufficient algebraic condition for existence of Ricci-flat metrics, which play an important role in string theory and mathematical physics. This result lead to the discovery of infinitely many new Einstein metrics on the 5-dimensional sphere. With Shing-Tung Yau and Adam Jacob, Collins is currently studying the relationship between categorical stability conditions and existence of solutions to differential equations arising from mirror symmetry.