Geometric Analysis, PDEs
Tristan Collins joined the mathematics faculty as Assistant Professor in September 2018. Collins earned his B.Sc at the University of British Columbia in 2009, after which he completed his Ph.D at Columbia University in 2014 under the direction of Duong H. Phong. Subsequently, he had a four year appointment as a Benjamin Peirce Assistant Professor at Harvard University.
Collins has produced important results 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 recent 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 five dimensional sphere. With Shing-Tung Yau and Adam Jacob, Collins is studying the relationship between categorical stability conditions and existence of solutions to differential equations arising from mirror symmetry.
Collins received the 2018 Sloan Research Fellowship; and in 2021, the André Aisenstadt Prize in Mathematics, awarded to a young outstanding Canadian mathematician.