Tony Yue Yu received his PhD in 2016 from Université Paris Diderot under the supervision of Maxim Kontsevich and Antoine Chambert-Loir. He works on non-archimedean geometry, tropical geometry and mirror symmetry. He aims to build a theory of enumerative geometry in the setting of Berkovich spaces. Such a theory will give us a new understanding of the enumerative geometry of Calabi-Yau manifolds, as well as the structure of their mirrors. It is also intimately related to the theory of cluster algebras and wall-crossing structures. Tony has been appointed as a Clay Research Fellow for a term of five years beginning 1 September 2016.
Will Sawin obtained his PhD in 2016 from Princeton University, under the supervision of Nicholas Katz. Since then he has worked with Emmanuel Kowalski as a Junior Fellow at ETH Zürich.
Sawin’s research is wide ranging, but focused on the interactions of analytic number theory and algebraic geometry. Amongst the many areas in which he has made ground-breaking contributions are the application of étale cohomology to estimates of exponential sums over finite fields and, with Tim Browning, the adaptation of classical counting arguments in analytic number theory to explore compactly supported cohomology in spaces of interest in algebraic geometry. In a recent paper with Kowalski and Philippe Michel, he used ℓ-adic cohomology to derive new bounds on certain bilinear forms that regularly arise in the study of automorphic forms. There are important applications, for example in the theory of twisted L-functions. He has also made many wider contributions to the mathematical community, not least through regular posts on diverse topics on the MathOverflow website.
Will was appointed as a Clay Research Fellow for a term of three years beginning 1 July 2018.
John Pardon received his PhD in 2015 from Stanford University under the supervision of Yakov Eliashberg. His most recent work concerns the construction of virtual fundamental cycles on moduli spaces of holomorphic curves in symplectic geometry. He is also interested in geometry and low-dimensional topology. John received his AB in Math from Princeton University in 2011. John was appointed as a Clay Research Fellow for a term of five years beginning 1 July 2015.
Aleksandr Logunov gained his PhD in 2015 under the supervision of Viktor Havin at the Chebyshev Laboratory, St Petersburg State University. After two years as a postdoctoral fellow at Tel-Aviv University, he moved to the Institute for Advanced Study at Princeton. He held his Clay Research Fellowship at Princeton University.
Together with Eugenia Malinnikova, he was given a Clay Research Award in 2017. The award recognised Logunov’s and Malinnikova’s introduction of a novel geometric combinatorial method to study doubling properties of solutions to elliptic eigenvalue problems. This led to the solution of long-standing problems in spectral geometry, for instance the optimal lower bound on the measure of the nodal set of an eigenfunction of the Laplace-Beltrami operator in a compact smooth manifold (Yau and Nadirashvili’s conjectures).
Aleksandr was invited to speak on his work at the 2018 International Congress of Mathematicians in Rio. He was appointed as a Clay Research Fellow for a term of two years beginning 1 July 2018.