Frontiers in Geometry Conference 2022

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The Frontiers in Geometry Conference will take place during the period August 1-12, 2022, at the Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. The conference is a two-week activity (a one-week graduate summer school, followed by a one-week conference) that is co-organized by Paul Feehan (Rutgers University), Lenhard Ng (Duke University), Peter Ozsváth (Princeton University), Yongbin Ruan (Zhejiang University), and Paul Seidel (MIT). Claudio Arezzo, Acting Head of the Mathematics Section, ICTP, is the local meeting co-organizer. The scientific themes of the event include low-dimensional and symplectic topology, knot theory, and analytical aspects of gauge theory. The summer school is led by five eminent early-career mathematicians and the conference features twenty-five well-known mathematicians, all leading scientists. The conference website links to that of the graduate summer school and will be developed and maintained by ICTP: http://indico.ictp.it/event/9706There has been exciting recent progress in low-dimensional and symplectic topology, spurred by the growing understanding of Floer homologies and Khovanov homology. Moreover, there is promise of entirely new invariants and methods, which arise out of progress in the analytical aspects of gauge theory (new compactness theorems and higher-dimensional gauge-theoretic equations) and of pseudo-holomorphic curves. For example, there is an ongoing effort to use the Kapustin-Witten equations to extract a more intrinsically geometric definition of the Jones polynomial and Khovanov homology and, eventually, new generalizations of those invariants. Gains in the understanding of any one of these topics will enrich the understanding of all. The proposed meeting will bring together experts at the frontier of research in these topics from around the world. The conference is expected to generate transfers of knowledge, new collaborations, and a cross-fertilization of ideas, and further inspire graduate students and early-career mathematicians. Because of the location of ICTP within a geographic concentration of leading European mathematics departments and near good public transportation facilities and because of ICTP's commitment to hosting mathematicians from developing countries as well, the U.S.-based participants will have the opportunity to interact with a distinguished and diverse group of mathematical leaders and rising stars. The meeting will thus help to support, train and encourage the next generation of researchers and strengthen international connections among them.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.