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Kyler Siegel's homepage

About me.

I'm an assistant professor in the mathematics department at the University of Southern California. Previously, I was a Ritt Assisant Professor in the mathematics department at Columbia University, and an NSF postdoctoral research fellow and pure mathematics instructor at Columbia during 2017-2019 and at MIT during 2016-2017. During Fall 2021 I was a member at the Institute for Advanced Study. My work is partially supported by NSF grant DMS-2105578.

Research interests.

My background is mostly in symplectic geometry, a branch of mathematics lying somewhere at the intersection of smooth topology, differential geometry, algebraic geometry, and mathematical physics, with some input from string theory. I like to study the complicated algebraic structures arising from pseudoholomorphic curve invariants such as Floer theory and symplectic field theory, which are defined by counting maps from Riemann surfaces into a target space subject to a certain elliptic PDE. At the moment I am particularly interested in interactions between quantitative symplectic geometry (e.g. Hamiltonian flows in Euclidean space) and complex algebraic geometry (e.g. singular algebraic curves).

Contact.

Mathematics papers.

Survey articles.

Some older papers.

Other projects.

Teaching.

Notes.

Conferences and seminars.