Semon Rezchikov

About Me

I am a Veblen Research Instructor and NSF Postdoctoral Fellow in the Mathematics Department at Princeton University and the Institute of Advanced Study.

As a mathematician, I am interested in symplectic geometry, which is the geometry of phase spaces of physical systems, or more generally the geometry of the principle of least action. While the importance of symplectic geometry was known since Lagrange, the subject remained underdeveloped until the 80s, when Gromov's introduction of pseudoholomorphic curve theory, a nonlinear version of complex analysis, led to a continual transformation of the field. It turns out that the pseudoholomorphic curves in a symplectic manifold are organized into elaborate algebraic structures, which can be interpreted as a supersymmetric field theory which mirrors simpler structures related to polynomials, and incidentally gives rise to a quantum generalization of topology. Remarkably, these exotic connections between disparate areas of mathematics and physics can be used to solve concrete problems in chaotic dynamics and even children's problems about drawing rectangles inside curves.

My research has focused on foundational aspects of the invariants built from pseudoholomorphic curves, as well as on applications of these "quantum" modifications of topology to dynamical systems theory. I have also recently been working on complexifying symplectic geometry, which turns out to be connected to a quaternionic version of pseudoholomorphic curve theory and to the mysterious subject of 3D mirror symmetry.

Beyond that, I am interested in applications of mathematics. The boundaries between physics, computer science, statistics, and mathematics have never been clear, and their interaction between remains a source of new ideas for me. In particular, I am working on rigorous ways to implement ideas from the renormalization group in machine-learning based models of physical systems.

In the past, you may have seen me at

My favorite book is Edmund Spenser's Faerie Queene.


Email: semonr at princeton dot edu

Snail mail:
Department of Mathematics
Princeton University
Fine Hall, Washington Rd


Applications of Mathematics

Invited Talks

Symplectic geometry seminars that I have been involved with:


In 2020, I taught Calculus II (UN1102) at Columbia University. In 2019 I co-organized with Kyler Siegel a Columbia REU program for undergraduate students. The students used numerical optimization methods, tools from symplectic integration, and Haim-Kislev's recent work to find new symplectic embeddings. I have also TAed for graduate and undergraduate courses.