About Me
“What I cannot create, I do not understand.”1
I am an academic mathematician seeking new challenges.
I am the world expert in the (extremely niche) intersection between polyfold theory and Gromov–Witten theory. Polyfolds are abstract infinite-dimensional spaces which allow for more general smooth translation actions as well as incorporating degenerative “bubbling” phenomena directly into their structures. Polyfold theory has made is possible to rigorously define smooth regularizations of Gromov–Witten moduli spaces. I worked for years on a proof of the Gromov–Witten axioms, a series of algebraic relations for the Gromov–Witten invariants of a symplectic manifold first conjectured in 1992. My research was ultimately successful in solving this problem completely and in full generality. Thanks in part to my own work, there are few interesting and tractable problems that remain in my sphere of mathematical expertise.
Education
PhD in Mathematics
University of California, Berkeley; Berkeley, CA
16 August 2012 - 11 May 2018
B.S. in Mathematics
University of Chicago; Chicago, IL
24 September 2007 - 11 June 2011
Postdoctoral Appointments
Faculty of Mathematics
Ruhr-Universität Bochum; Bochum, Germany
1 March 2020 - 31 December 2024
Mathematics Institute
Justus-Liebig University; Gießen, Germany
1 January 2018 - 29 February 2020
Papers
Pseudocycle Gromov–Witten invariants are a strict subset of polyfold Gromov–Witten invariants
Non-fillability of overtwisted contact manifolds via polyfolds (joint with S. Suhr, K. Zehmisch)
The Gromov–Witten axioms for symplectic manifolds via polyfold theory
Naturality of polyfold invariants and pulling back abstract perturbations
The Steenrod problem for orbifolds and polyfold invariants as intersection numbers
Invited Talks
Orbifold Intersection Theory and Polyfold Gromov–Witten Invariants
28 November 2023; Heidelberg Geometry Seminar; Heidelberg, Germany
Pseudocycle Gromov–Witten Invariants \(\subsetneq\) Polyfold Gromov–Witten Invariants
11 February 2021; Arbeitsgemeinschaft; Bochum, Germany
The Steenrod problem for orbifolds and polyfold Gromov–Witten invariants
10 December 2020; Oberseminar Dynamische Systeme; Bochum, Germany
Gromov–Witten Axioms for Symplectic Manifolds via Polyfold Theory
15 April 2019; Berlin-Hamburg-Seminar; Berlin, Germany
Gromov–Witten Axioms for Symplectic Manifolds via Polyfold Theory
24 October 2018; SISSA; Trieste, Italy
Gromov–Witten Axioms for Symplectic Manifolds via Polyfold Theory
30 August 2018; Symplectic Field Theory IX: Polyfolds for SFT; Augsburg, Germany
Gromov–Witten Axioms for Symplectic Manifolds via Polyfold Theory
5 July 2018; Justus-Liebig University; Gießen, Germany
Naturality of Polyfold Invariants
2 May 2018; Mathematical Sciences Research Institute; Berkeley, California
The Polyfold Gromov–Witten Invariants & Gromov–Witten Axioms for Symplectic Manifolds via Polyfold Theory
25 April 2018; Berkeley Topology Seminar; Berkeley, California
Footnotes
from Richard Feynman’s blackboard at the time of his death, February 1988↩︎