I got my PhD in 2013 from UC Berkeley, working with Peter Teichner, and then was a Szego Assistant Professor at Stanford from 2013-2015 before moving to UIUC. My research studies connections between supersymmetric (quantum) field theories, differential geometry, and algebraic topology. At the moment, I am writing up results outlined in this talk. The first three papers in this series are Chern characters for supersymmetric field theories, The families Clifford index and differential KO-theory, and The families index for 1|1-dimensional Euclidean field theories, linked below.
Chern characters for supersymmetric field theories, to appear in Geometry and Topology. Power operations in the Stolz--Teichner program, with Tobias Barthel and Nathaniel Stapleton, to appear in Geometry and Topology. Supersymmetric localization, modularity and the Witten genus, to appear in Journal of Differential Geometry. Equivariant elliptic cohomology, gauged sigma models, and discrete torsion, Transactions of the American Mathematical Society (2021). Supersymmetric field theories and the elliptic index theorem with complex coefficients, Geometry & Topology (2021). A de Rham model for complex analytic equivariant elliptic cohomology, with Arnav Tripathy, Advances in Mathematics (2021). Lie 2-algebras of vector fields, with Eugene Lerman, Pacific Journal of Math (2020). Representation Theory and the Elliptic Frontier, with Emily Cliff, Nora Ganter, Arnav Tripathy, and Josh Wen, Notices of the AMS (2019). Perturbative N=2 supersymmetric quantum mechanics and L-theory with complex coefficients, Letters in Mathematical Physics (2016). The Chern-Gauss-Bonnet Theorem via supersymmetric Euclidean field theories, Communications in Mathematical Physics (2015).
The families index for 1|1-dimensional Euclidean field theories, (2022). The families Clifford index and differential KO-theory, (2022). String structures, 2-group bundles, and a categorification of the Freed-Quinn line bundle, with Emily Cliff, Laura Murray, Apurva Nakade, and Emma Phillips (2021). Discrete vector bundles with connection and the Bianchi identity, with Anil Hirani and Mark Schubel (2021). A model for complex analytic equivariant elliptic cohomology from quantum field theory, with Arnav Tripathy (2018, updated in 2020). Classifying spaces of infinity-sheaves, with Pedro Boavida de Brito and Dmitri Pavlov (2019). The equivariant Chern character as super holonomy on loop stacks, with Fei Han (2016). Twisted equivariant differential K-theory from gauged supersymmetric mechanics (2015). Topological q-expansion and the supersymmetric sigma model (2015). Smooth one-dimensional topological field theories are vector bundles with connection, with Dmitri Pavlov (2015). Perturbative sigma models, elliptic cohomology and the Witten genus (2013).
My master's thesis in astrophysics. |