I got my PhD in 2013 from UC Berkeley, working with Peter Teichner, and then was a Szego Assistant Professor
at Stanford from 20132015 before moving to UIUC.
My research studies connections between supersymmetric (quantum) field theories, differential geometry, and algebraic topology.
Papers accepted for publication:
Chern characters and supersymmetric field theories, to appear in Geometry and Topology.
Power operations in the StolzTeichner 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 2algebras 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 Ltheory with complex coefficients, Letters in Mathematical Physics (2016).
The ChernGaussBonnet Theorem via supersymmetric Euclidean field theories,
Communications in Mathematical Physics (2015).
Preprints:
String structures, 2group bundles, and a categorification of the FreedQuinn 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 infinitysheaves, 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 Ktheory from gauged supersymmetric mechanics (2015).
Topological qexpansion and the supersymmetric sigma model (2015).
Smooth onedimensional topological field theories are vector bundles with connection, with Dmitri Pavlov (2015).
Perturbative sigma models, elliptic cohomology and the Witten genus (2013).
Other writing:
My master's thesis in astrophysics.
