Research

Papers

Asymptotic geometry of the moduli space of parabolic SL(2, ℂ)-Higgs bundles. With Rafe Mazzeo, Jan Swoboda, and Hartmut Weiss. 2001.03682 [+]
Parabolic Higgs bundles, tt connections and opers. With Murad Alim and Florian Beck. 1911.06652 [+]
Exponential decay for the asymptotic geometry of the Hitchin metric. 1810.01554 [+]
Generic Ends of the Moduli Space of SL(n, ℂ)-Higgs bundles. 1810.01556 [+]
Perspectives on the asymptotic geometry of the Hitchin moduli space. 1809.05735 [+]
Singular geometry and Higgs bundles in string theory. With Lara B. Anderson, Mboyo Esole, and Laura P. Schaposnik. 1710.08453 [+]
From S1-fixed points to W-algebra representations. With Andy Neitzke. 1710.06142 [+]
Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters. With Du Pei, Wenbin Yan, Ke Ye. 1701.08782 [+]
Opers versus nonabelian Hodge. With Olivia Dumitrescu, Georgios Kydonakis, Rafe Mazzeo, Motohico Mulase, Andy Neitzke. 1607.02172 [+]

Events Organized

MSRI: Analytic and Geometric Aspects of Gauge Theory Fall 2022 Website
AIM: Geometry and Physics of ALX metrics in gauge theory Aug 16 - 20, 2021 Website
MSRI: Connections for Women: Holomorphic Differentials in Mathematics and Physics, August 15-16, 2019 Website
AIM: Singular geometry and Higgs bundles in string theory, October 30 to November 3, 2017 Website [+]

Talks

I give most of my talks on the blackboard. Here are the talks for which I have slides or video.

Western Hemisphere Colloquium on Geometry and Physics, August 2020 Slides, Video [+]
SIAM: Minisymposium on Gauge Theory and PDEs, Decemeber 2019 Slides [+]
MSRI: Introductory Workshop for ``Holomorphic Differentials in Mathematics and Physics", August 2019 Video [+]
(Mini-Course) Hamburg: Higgs Bundles in Mathematics and Physics, September 2018 Poster [+]
CMO, Oaxaca, July 2018. Video [+]
CIRM, Luminy, June 2018. Video [+]
(Mini-Course) UIC: Workshop on the geometry and physics of Higgs bundles II, November 2017 Poster [+]
GEAR Workshop on compactifications of moduli spaces of representations, June 2017 Notes

A construction of limiting solutions of Hitchin's equations. Isaac Newton Institute, August 2015. Video [+]
Survey of Taubes' "PSL(2,C)-connections on 3-manifolds with L2 bounds on curvature" January 2015. Notes [+]

Notes

Notes from Sergei Gukov's talk "Quantization via Mirror Symmetry" Notes [+]
Notes from Karen Uhlenbeck's lecture series "Equations of Gauge Theory" Notes [+]