Research
Papers
All of my papers are posted on the
arXiv.
Most are linked on
orcID.
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
[+]
The survey 1710.08453
summarizes some of the possible ideas to be discussed.
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
[+]
Title: The asymptotic geometry of the Hitchin moduli space
SIAM: Minisymposium on Gauge Theory and PDEs, Decemeber 2019
Slides
[+]
Title: The asymptotic geometry of the Hitchin moduli space
MSRI: Introductory Workshop for ``Holomorphic Differentials in Mathematics and Physics",
August 2019
Video
[+]
Title: The asymptotic geometry of the Hitchin moduli space
Abstract: Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichmuller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperkahler metric. A conjectural description of its asymptotic structure appears in the work of physicists Gaiotto-Moore-Neitzke and there has been a lot of progress on this recently. I will discuss some recent results.
(Mini-Course)
Hamburg: Higgs Bundles in Mathematics and Physics, September 2018
Poster
[+]
The topic of my three-hour mini-course was ``The asymptotic geometry of the Hitchin moduli space.''
Here is the workshop website.
This survey is based on these mini-course notes: 1809.05735.
(Mini-Course)
UIC: Workshop on the geometry and physics of Higgs bundles II, November 2017
Poster
[+]
The topic of my mini-course was ``An introduction to limits in the moduli space of Higgs bundles.''
I gave a three-hour mini-course plus three 45 minute problem sessions, in addition to a talk.
This survey is based on these mini-course notes: 1809.05735.
From the workshop website:
"This workshop, second in a series of Graduate workshops on Higgs bundles,
is aimed at graduate students and young postdocs, will expose participants
to some current research topics on the geometry and physics of Higgs bundles.
The workshop will have two mini-courses by experts on topics close to their own research,
including a mix of lectures and problem sessions.
The workshop will be followed by the meeting
``Current trends in Higgs bundles III"
to be held at the University of Illinois at Chicago
November 13-14 2017.''
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
[+]
Abstract: I'll describe a construction of solutions of Hitchin's equations
on a compact Riemann surface near the "ends" of the SL(n,C)-Hitchin
moduli space. This construction generalizes Mazzeo-Swoboda-Weiss-Witt's
construction of SL(2,C) solutions of Hitchin's equations where the Higgs
field is "simple." In the generalized construction, moduli spaces of irregular connections arise.
This is ongoing work.
This talk was given at the Metric and Analytic Aspect of Moduli Spaces program at the Isaac Newton Institute.
Survey of Taubes' "PSL(2,C)-connections on 3-manifolds with L2 bounds on curvature"
January 2015.
Notes
[+]
Notes
Notes from Sergei Gukov's 2014 talk "Quantization via Mirror Symmetry"
Notes
[+]
These are my notes from Sergei Gukov's talk at the GEAR Junior Retreat (Ann Arbor, MI) on May 28, 2014.
All errors are my own.
Notes from Karen Uhlenbeck's 2012 lecture series "Equations of Gauge Theory"
Notes
[+]
These are my notes from Karen Uhlenbeck's lecture series at the Temple University (Philadelphia, PA) on February 7-9, 2012.
All errors are my own.
