I am a member of the Geometry Group at UT Austin.
Here is my curriculum vitae, current as of 24 Jul 2014.
I can be reached at:
My surname is most correctly pronounced "Night-Ski".
All listed courses are at UT Austin.
(Applications of Quantum Field Theory to Geometry)
(Introduction to Real Analysis)
(Matrices and Matrix Calculations)
I work on problems in string theory and supersymmetric field theory, usually ones which
have some overlap with geometry.
My most recent papers/preprints are (click [+]
for a short account):
Cluster-like coordinates in supersymmetric field theory.
Proceedings of the National Academy of Sciences.
An R^3 index for four-dimensional N=2 field theories.
Hyperkahler sigma model and field theory on Gibbons-Hawking spaces.
Spectral networks and Fenchel-Nielsen coordinates.
Line defects, tropicalization, and multi-centered quiver quantum mechanics.
Notes on a new construction of hyperkahler metrics.
To appear in proceedings of the conference Mirror Symmetry & Tropical Geometry, Cetraro 2011.
Spectral networks and snakes.
Annales Henri Poincare.
On a hyperholomorphic line bundle over the Coulomb branch.
Wall-crossing, Hitchin Systems, and the WKB Approximation.
A note on conformal symmetry in projective superspace.
Argyres-Seiberg duality and the Higgs branch.
Commun. Math. Phys. 294 (2010) 389-410.
Four-dimensional wall-crossing via three-dimensional field theory.
Commun. Math. Phys. 299 (2010) 163-224.
Background Independence and the Open Topological String Wavefunction.
In "From Hodge theory to integrability and TQFT" (2008), American Mathematical Society.
Asymptotic Spectroscopy of Rotating Black Holes.
Phys. Rev. D78 (2008) 044006.
Since I give most of my talks on the blackboard, I have relatively few
sets of Web-ready notes (but the situation is improving as more talks are recorded).
Here is what I do have:
A smooth R^3 index for four-dimensional N=2 theories.
Princeton (STRINGS 2014), June 2014.
Spectral networks and their uses.
Pisa, June 2014.
Gluing construction for a hyperholomorphic line bundle.
UC Davis, May 2014.
Open string mirror symmetry and Hitchin systems.
Miami, January 2014.
On the utility of the equation 2+4=6 in supersymmetric quantum field theory.
Austin (physics colloquium), February 2013.
Introduction to wall-crossing (through spaces of quadratic differentials).
IHES, November 2011.
KITP, August 2011.
A 2d-4d wall-crossing formula.
Cetraro, July 2011.
A 2d-4d wall-crossing formula.
String-Math, UPenn, June 2011.
Lectures on wall-crossing (introductory).
Jeju, South Korea, January 2011.
Transcript: 1, 2, 3
Hitchin systems and enumerative invariants.
Michigan, December 2010.
2d-4d wall-crossing and hyperholomorphic bundles.
DESY, December 2010.
4d and 2d-4d wall-crossing.
Simons Center for Geometry and Physics, August 2010.
BPS wall-crossing, field theory and hyperkahler geometry.
Oxford, June 2009.
Asymptotic quasinormal mode frequencies.
Penn State, May 2008.
An idiosyncratic view of the holomorphic anomaly of the topological string.
Northwestern, February 2008.
Quantum Maxwell theory.
IAS, September 2007.
In various stages of completion, no warranty express or implied. Feedback very much appreciated.
Comparing signs in wall-crossing formulas.
(Last update: 14 Jan 2014)
Hitchin systems in N=2 field theory.
(Last update: 25 Nov 2013)
What is a BPS state?
(Last update: 19 Aug 2012)
Absolutely undocumented at the moment, but questions are welcome.
The CurvesGraphics6 notebook by Gianluca Gorni is available
; this notebook
contains instructions on how to generate the file CurvesGraphics6.m, which is used by the spectral network
Notebook for plotting spectral networks.
(Last update: 29 Apr 2014)
Physics for mathematicians
This is a new series of videos aimed at explaining notions from physics for a mathematical audience.
So far only the raw videos are here; some organizational superstructure and
guidance about prerequisites will follow.
What is mirror symmetry?
The Kaluza-Klein mechanism.