Andrew Neitzke

About Me

Here is my curriculum vitae, current as of 18 Jan 2022.

I can be reached at:
Department of Mathematics
Attn: Andrew Neitzke
PO Box 208283
New Haven, CT 06520-8283
Mailcode: 376

Office: DL (Dunham Laboratory) 425

My surname is most correctly pronounced "Night-Ski".
Headshot Spectral network movies


Fall 2022. Math 302 (Vector Analysis and Integration on Manifolds)
Spring 2022. Math 706 (Geometry of Stokes Phenomena)
Fall 2021. Math 302 (Vector Analysis and Integration on Manifolds)
Spring 2021. Math 435 (Differential Geometry)
Fall 2020. Math 250 (Vector Analysis)
Spring 2020. Math 225 (Linear Algebra and Matrix Theory)
Spring 2019. Math 361 (Theory of Functions of a Complex Variable) Course page
Fall 2018. Math 408C (Differential and Integral Calculus) Course page
Fall 2017. Math 392C (Applications of QFT to Geometry) Course page
Fall 2017. Math 408L (Integral Calculus) x2 Course page
Spring 2016. Math 392C (Moduli of Higgs Bundles) Course page
Fall 2015. Math 408C (Differential and Integral Calculus) x2 Course page
Spring 2015. Math 382D (Differential Topology) Course page
Fall 2014. Math 408M (Multivariable Calculus) Course page
Spring 2014. Math 392C (Complex Geometry) Course page
Fall 2013. Math 365C (Real Analysis) Course page
Spring 2013. Math 392C (Riemannian Geometry) Course page
Fall 2012. Math 408L (Integral Calculus) Course page
Spring 2012. Math 392C (Applications of Quantum Field Theory to Geometry) Course page
Fall 2011. Math 361K (Introduction to Real Analysis) Course page
Spring 2011. Math 392C (Complex Geometry) Course page
Fall 2010. Math 340L (Matrices and Matrix Calculations) Course page
Spring 2010. Math 408L (Integral Calculus) Course page


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):

3d spectral networks and classical Chern-Simons theory. With Dan Freed. 2208.07420 [ ]
Exponential Networks, WKB and the Topological String. With Alba Grassi and Qianyu Hao. 2201.11594 [ ]
The quantum UV-IR map for line defects in gl(3)-type class S theories. With Fei Yan. 2112.03775 [ ]
Exact WKB methods in SU(2) Nf=1. With Alba Grassi and Qianyu Hao. 2105.03777 [ ]
Deformations of surface defect moduli spaces. With Ali Shehper. JHEP. 2011.01970 [ ]
Factorized class S theories and surface defects. With Behzat Ergun, Qianyu Hao and Fei Yan. 2010.06722 [ ]
Opers and nonabelian Hodge: numerical studies. With David Dumas. 2007.00503 [ ]
The dilogarithm and abelian Chern-Simons. With Dan Freed. J. Diff. Geom. 2006.12565 [ ]
q-nonabelianization for line defects. With Fei Yan. JHEP. 2002.08382 [ ]
Exact WKB and abelianization for the T3 equation. With Lotte Hollands. Commun. Math. Phys. 1906.04271 [ ]
BPS states in the Minahan-Nemeschansky E7 theory. With Qianyu Hao and Lotte Hollands. JHEP. 1905.09879 [ ]
On the BPS Spectrum of the Rank-1 Minahan-Nemeschansky Theories. With Jacques Distler and Mario Martone. JHEP. 1901.09929 [ ]
Secondary products in supersymmetric field theory. With Chris Beem, David Ben-Zvi, Mat Bullimore and Tudor Dimofte. Annales Henri Poincare. 1809.00009 [ ]
Asymptotics of Hitchin's metric on the Hitchin section. With David Dumas. Commun. Math. Phys. 1802.07200 [ ]
Moduli of Higgs bundles on CP^1 with C*-actions. With Laura Fredrickson. Math. Proc. Camb. Phil. Soc. 1709.06142 [ ]
Line defect Schur indices, Verlinde algebras and U(1)_r fixed points. With Fei Yan. JHEP. 1708.05323 [ ]
Integral iterations for harmonic maps. 1704.01522 [ ]
From the Hitchin section to opers through nonabelian Hodge. With Olivia Dumitrescu, Laura Fredrickson, Georgios Kydonakis, Rafe Mazzeo and Motohico Mulase. J. Diff. Geom. 1607.02172 [ ]
BPS states in the Minahan-Nemeschansky E6 theory. With Lotte Hollands. Commun. Math. Phys. 1607.01743 [ ]
Hitchin systems in N=2 field theory. 1412.7120 [ ]
Twistorial Topological Strings and a tt* Geometry for N=2 Theories in 4d. With Sergio Cecotti and Cumrun Vafa. ATMP. 1412.4793 [ ]
Cluster-like coordinates in supersymmetric field theory. Proceedings of the National Academy of Sciences. PNAS link [ ]
An R^3 index for four-dimensional N=2 field theories. With Sergei Alexandrov, Gregory W. Moore and Boris Pioline. Phys Rev Lett. 1406.2360 [ ]
Hyperkahler sigma model and field theory on Gibbons-Hawking spaces. With Anindya Dey. JHEP. 1401.0349 [ ]
Spectral networks and Fenchel-Nielsen coordinates. With Lotte Hollands. Letters in Mathematical Physics. 1312.2979 [ ]
Line defects, tropicalization, and multi-centered quiver quantum mechanics. With Clay Cordova. JHEP. 1308.6829 [ ]
Notes on a new construction of hyperkahler metrics. In proceedings of the conference Mirror Symmetry & Tropical Geometry, Cetraro 2011. 1308.2198 [ ]
Wild wall crossing and BPS giants. With Dmitry Galakhov, Pietro Longhi, Tom Mainiero, and Gregory W. Moore. JHEP. 1305.5454 [ ]
Spectral networks and snakes. With Davide Gaiotto and Gregory W. Moore. Annales Henri Poincare. 1209.0866 [+]
Spectral networks. With Davide Gaiotto and Gregory W. Moore. Annales Henri Poincare. 1204.4824 [+]
On a hyperholomorphic line bundle over the Coulomb branch. 1110.1619 [+]
Wall-Crossing in Coupled 2d-4d Systems. With Davide Gaiotto and Gregory W. Moore. JHEP. 1103.2598 [+]
R-twisting and 4d/2d Correspondences. With Sergio Cecotti and Cumrun Vafa. 1006.3435 [+]
Framed BPS States. With Davide Gaiotto and Gregory W. Moore. ATMP. 1006.0146 [+]
Wall-crossing, Hitchin Systems, and the WKB Approximation. With Davide Gaiotto and Gregory W. Moore. Adv Math. 0907.3987 [+]
A note on conformal symmetry in projective superspace. With Radu Ionas. 0811.2048 [+]
Argyres-Seiberg duality and the Higgs branch. With Davide Gaiotto and Yuji Tachikawa. Commun. Math. Phys. 294 (2010) 389-410. 0810.4541 [+]
Four-dimensional wall-crossing via three-dimensional field theory. With Davide Gaiotto and Gregory W. Moore. Commun. Math. Phys. 299 (2010) 163-224. 0807.4723 [+]
Background Independence and the Open Topological String Wavefunction. With Johannes Walcher. In "From Hodge theory to integrability and TQFT" (2008), American Mathematical Society. 0709.2390 [+]
Asymptotic Spectroscopy of Rotating Black Holes. With Uri Keshet. Phys. Rev. D78 (2008) 044006. 0709.1532 [+]
For a fuller list of my papers see inSPIRE.


Since I give most of my talks on the blackboard, I have relatively few sets of Web-ready notes. Here are some I do have:

Lectures on spectral networks. Moscow, 2021. Notes
Protected spin characters, link invariants and spectral networks. String-Math (online), 2020. Notes, Video
An update on hyperkahler metrics on moduli of Higgs bundles. Moduli of special holonomy metrics and their periods (Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics) (online), 2020. Video
Lectures on spectral networks. MSRI, 2019. Notes 1,2,3,4
WKB and abelianization. Austin, 2018. Notes
Precision studies of nonabelian Hodge for irregular Higgs bundles on CP^1. GEAR retreat, 2017. Notes, Video
Abelianization and Chern-Simons theory. QGM Aarhus, 2017. Notes
Abelianization, WKB and Chern-Simons theory. Stanford, November 2016. Notes
Hitchin systems, spectral networks and noncommutative clusters. MSRI, March 2016. Notes
WKB and the conformal limit. Montreal, January 2016. Notes
Some new geometric applications of quantum field theory. Bonn (Panorama of Mathematics), October 2015. Slides
A smooth R^3 index for four-dimensional N=2 theories. Princeton (STRINGS 2014), June 2014. Slides
Spectral networks and their uses. Pisa, June 2014. Notes
Gluing construction for a hyperholomorphic line bundle. UC Davis, May 2014. Notes
Open string mirror symmetry and Hitchin systems. Miami, January 2014. Notes
Spectral networks in 2 and 3 dimensions. String-Math, June 2013. Notes (with animations), Video
On the utility of the equation 2+4=6 in supersymmetric quantum field theory. Austin (physics colloquium), February 2013. Notes
Introduction to wall-crossing (through spaces of quadratic differentials). IHES, November 2011. Notes, Video
Spectral networks. KITP, August 2011. Notes, Video
A 2d-4d wall-crossing formula. Cetraro, July 2011. Slides
A 2d-4d wall-crossing formula. String-Math, UPenn, June 2011. Slides, Video
Lectures on wall-crossing (introductory). Jeju, South Korea, January 2011. Transcript: 1, 2, 3
Hitchin systems and enumerative invariants. Michigan, December 2010. Slides
2d-4d wall-crossing and hyperholomorphic bundles. DESY, December 2010. Slides
4d and 2d-4d wall-crossing. Simons Center for Geometry and Physics, August 2010. Video
BPS wall-crossing, field theory and hyperkahler geometry. Oxford, June 2009. Notes
Asymptotic quasinormal mode frequencies. Penn State, May 2008. Notes
An idiosyncratic view of the holomorphic anomaly of the topological string. Northwestern, February 2008. Notes
Quantum Maxwell theory. IAS, September 2007. Notes

Expository notes

These notes are in various stages of completion. I very much appreciate any feedback, which also serves as encouragement to finish these.

PCMI lectures on BPS states and spectral networks. (Last update: 16 Jan 2021) Draft
On the metrics on moduli spaces of Higgs bundles. (Last update: 29 Nov 2021) Draft
Moduli of Higgs bundles (notes from 2016 course). (Last update: 28 Nov 2021) Draft
Comparing signs in wall-crossing formulas. (Last update: 17 May 2021) Draft
What is a BPS state? (Last update: 17 May 2021) Draft

Mathematica files

Absolutely undocumented at the moment, but questions are welcome.

The CurvesGraphics6 notebook by Gianluca Gorni is available here; this notebook contains instructions on how to generate the file CurvesGraphics6.m, which is used by the spectral network notebook below.

Notebook for plotting spectral networks. (Last update: 17 May 2021) Notebook

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? Video
The Kaluza-Klein mechanism. Video