Geometry and String Theory
HomePage

This is the homepage for the UT Geometry and Quantum Field Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get us started.

There is a mailing list. To subscribe, send an email to sympa@utlists.utexas.edu with subject
“subscribe math-gst Your Name”.

Fall 2024 Schedule

Date	Speaker	Topic
8/28		Organizational Meeting
9/4	David Ben Zvi	Categorical Symmetries
9/11
9/18	Ryan Spieler	Gapped Phases with Non-Invertible Symmetry in 2+1 D
9/25
10/2	Alex Lu	Gauging Non-Invertible Symmetries
10/9
10/16
10/23	David Ben-Zvi	Deformation Quantization and Unitarity I
10/30	Lucas Mason-Brown	Deformation Quantization and Unitarity II
11/6	David Ben-Zvi	Deformation Quantization and Unitarity III
11/13	David Ben-Zvi	Twistor structures
11/20
12/4

Spring 2025 Schedule

Date	Speaker	Topic
1/15		Organizational Meeting
1/22	Bahaa Elshimy	Chatterjee-Witten I
1/29	Bahaa Elshimy	Chatterjee-Witten II
2/5	Bahaa Elshimy	Chatterjee-Witten III
2/12	Yasin Alam	Liouville theory, QG, and Random Surfaces I
2/19	Yasin Alam	Liouville theory, QG, and Random Surfaces II
2/26	Monica Kang	Operator algebras in holographic spacetime
3/5
3/12
3/26
4/2
4/9
4/16
4/23
4/30

Possible list of Topics for Spring 2025

Liouville Theory

• Chatterjee and Witten, “Liouville Theory: An Introduction to Rigorous Approaches”
• Guillarmou, Kupiainen and Rhodes, “Review on the probabilistic construction and conformal bootstrap in Liouville theory”
• Nathanaël Berestycki, Ellen Powell, “Gaussian free field and Liouville quantum gravity”

We mentioned “7” and “23” which are referred in the above paper.

• Sheffield, “What is a random surface?”
• Benjamin, Collier, Maloney and Meruliya “Resurgence in Liouville Theory”

Gaiotto’s papers

• Gaiotto, Teschner “Schur Quantization and Complex Chern-Simons theory”

• Gaiotto, Teschner “Quantum Analytic Langlands Correspondence”

• Gaiotto, Witten “Gauge Theory and the Analytic Form of the Geometric Langlands Program”

References

Deformation Quantization and Unitarity

• Beem, Peelaers and Rastelli, “Deformation quantization and superconformal symmetry in three dimensions”
• Etingof and Stryker, “Short Star-Products for Filtered Quantizations, I”
• Gaiotto, “Sphere quantization of Higgs and Coulomb branches and Analytic Symplectic Duality”
• Losev, “Deformations of symplectic singularities and Orbit method for semisimple Lie algebras”
• Simpson, “Mixed Twistor Structures”

Fusion Category Symmetry Basics and Reviews

• L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions”
• S. Schafer-Nameki, “ICTP Lectures on (Non)-Invertible Generalized Symmetries”
• S. Shao “What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry”

SymTFT and (Higher-)Categorical Landau Paradigm

• D. Freed, G. Moore, and C. Teleman, “Topological symmetry in quantum field theory”
• L. Bhardwaj and S. Schafer-Nameki, “Generalized Charges, Part II: Non-Invertible Symmetries and the Symmetry TFT”
• Oxford Group, “Hasse Diagrams for Gapless SPT and SSB Phases with Non-Invertible Symmetries”
• Oxford Group,“Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I”

Gauging Non-Invertible Symmetries

• A. Perez-Lona, D. Robbins, E. Sharpe, T. Vandermeulen, X. Yu, “Notes on gauging noninvertible symmetries, part 1: Multiplicity-free cases”

• A. Perez-Lona, D. Robbins, E. Sharpe, T. Vandermeulen, X. Yu, “Notes on gauging noninvertible symmetries, part 2: higher multiplicity cases”

Donaldson Theory and $\mathcal{N}=2$ SUSY Field Theory

• Alexandru Scorpan, “The Wild World of 4-Manifolds”
• J.D. Moore, “Lecture Notes on Seiberg-Witten Invariants”
• Gompf & Stipsicz “[4-Manifolds and Kirby Calculus]”
• Griffiths & Harris “[Principles of Algebraic Geometry]”
• G. Moore, “Lectures On The Physical Approach To Donaldson And Seiberg-Witten Invariants Of Four-Manifolds”
• E. Witten, “Supersymmetric Yang-Mills theory on a four manifold”
• N. Seiberg, E. Witten, “Monopole Condensation, and confinement in N=2 supersymmetric Yang-Mills theory”
• E. Witten, “Monopoles and four manifolds”
• G. W. Moore, E. Witten, “Integration over the u-plane in Donaldson theory.”
• D. Baraglia, H. Konno, “On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds”
• P. Kronheimer, T. Mrowka, “The Dehn twist on a sum of two K3 surfaces”
• J. Cushing, G. W. Moore, M. Rocek, V. Saxena, “Superconformal gravity and the topology of diffeomorphism groups”

Old

Algebra of Observables in Curved Spacetime

• E. Witten, “A Background Independent Algebra in Quantum Gravity”
• E. Witten, “Algebras, Regions, and Observers”

Non-Invertible Symmetries

• S. Shao, “What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry”
• Y. Choi, B. Rayhaun, Y. Sanghavi, S. Shao, “Comments on Boundaries, Anomalies, and Non-Invertible Symmetries”
• L. Bhardwaj and Y. Tachikawa, “On finite symmetries and their gauging in two dimensions”
• S. Schafer-Nameki, “ICTP Lectures on (Non)-Invertible Generalized Symmetries”

Brane Quantization and Analytic Geometric Langlands

• S. Gukov, E. Witten, “Branes and Quantization”
• D. Gaiotto, E. Witten, “Probing Quantization Via Branes”
• E. Witten, ICTS Lecture 1: “The Problem of Quantization”
• A. Kapustin, E. Witten, “Electric-Magnetic Duality and the Geometric Langlands Program”
• E. Witten, ICTS Lecture 2: “Quantization by Branes and Geometric Langlands”
• D. Gaiotto, E. Witten, “Gauge Theory and the Analytic Form of the Geometric Langlands Program”
• E. Witten, ICTS Lecture 3: the Analytic Approach to Geometric Langlands
• See also the lectures by Teschner at the same program.

Anomaly in S-duality Symmetry of IIB

• A. Debray, M. Diergl, J. Heckman, M. Montero, “The anomaly that was not meant IIB”

Topological Holography

• H. Moradi, S.F. Moosaven, and A. Tiwari. “Topological holography: Towards a unification of Landau and beyond-Landau physics” Rem: If need be, Ryan is flexible with talk time. Please do not move it sooner or to 11/19, since he has already scheduled a talk that week.

Categorical Symmetries

• B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius, I. Valanzuela, “Non-invertible global symmetries and completeness of the spectrum”

• Y. Choi, C. Cordova, P. Hsin, H. Lam, S. Shao, “Non-Invertible Duality Defects in 3+1 Dimensions”

Mass Gap in 2D Gauge Theory

• D. Delmastro, J. Gomis, M. Yu, “Infrared phases of 2d QCD”

Twisted supergravity and Koszul duality

• K. Costello, N. M. Paquette, “Twisted supergravity and Koszul duality: a case study in AdS₃”

Topological Defect Networks

• D. Aasen, D. Bulmash, A. Prem, K. Slagle, D. Williamson,“Topological Defect Networks for Fractons of all Types”

• D. Aasen, “Topological Defect Networks for Fracton Models - IPAM at UCLA”

• D. Bulmash “Insights into type-II fractons via topological order - Harvard CMSA”

Haah Codes

• J. Haah “Local stabilizer codes in three dimensions without string logical operators”

• J. Haah “Bifurcation in entanglement renormalization group flow of a gapped spin model”

Entanglement in Quantum Field Theory

• E. Witten, “Notes on Some Entanglement Properties of Quantum Field Theory”
• H. Casini, M. Huerta, “Lectures on entanglement in quantum field theory”
• E. Witten, “Gravity and the Crossed Product”
• E. Witten, “Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?”
• J. Yngvason, “The Role of Type III Factors in Quantum Field Theory”

Complex Chern-Simons theory, resurgence, and quantum modularity

• S. Gukov, M. Marino, P. Putrov, “Resurgence in complex Chern-Simons theory”
• S. Garoufalidis, J. Gu, M. Marino, “Peacock patterns and resurgence in complex Chern-Simons theory”
• S. Garoufalidis, J. Gu, M. Marino, C. Wheeler, “Resurgence of Chern-Simons theory at the trivial flat connection”
• S. Garoufalidis, D. Zagier, “Knots, perturbative series and quantum modularity”
• S. Garoufalidis, C. Wheeler, “Modular q-holonomic modules”
• Z. Duan, J. Gu, “Resurgence in complex Chern-Simons theory at generic levels”

3d/3d correspondence, spectral networks, and abelianization

• S. Cecotti, C. Cordova, C. Vafa, “Braids, Walls, and Mirrors”
• T. Dimofte, D. Gaiotto, S. Gukov, “3-Manifolds and 3d Indices”
• S. Garoufalidis, R. Kashaev, “A meromorphic extension of the 3D Index”
• A. Neitzke, F. Yan, “q-nonabelianization for line defects”
• D. Freed, A. Neitzke, “3d spectral networks and classical Chern-Simons theory”

Non-semisimple TQFTs

• T. Creutzig, T. Dimofte, N. Garner, N. Geer, “A QFT for non-semisimple TQFT”