Lecture series
Tannakian QFT's, 4 lectures, at the Hamburg CRC on Higher Structures, Moduli Spaces, and Integrability (Oct-Nov 2024)
VOA’s and 3d TQFT’s from supersymmetric QFT’s (5 lectures), Hausdorff School: "TQFTs and their connections to representation theory and mathematical physics", Bonn, Germany (June 19-23, 2023)
LAWRGe 2023: 3d Mirror Symmetry and 3d TQFT (18 lectures, problem sessions) w/ J. Hilburn and P. Safronov, University of Southern California (June 12-16, 2023)
3d gauge theories: vortices and vertex algebras [1,2], Workshop on Vortex Moduli, ICTS Bangalore (Feb 13-14, 2023)
Algebra, geometry, and twists in 3d N=4 gauge theory (4 lectures), Winter School in Mathematical Physics, SwissMAP Research Station in Les Diablerets (Jan 8-13, 2023)
3d Mirror Symmetry and Link Homology (3 lectures), Thematic Program on Arithmetic, Geometry, and Physics: Higher Algebraic Structure, KIAS Seoul/online (July 26-28, 2022)
3d Theories and Twists (w/ K. Costello) [1,2] QFT for Mathematicians 2022, Perimeter Institute (June 20&22, 2022)
Derived geometry in twists of gauge theories (4 lectures), PIMS Summer School on Algebraic Geometry in High-Energy Physics, U. Alberta (August 23-27, 2021)
Twisted Quantum Field Theory, 13-part informal online seminar, with Brian Williams (February-April 2021)
Algebraic structure of boundary conditions in (T)QFT, 2 lectures, online seminar on Arithmetic Geometry and Quantum Field Theory (June 17&24, 2020)
Boundaries, Defects, and Dualities in SUSY Gauge Theory, 3 lectures, Introductory Workshop on 3D mirror symmetry and AGT conjecture, Inst. for Adv. Studies in Mathematics, Zhejiang University, China (Oct 1-4, 2019)
Boundary Conditions and Extended Defects, 3 lectures, QFT for Mathematicians, Perimeter Institute (June 24-28, 2019)
Higher Structures in SUSY QFT, 3 lectures, KIAS Seoul (July 30-Aug 3, 2018)
Higher Algebra in SUSY QFT, 3 lectures [1 2 3], ICTS Bangalore (July 23-27, 2018)
Dual Boundary Conditions for 3d N=2 Gauge Theories, 2 lectures, Fields and Duality, LMU Munich (Oct 11-12, 2017)
Quantum Field Theory (a survey), 2 lectures, Arithmetic Chern-Simons Theory, U. Leiden (May 23, 2017)
3d Gauge Theories, Symplectic Duality and Knot Homology, 4 lectures, Mathematical Aspects of Six-Dimensional Quantum Field Theories, UC Berkeley (Dec 8-12, 2014)
Holomorphic Blocks for 3d SCFT’s, 2 lectures [1 2], Simons Summer Workshop (Aug 16, 2012)
Colloquiua
Representing (Topological) Line Operators, Dublin Area Theoretical Physics Colloquium (Feb 12, 2025)
Taming categories in QFT, 23rd Geometry and Physics Seminar, Uppsala University (May 8, 2024)
Holomorphic twists and boundary vertex algebras, QFT and Geometry Seminar, online (Aug 6, 2020)
3d Gauge Theories and Representation Theory, Hamburg ZMP Colloquium (Dec 5, 2019)
An Introduction to Physical Mathematics at St. John’s College, Oxford, Research Soirée, (May 3, 2018)
A 3d bridge between mathematics and physics, Amsterdam Math-Physics Colloquium (Apr 9, 2015)
A three-dimensional bridge between physics and mathematics, UT Austin (Jan 29, 2015)
A three-dimensional bridge between physics and mathematics, UC Davis (Jan 23, 2015)
Chern-Simons theory with complex gauge group, UI Urbana-Champaign (Dec 17, 2014)
Six is the new ten, IAS Math Conversation (Apr 9, 2014)
International conferences and workshops
Tannakian QFT: from sparks to quantum groups, MaPhyAG workshop on Integrability, Geometry, and QFT Madrid (Oct 10, 2024)
Meromorphic tensor categories and shifted r-matrices, Quantization in Representation Theory, Derived Algebraic Geometry, and Gauge Theory, SwissMAP Les Diablerets, Switzerland (Sept 20, 2024)
Tannakian QFT, Recent Developments in Topological Quantum Field Theory, BIMSA Beijing (Sept 5, 2024)
Finding Quantum Groups in 3d TQFT, workshop on BPS Dynamics and Quantum Mathematics, Galileo Galilei Institute, Florence (July 5, 2024)
Sparks, Quantum Groups, and Kazhdan-Lusztig Correspondences, New Directions in Conformal Field Theory Hamburg CRC (March 21, 2024)
Spark Algebras and Quantum Groups, European Quantum Algebra Lectures (online) (March 14)
Spark Algebras and Quantum Groups, Quantum Topology Biennial: Focus on Reprepresentation Theory, SwissMAP Les Diablerets, Switzerland (Jan 17, 2024)
Spark Algebras and Quantum Groups, Quantization Days 4.0 [virtual workshop] (Dec 12, 2023)
Quantum groups in 3d N=4 theories, Recent Trends in Supersymemtric Field Theories, Jeju, Korea (Oct 29, 2023)
Boundary VOA's and line operators in SUSY QFT, Supersymmetric QFT and Mathematics, Pollica, Italy (Sept 20, 2023)
From Symplectic Singularities to Braided Tensor Categories, Symplectic Singularities & SUSY QFT, Amiens (July 17, 2023)
Braided tensor categories in 3d N=4 theories, 29th Nordic Congress of Mathematicians, Aalborg, Denmark (July 7, 2023)
Higgs branches, Coulomb branches, and link homology, ICMS conference on The Geometry of Double Affine Hecke Algebras and Coulomb Branches, Edinburgh (March 24, 2023)
Vortices and VOA's [slides], "Gauge Theory, Moduli Spaces and Representation Theory," in honor of the 60th birthday of Hiraku Nakajima, RIMS Kyoto (Feb 20, 2023)
Vortices, Affine Springer Fibers, and Link Homology, Gauged maps, vortices, and their moduli, SwissMAP Research Station in Les Diablerets (Aug 27, 2022)
TQFT's and Flat Connections, "Global Categorical Symmetries," Perimeter Institute (June 10, 2022)
Aspects of 3d N=4 TQFT, Mirrors, Moduli, and M-Theory in the Midlands, LMS Regional Meeting (April 5, 2022)
Derived and Deformable 3d TQFT, "Vertex Algebras and Poisson Geometry," SwissMAP Research Station in Les Diablerets (Feb 23, 2022)
A QFT for Non-Semisimple TQFT, RIND Seminar on Mathematical Physics and String Theory/online (Jan 31, 2022)
Non-semisimple and derived QFT’s for quantum groups at a root of unity, “Quantum Field Theories and Quantum Topology Beyond Semisimplicity,” BIRS, Banff/online (Nov 4, 2021)
3d SUSY gauge theory and quantum groups at roots of unity, “Enumerative Geometry, Physics, and Representation Theory,” IHES Summer School/online (July 9, 2021)
QFT’s for Non-Semisimple TQFT’s, “Number Theory, Strings, and Quantum Physics,” IPMU Tokyo/online (June 2, 2021)
QFT’s for Non-Semisimple TQFT’s, “Perspectives on Knot Homology,” BIRS, Banff (May 17, 2021)
Categorifying the Schur Index, North British Math. Phys. Seminar (Nov 24, 2020)
Twists and Operators in 3d SUSY Gauge Theories, “GLSMs 2020,” Virginia Tech/online (Aug 18, 2020)
3d Mirror Symmetry and HOMFLY-PT Homology, String-Math 2020, Stellenbosch, South Africa/online (July 27, 2020)
Boundary Vertex Algebras, “Higher Structures in Geometry and Physics,” Fields Institute (Nov 20, 2019)
Vortices and Categories of Line Operators, “Novel Vistas on Vortices,” Simons Center (Nov 15, 2019)
Boundary Vertex Algebras, “BPS/CFT Correspondence,” CIRM Luminy (Sept 11, 2019)
Boundary Vertex Algebras, “Arithmetic Geometry and Quantum Field Theory,” KIAS Seoul (Aug 15, 2019)
Higher algebraic structures in SUSY QFT, 11th Internat. Symposium on Quantum Theories and Symmetry, CRM Montreal (July 1, 2019)
3d Mirror Symmetry and HOMFLY-PT Homology, “Geometric representation theory and low-dimensional topology,” Edinburgh (June 14, 2019)
HOMFLY homology and 3d mirror symmetry, “Quantum Knot Invariants and Supersymmetric Gauge Theories,” KITP Santa Barbara (Dec 12, 2018)
Categories of line operators in 3d N=4 gauge theories, “Quantum Fields, Knots, and Strings,” U. Warsaw (Sept 26, 2018)
(0,2) Dualities and 4-Simplices, “Geometry, Quantum Topology and Asymptotics,” Sandbjerg, Denmark (July 12, 2018)
Quantized symplectic resolutions and quantum gauge theories, CIME school on Geometric Representation Theory and Gauge Theory, Cetraro, Italy (June 29, 2018)
(0,2) Theories and the 4-Simplex, “Categorification in mathematical physics,” Simons Center (April 13, 2018)
G-Actions in Quantum Mechanics, “QFT on Manifolds with Boundary and the BV Formalism,” Perimeter Institute (May 8, 2017)
Koszul duality patterns in physics, String-Math 2017, Hamburg (July 27, 2017)
G-actions and Koszul duality in supersymmetric quantum mechanics, “Enumerative Geometry, Mirror Symmetry, and Physics” (Sheldon Katz’ 60th), UI Urbana-Champaign, (July 18, 2017)
Vortices and Vermas (and other applications of 3d gauge theory to geometric representation theory), “Homology theories in low dimensional topology” Newton Institute, Cambridge (Apr 6, 2017)
A Mathematical Definition of 3d Indices, “Hitchin Systems in Mathematics and Physics,” Perimeter Institute (Feb 14, 2017)
Counting Vortices in the 3D Index, “Topological Recursion and Modularity,” MATRIX, Melbourne (Dec 20, 2016)
Toward categorification of hyperbolic geometry, “Mathematics of QFT,” IBS, Pohang, South Korea (Aug 23, 2016)
Vortices, monopoles, and finite AGT, “Advances in Geometric Representation Theory,” U. Michigan (May 11, 2016)
3d BPS states, monopoles, and a finite version of AGT, “String Geometry and BPS State Counting,” IHP, Paris (Apr 25, 2016)
Quantum Modularity and Chern-Simons Theory, “Topological Recursion and TQFT’s,” MFO Oberwolfach (Feb 17, 2016)
Applications of 3d N=4 theories in geometric representation theory, “Geometric Representation Theory,” Simons Center (Jan 14, 2016)
Toward Categorification of Hyperbolic Geometry, “New Developments in TQFT,” QGM Aarhus (July 29, 2015)
Categorified Hyperbolic Geometry, “Classical and quantum hyperbolic geometry and topology,” U. Paris Sud (Orsay) (July 9, 2015)
The Coulomb branch of 3d N=4 theories, “Geometric Unification from Six Dimensions,” BIRS, Canada (May 26, 2015)
Aspects of the 3d-3d correspondence, ENS Summer Institute, ENS Paris (Aug 26, 2014)
A Spectral Perspective on Neumann-Zagier, “Low-dimensional topology and number theory,” MFO Oberwolfach (Aug 20, 2014)
3d-3d correspondence, lens spaces, and quantizations of Teichmuller theory, “Geometry, topology and physics of moduli spaces of Higgs bundles,” IMS Singapore (Aug 6, 2014)
A Spectral Perspective on Neumann-Zagier, “Geometry, Quantum Topology and Asymptotics,” Geneva (July 3, 2014)
Quantum Curves and Quantum Knot Invariants, “Quantum Curves and Quantum Knot Invariants,” BIRS, Canada (June 18, 2014)
3d N=4 theories and symplectic duality, String-Math 2014, Edmonton (June 9, 2014)
3d N=4 theories, symplectic duality, and knot homology, Mathematics of String Theory, King’s College London (June 2, 2014)
q-Teichmuller Theory from 3d, “Pressure Metrics and Higgs Bundles,” QGM Aarhus (Aug 20, 2013)
Framed 3-manifolds and flat SL(2,C) connections, “Geometric Topology in New York,” Columbia U. (Aug 14, 2013)
BPS domain walls in 4d N=2 theories, Mathematics of Superconformal Field Theory, ACP Aspen (July 30, 2013)
RG Domain Walls and Janus Attractors, String-Math 2013, Simons Center (June 18, 2013)
From framed flat connections on 3-manifolds to RG domain walls in 4d gauge theory, “Moduli Spaces in Mathematical Physics,” CRM Montreal (June 7, 2013)
Flags, Triangulations, and Quantization, “Topology and Hyperbolic Geometry,” Nha Trang, Vietnam (May 14, 2013)
K-decompositions and framed flat connections on 3-manifolds, “Teichmuller theory: quantization and relations with physics,” Erwin Schrodinger Institute, Vienna (Apr 17, 2013)
RG Domain Walls, “New mathematical structures in SUSY gauge theory?” Perimeter Institute (March 2, 2013)
SL(N) local systems on 3-manifolds, “Mathematics and Physics of Moduli Spaces,” MATCH Heidelberg (Sept 24, 2012)
Supersymmetric Vortices, 3d BPS states, and 3-Manifolds, “Geometry of Gauged Vortices,” Hausdorff Institute, Bonn (Sept 18, 2012)
Spin Networks, Teichmüller Theory, and RG Domain Walls, “New Perspectives in Topological Field Theories,” Hamburg (Aug 31, 2012)
Class R: A User’s Guide, Strings 2012, Munich (July 25, 2012)
Holomorphic Blocks and Stokes Phenomena, String-Math 2012, HCM Bonn (July 16, 2012)
Class R: The Bloch Group on Steroids, “Algebraic Topology, Field Theory, and Strings,” Simons Center (May 25, 2012)
Nonabelian Torsion and the Neumann-Zagier Equations, “Low Dimensional Topology and Number Theory,” Fukuoka (March 16, 2012)
3-Manifolds and Duality Domain Walls, “New Perspectives on Supersymmetric Gauge Theories,” LMU Munich (March 1, 2012)
3-Manifolds and 3d Gauge Theory, “Classical and Quantum Integrable Systems,” Dubna, Russia (Jan 24, 2012)
3-Manifolds and 3d Gauge Theory, “Geometric Correspondences of Gauge Theories,” SISSA Trieste (Oct 30, 2012)
Tetrahedra, 3-Manifolds, and 3d Gauge Theory, “Nonperturbative Effects and Dualities in QFT and Integrable Systems,” KITP Santa Barbara (July 27, 2011)
Chern-Simons with Complex Gauge Groups, Mathematische Arbeitstagung, MPIM Bonn, (June 29, 2011)
S-duality and Mirror Symmetry in Chern-Simons Theory, “Derived Categories,” Newton Institute, Cambridge (Apr 14, 2011)
Gluing Tetrahedra in TQFT, Quantum A-Polynomials, and Chern-Simons Theory, “Spring School in Geometry and Quantum Topology,” Les Diablerets (March 25, 2011)
Modularity in Chern-Simons Theory, “Modular Forms and Mock Modular Forms,” ICTP, Trieste (March 17, 2011)
Triangles and tetrahedra: from wall crossing to complex Chern-Simons theory, “New Mathematical Methods in Quantum Gauge Theories,” ACP Aspen (July 7, 2010)
TQFT and the Volume Conjecture, “Low dimensional topology and number theory II,” U. Tokyo (March 17, 2010)
Refined and Motivic BPS Invariants, Simons Summer Workshop (Aug 11, 2009)
Refined and Motivic Wall Crossing, “Focus Week on New Invariants and Wall Crossing,” IPMU Tokyo (May 21, 2009)
Departmental seminars
Vortex Lines and dg-Shifted Yangians, Mathematical physics seminar, Perimeter Institute (Dec 5, 2024)
Tannakian QFT's, Mathematical physics seminar, Purdue University/online (Oct 29, 2024)
Finding Quantum Groups in 3d TQFT, Geometry and physics seminar, ICTP, Trieste (May 30, 2024)
Spark Algebras and Quantum Groups, Geometry Seminar, Chinese University of Hong Kong (Feb 22, 2024)
Spark Algebras and Quantum Groups, Mathematical physics seminar, Perimeter Institute (Dec 7, 2023)
Braided tensor categories in 3d N=4 theories, Imperial College London (May 17, 2023)
3d N=4 Vertex Algebras and Quantum Groups, Berkeley Informal String-Math Seminar (Nov 28, 2022)
Line Operators, Flat Connections, and VOA's, Berkeley Informal String-Math Seminar (May 2, 2022)
A QFT for Non-Semisimple TQFT, TQFT Journal Club, Queen Mary University, London/online (March 17, 2022)
A QFT for Non-Semisimple TQFT, Rutgers Physics NHETC/online (March 8, 2022)
A QFT for Non-Semisimple TQFT, Trinity College Dublin/online (Jan 24, 2022)
Classical and quantum A-polynomials, Cluster Geometry Lab Seminar, HSE Moscow/online (Nov 18, 2021)
QFT’s for Non-Semisimple TQFT’s, QMAP Seminar, UC Davis /online(Oct 1, 2021)
QFT’s for Non-Semisimple TQFT’s, iGAP Trieste/online (May 18, 2021)
QFT’s for Non-Semisimple TQFT’s, BIMSA (Beijing) Mathematical Physics Seminar/online (May 13, 2021)
3d Mirror Symmetry and HOMFLY-PT Homology, Lisbon TQFT Club/online (Nov 20, 2020)
The d=1,2,3 of TQFT (pre-talk); 3d Mirror Symmetry and HOMFLY-PT Homology (main talk), Univ. of Edinburgh Hodge Seminar/online (Oct 28, 2020)
3d Mirror Symmetry and HOMFLY-PT Homology, U. Mass Amherst Rep. Theory Seminar/online (Oct 26, 2020)
3d Twists, Mirror Symmetry, and Knot Homology, Boston Univ. Geometry & Physics Seminar/online (Oct 21, 2020)
3d Mirror Symmetry and HOMFLY-PT Homology, Kansas State M-Seminar/online (July 23, 2020)
Algebra, Geometry, and Duality in 3d Gauge Theory, Edinburgh (Dec 9, 2019)
3d Mirror Symmetry and Line Operators, Niels Bohr Institute, Copenhagen (Nov 26, 2019)
3d Mirror Symmetry and HOMFLY-PT Homology, Yale (Nov 11, 2019)
3d Homological Mirror Symmetry, U Penn (Nov 7, 2019)
3D Mirror Symmetry and HOMFLY-PT Homology, Perimeter Institute (Oct 31, 2019)
3D Mirror Symmetry and HOMFLY-PT Homology, UC Berkeley (Oct 21, 2019)
Categories of Line Operators in 3d N=4 Theories, Kavli IPMU (Oct 15, 2019)
Categories of line operators in 3d gauge theories, and homological 3d mirror symmetry, Oxford (May 6, 2019)
Categories of Line Operators in 3d N=4 Gauge Theories, Kansas State (April 8, 2019)
Categories of Line Operators in 3d N=4 Gauge Theories, Perimeter Institute (Oct 29, 2018)
Higher algebraic structures in SUSY QFT, Princeton (Oct 22, 2018)
Higher Products in Supersymmetric QFT, Imperial College London (Oct 4, 2018)
G-actions in quantum mechanics and Koszul duality, Oxford (May 14, 2018)
(0,2) dualities and 4-simplices, Oxford (June 4, 2018)
Koszul duality patterns in quantum field theory, UC Berkeley (Sept 18, 2017)
Equivariance and the Cosmological Constant, UT Austin geometry seminar (Apr 27, 2017)
Equivariance and the Cosmological Constant, Caltech (Mar 24, 2017)
3d Theories, Boundaries, and Representations, UC Berkeley (Dec 6 2016)
3d Index, Normal Surfaces, and Categorification, UT Austin (Apr 23, 2016)
Vortices, Monopoles, and Finite AGT, Rutgers (Apr 19, 2016)
3d Gauge Theory and Geometric Representation Theory, U. Western Ontario, (Apr 6, 2016)
Applications of 3d Gauge Theory to Geometric Representation Theory, U. Melbourne (March 2, 2016)
The 3d Index, U. Melbourne (Feb 24, 2016)
Vortices, Monopoles, and Finite AGT, UC Santa Barbara (Feb 3, 2016)
Applications of 3d gauge theory to geometric representation theory, U. Toronto (Jan 25, 2016)
Symplectic duality and 3d gauge theory, Northeastern (Nov 16, 2015)
SL(2,C) Chern-Simons Theory, Perimeter Institute (Nov 4, 2015)
3d Mirror Symmetry and Symplectic Duality, Princeton Mathematics (Oct 16, 2015)
3d Gauge Theory and Symplectic Duality, Perimeter Institute (Oct 1, 2015)
Boundaries and D-modules in 3d N=4 theories, Perimeter Institute (Oct 1, 2015)
The Coulomb branch of 3d N=4 theories, U. Amsterdam (April 8, 2015)
The Coulomb Branch of 3d N=4 Theories, Oxford (March 9, 2015)
Geometric representation theory, symplectic duality, and 3d supersymmetric gauge theory, Georgia Tech (Jan 9, 2015)
Boundary conditions and symplectic duality in 3d N=4 theories, UC Davis (Dec 12, 2014)
3d N=4 theories and knot homologies, UI Urbana-Champaign (Apr 24, 2014)
Boundary conditions and braids in 3d N=4 gauge theory, MIT (Apr 17, 2014)
A Spectral Perspective on Neumann-Zagier, Michigan State (March 10, 2014)
Knot homology, symplectic duality, and 3d gauge theory, UT Austin (Feb 26, 2014)
A Spectral Perspective on Neumann-Zagier, Temple U. (Feb 18, 2014)
Framed flat connections, K-decompositions, and the 3d-3d correspondence at higher rank, Harvard (Feb 7, 2013)
A Spectral Perspective on Neumann-Zagier, UC Berkeley, (Jan 27, 2014)
A Spectral Perspective on Neumann-Zagier, U. Maryland (Nov 8, 2013)
Domain Walls and Janus Attractors, Rutgers (Oct 8, 2013)
3-Manifolds and 3d Gauge Theories, U. Michigan (Jan 21, 2013)
3-Manifolds and 3d Gauge Theories, UI Urbana-Champaign (Nov 30, 2012)
3-Manifolds, K2-Lagrangians, and Quantization, UT Austin (Oct 18, 2012)
Supersymmetric boundary conditions, symmetry enhancement, and E7 surprises, Rutgers (Nov 27, 2012)
Holomorphic Blocks in 3d, Perimeter Institute (Nov 6, 2012)
The Quantum Content of the Gluing Equations, UC Berkeley (May 22, 2012)
3d Domain Walls of Class R, U. Penn (April 10, 2012)
Non-Abelian Torsion and the Neumann-Zagier Equations, Columbia (Feb 3, 2012)
3-Manifolds, 3d Gauge Theory, and 3d Indices, Caltech (Jan 6, 2012)
3-Manifolds, 3d Gauge Theory, and 3d Indices, UC Berkeley (Nov 16, 2011)
3-Manifolds and 3d Indices, Georgia Tech (Nov 4, 2011)
3-Manifolds and 3d Indices, MIT (Oct 24, 2011)
3-Manifolds, 3d Gauge Theory, and 3d Indices, Institute for Advanced Study (Oct 2011)
Liouville Theory and D-Modules, Rutgers (Apr 19, 2011)
A New Perspective on Gluing in TQFT, Caltech (Feb 11, 2011)
Quantum Curves in Chern-Simons Theory, Georgia Tech (Jan 19, 2011)
Quantum Riemann Surfaces, CERN, Geneva (Nov 25, 2010)
Quantum Riemann Surfaces, King’s College London (Nov 12, 2010)
Motivic Wall Crossing in Seiberg-Witten Theory, AMS Sectional Meeting, Mathematical String Theory (March 27, 2010)
Motivic Wall Crossing in Seiberg-Witten Theory, UC Berkeley (Dec 2009)
Multicenter black holes and refined microstate counting, Stanford (Apr 20, 2009)
A hyperbolic state sum model for SL(2,C) Chern-Simons theory, UC Santa Barbara (May 3, 2008)