talks given

Lecture series

• 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

• 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

• 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

• 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)