Note: This website is out of date. Current information here.

Employment

• July 2020-  Reader, Hodge Institute (Mathematics), University of Edinburgh
• July 2021-  Professor of Mathematics, UC Davis (on leave)
• July 2019-June 2021 Associate Professor of Mathematics, UC Davis
• July 2015-June 2019 Assistant Professor of Mathematics, UC Davis
• Sep. 2015-June 2016 Senior Postdoc, Perimeter Institute for Theoretical Physics
• Dec. 2013-Aug 2015 Long-Term Member, Institute for Advanced Study
• Jan. 2011-Nov. 2013 Member, Institute for Advanced Study
• Oct. 2010-Sep. 2015 Junior Research Fellow, Trinity College, Cambridge
• Sep. 2010 Postdoc, Max Planck Institute for Mathematics, Bonn

Education

• 2010 Ph.D. in Physics, Caltech
• 2005 MASt in Theoretical Physics (Part III Maths), Cambridge
• 2004 A.B. in Mathematics, Princeton

Honors and Awards

• 2018-23 NSF CAREER Grant
• 2017-18 UC Davis Hellman Fellow
• 2010 Caltech Clauser Prize for Ph.D. Thesis
• 2006-09 NDSEG Graduate Fellowship
• 2004-05 Studentship in Mathematics, Trinity College, Cambridge
• 2000 US Presidential Scholar

Grants

• 2018-23 NSF Career Grant No. 1753077 The Algebraic Structures of 3d Gauge Theory $400,000
• 2017-21 NSF Focused Research Group Grant No. 1664454 Homotopy Renormalization of Topological Field Theories $113,937
• 2014-18 (Co-PI, PI: Piotr Sulkowski) ERC Support for Frontier Research Grant No. 335739 Quantum Fields and Knot Homologies $70,000

Publications

Recent teaching

Workshops and conferences organized

Talks and seminars given

Lecture series

• Derived geometry in twists of gauge theories, 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)
• 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)

International conferences and workshops

• Non-semisimple and derived QFT’s for quantum groups at a root of unity, “Quantum Field Theories and Quantum Topology Beyond Semisimplicity,” BIRS, Banff (Nov 4, 2021)
• 3d SUSY gauge theory and quantum groups at roots of unity, “Enumerative Geometry, Physics, and Representation Theory,” IHES Summer School (July 9, 2021)
• QFT’s for Non-Semisimple TQFT’s, “Number Theory, Strings, and Quantum Physics,” IPMU Tokyo (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

• Classical and quantum A-polynomials, Cluster Geometry Lab Seminar, HSE Moscow (Nov 18, 2021)
• QFT’s for Non-Semisimple TQFT’s, QMAP Seminar, UC Davis (Oct 1, 2021)
• QFT’s for Non-Semisimple TQFT’s, iGAP Trieste (May 18, 2021)
• QFT’s for Non-Semisimple TQFT’s, BIMSA (Beijing) Mathematical Physics Seminar (May 13, 2021)
• 3d Mirror Symmetry and HOMFLY-PT Homology, Lisbon TQFT Club (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 (Oct 28, 2020)
• 3d Mirror Symmetry and HOMFLY-PT Homology, U. Mass Amherst Rep. Theory Seminar (Oct 26, 2020)
• 3d Twists, Mirror Symmetry, and Knot Homology, Boston Univ. Geometry & Physics Seminar (Oct 21, 2020)
• 3d Mirror Symmetry and HOMFLY-PT Homology, Kansas State M-Seminar (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)
• An Introduction to Physical Mathematics at St. John’s College, Oxford, Research Soiree, (May 3, 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)
• Six is the new ten, IAS Math Conversation (Apr 9, 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)