**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

**Workshops and conferences organized**

**Talks and seminars given**

Lecture series

- TBA, 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

*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)*T**he**Coulomb branch**of**3**d 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

*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 theorie*s, 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)