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# Ben Webster

University of Waterloo

Area of Research:
Email: bwebster@perimeterinstitute.ca

My research is on connections between representation theory, mathematical physics, geometry and topology, including knot homology, the geometry of symplectic singularities, and categorification. I moved to Waterloo and Perimeter in 2017. In the past, I've been an Assistant Professor at the University of Virginia, Northeastern University and the University of Oregon, a C.L.E. Moore Instructor at MIT, and a postdoctoral fellow at the Institute for Advanced Study.

I received my Ph.D. in 2007 from UC Berkeley, under the supervision of Nicolai Reshetikhin, and spent the fall of 2006 at the Center for the Topology and Quantization of Moduli Spaces in Aarhus, Denmark. In Spring 2014, I was a Junior Chair at Université Denis-Diderot (Paris 7) with support from Fondation Sciences Mathématiques de Paris. Before that, I studied at Simon's Rock College and the Budapest Semesters in Mathematics Program. Before I moved to Canada, my research was supported by the NSF under a CAREER award, and graduate and postdoctoral fellowships, and by a Sloan Research Fellowship.

## AFFILIATIONS

Department of Pure Mathematics, University of Waterloo

## Research Interests

My research is on the interface between representation theory, algebraic geometry and mathematical physics. Hyperkahler cones appear naturally in physics as branches of moduli spaces of vacua for N=4 d=3 field theories; on the other hand, they are of mathematical interest because of their symplectic resolutions of singularities, and the fact that they can be quantized to produce interesting non-commutative algebras such as universal enveloping algebras and Cherednik algebras. I'm interested in the representation theory of algebras that appear this way, and how it relates to fields like topology and combinatorics; now that I'm at Perimeter, I also hope to investigate further how understanding these varieties in the context of field theory gives us insight into the mathematics.

## Positions Held

• 2017-present Associate Professor, University of Waterloo
• 2016-2017 Associate Professor, University of Virginia.
• 2013-2016 Assistant Professor, University of Virginia.
• 2011-2013 Assistant Professor, Northeastern University.
• 2010-2011 Assistant Professor, University of Oregon.
• 2008-2010 C.L.E. Moore Instructor and NSF Postdoctoral Fellow, M.I.T.
• 2007-2008 Member and NSF Postdoctoral Fellow, Institute for Advanced Study.

## Awards

• Cory Family Teaching Award (recognizes excellence in lower division teaching; one awarded for all STEM fields at UVA per year)
• International Researcher Collaboration Award from Sydney University
• Sloan Research Fellowship ($50,000) • NSF conference grant "Algebra, Combinatorics, and Representation Theory." ($40,000)
• NSF CAREER grant: "Representation theory of symplectic singularities" ($416,905) • NSA Young Investigator Grant ($30,000)
• NSF Postdoctoral Research Fellowship
• Clay Liftoff Fellowship

## Recent Publications

• Knot invariants and higher representation theory. Memoirs of the American Mathematical Society 250, no. 1191, pp. 133. arXiv: 1309.3796
• A geometric construction of colored HOMFLYPT homology (with G. Williamson). Geometry & Topology 21-5 (2017), 2557--2600. arXiv: 0905.0486
• Rouquier's conjecture and diagrammatic algebra. to appear in Forum of Mathematics Sigma arXiv: 1306.0074
• On generalized category O for a quiver variety. Mathematische Annalen 368 (2017), no. 1-2, 483-536. arXiv: 1409.4461
• Current algebras and categorified quantum groups (with A. Beliakova, K. Habiro and A. Lauda). Journal of the London Mathematical Society, 95, 248-276 arXiv: 1412.1417
• Quantizations of conical symplectic resolutions II: category O and symplectic duality. (with T. Braden, A. Licata and N. Proudfoot). Astérisque No. 384, 75-179. arXiv: 1407.0964
• Quantizations of conical symplectic resolutions I: local and global structure (with T. Braden and N. Proudfoot). Astérisque No. 384, 1-73. arXiv: 1208.3863
• A quantum Mirkovic-Vybornov isomorphism. (with Alex Weekes and Oded Yacobi) arXiv: 1706.03841
• Koszul duality between Higgs and Coulomb categories $\mathcal{O}$. arXiv: 1611.06541
• Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra. arXiv: 1609.05494
• Geometry and categorification. "Categorification in Geometry, Topology and Physics," 1-22, Contemp. Math., 680, AMS, 2017. arXiv: 1602.05992
• Tensor product algebras, Grassmannians and Khovanov homology. "Physics and mathematics of link homology," 23-58, Contemp. Math., 680, AMS, 2016. arXiv: 1312.7357

## Seminars

• Waterloo (Colloquium): Representation theory of symplectic singularities
• Newton Institute (Quantum topology and categorified representation theory): Representation theory and the Coulomb branch
• GWU (Knots in Washington): Knot invariants via quantizations of Hecke modifications
• UCLA (Gauge Theory and Categorification): Knot invariants via quantizations of Hecke modifications
• Univ. of Texas (Colloquium): Representation theory of symplectic singularities
• Rice (Colloquium): Representation theory of symplectic singularities
• UNC (Symplectic Varieties and Geometric Representation Theory): Representation theory and the Coulomb branch
• PIRSA:17030051, Three-dimensional mirror symmetry: a mathematical perspective, 2017-03-02, Colloquium