# Ben Webster

University of Waterloo

Areas of research:

### Overview

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.

### Teaching Affiliations

If you are interested in working with me as a PhD student, please send me an email at [email protected]. Perimeter Institute is committed to diversity within its community and I welcome applications from underrepresented groups. Information about working with me as a graduate student can be found on my webpage here: https://uwaterloo.ca/scholar/b2webste/info-students

### 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; since coming to Perimeter, one of my focuses has been how understanding these varieties in the context of field theory gives us insight into the mathematics.

### Positions Held

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

### Awards

- Golden Jubilee Research Excellence Award, Faculty of Math, University of Waterloo, 2019
- Discovery Grant - "Diagrammatic and geometric techniques in representation theory", Natural Sciences and Engineering Research Council of Canada (NSERC), 2018-2023
- Cory Family Teaching Award, University of Virginia, 2016
- International Researcher Collaboration Award, Sydney University, 2015
- Conference Grant - "Algebra, Combinatorics, and Representation Theory", National Science Foundation (NSF), 2013
- Career Grant - "Representation theory of symplectic singularities", National Science Foundation (NSF), 2012-2017

### Recent Publications

- Kamnitzer, J., Webster, B., Weekes, A., & Yacobi, O. (2024). Lie algebra actions on module categories for truncated shifted yangians. Forum of Mathematics Sigma, 12, e18. doi:10.1017/fms.2024.3
- Webster, B., & Yoo, P. (2023). 3-dimensional mirror symmetry. Notices of the American Mathematical Society. https://arxiv.org/abs/2308.06191
- Gaiotto, D., Hilburn, J., Redondo-Yuste, J., Webster, B., & Zhou, Z. (2023). Twisted traces on abelian quantum Higgs and Coulomb branches. arxiv:2308.15198v1
- Munasinghe, D., & Webster, B. (2023). On the representation theory of Schur algebras in type $B$. arxiv:2307.10406v2
- Brundan, J., Wang, W., & Webster, B. (2023). Nil-Brauer categorifies the split $\imath$-quantum group of rank one. doi:10.48550/arxiv.2305.05877
- Brundan, J., Wang, W., & Webster, B. (2023). The nil-Brauer category. doi:10.48550/arxiv.2305.03876
- Webster, B. (2023). RoCK blocks for affine categorical representations. doi:10.48550/arxiv.2301.01613
- Webster, B. (2022). Coherent sheaves and quantum Coulomb branches II: quiver gauge theories and knot homology. doi:10.48550/arxiv.2211.02099
- Kamnitzer, J., Webster, B., Weekes, A., & Yacobi, O. (2022). Lie algebra actions on module categories for truncated shifted Yangians. doi:10.48550/arxiv.2203.12429
- Alekseev, A., Frenkel, E., Rosso, M., Webster, B., & Yakimov, M. (Eds.) (2021). Representation Theory, Mathematical Physics, and Integrable Systems. Springer International Publishing. doi:10.1007/978-3-030-78148-4

### Seminars

- W-algebras as Coulomb branches, University of Edinburgh, International Centre for Mathematics Sciences, Edinburgh, United Kingdom, 2023/08/29
- Coulomb Branches and Knot Homology, Massachusetts Institute of Technology, Cambridge, United States, 2023/06/19
- Noncommutative resolutions and Coulomb branches, Imperial College London, London, United Kingdom, 2023/03/29
- Categorical sl2 actions and RoCK blocks, University of Sydney, Sydney, Australia, 2023/02/14
- Categorical sl2 representations and modular representation theory, University of Sydney, Sydney, Australia, 2023/02/06
- Noncommutative resolutions and Coulomb branches, University of Melbourne, Mathematics, Melbourne, Australia, 2023/01/25
- The noncommutative Springer resolution of type A and KLR W algebras, National University of Singapore, Mathematics, Singapore, Singapore, 2023/01/06
- Fun with Coulomb branches, American Institute of Mathematics, Palo Alto, United States, 2022/12/13
- Heisenberg and Kac-Moody categorification, Mathematical Research Institute of Oberwolfach, Oberwolfach, Germany, 2022/08/31
- Discussion on knot homology, QFT for Mathematicians 2022, 2022/06/27, PIRSA:22060082
- Representation theory and a little bit of quantum field theory, GASC Seminar, Northeastern, 2022/01/01
- Coulomb branches and KLRW algebras, Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, Northeastern, 2022/01/01
- Mirror symmetry for hypertoric varieties, Geometry seminar, Boston University, 2022/01/01
- Representation theory and a little bit of quantum field theory, McMaster, 2022/01/01
- Representation theory and a little bit of quantum field theory, Queens, 2022/01/01
- 3d mirror symmetry and symplectic singularities, Geometry and Physics Seminar, Zhejiang University, Zoom, 2022/01/01