Brian R. Williams Northeastern University [email protected] Department of Mathematics https://web.northeastern.edu/brwilliams 360 Huntington Ave. Boston, MA 02115 Phone: +1 (561) 512-4903

Employment

2018–present Northeastern University Zelevinsky Research Instructor (3 year postdoctoral position). Education

2012–2018 Northwestern University Ph.D., Mathematics. Thesis: The holomorphic σ-model and its symmetries. Advisors: John Francis, Kevin Costello.

2008–2012 University of Florida B.S., summa cum laude, Mathematics and Physics. Advisors: David Groisser, Pierre Ramond. Papers

· Higher Kac-Moody algebras and symmetries of holomorphic field theories. 2018. With Owen Gwilliam. Submitted. Available at arxiv:1810.06534.

· Renormalization for holomorphic field theories. 2018. Submitted. Available at arxiv:1809.02661.

· The holomorphic bosonic string. 2017. With Owen Gwilliam. To appear in Contemporary Mathematics. Available at arXiv:1711.05823.

· Homotopy RG flow and the non-linear σ-model. 2017. With Ryan Grady. To appear in Contemporary Mathematics. Available at arxiv:1710.05973.

· Asymptotic Freedom in the BV-formalism. With Chris Elliott and Philsang Yoo. Published in Journal of Geometry and Physics, 123 (C): 246–283, 2017.

· Chiral differential operators via Batalin-Vilkovisky quantization. 2017. With Owen Gwilliam and Vasily Gorbounov. Submitted. Available at arxiv:1610.09657. Papers (cont.) · The Virasoro vertex algebra and factorization algebras on Riemann surfaces. Published in Letters in Mathematical Physics, 107 (12):2189–2237, 2017.

Awards and National Science Foundation Graduate Research Fellowship (GRFP) Fellowships 2012–2018

Goldwater Scholar 2011–2012

Invited Talks The spooky side of factorization algebras and an index theorem. Northeastern University. “Pick my Brain” Seminar. Fall 2018.

The higher dimensional Kac-Moody and Virasoro algebras Boston Univeristy. Geometry and Physics Seminar. Fall 2018.

The higher dimensional Kac-Moody and Virasoro algebras MIT Geometry and Representation theory Seminar. Fall 2018.

Higher dimensional Kac-Moody algebras as boundary SUSY gauge theories S´eminairede math´ematiquessup´erieures(Fields Institute): Derived Geometry and Higher Categorical Structures in Geometry and Physics. Summer 2018.

The chiral algebraic index theorem. Structures sup´erieuresen Alg`ebreet Topologie: Workshop on Factorisation Algebras and Homology and the Cobordism Hypothesis. Winter 2018.

Factorization algebras: axiomatizing the observables of a quantum field theory Florida Atlantic University Math Colloquium. Winter 2018.

Part I: Noether’s theorem and factorization; Part II: Higher dimensional Kac-Moody algebras. Notre Dame. Topology Seminar. Fall 2017.

Symmetries of higher dimensional holomorphic field theories Yale University. Geometry, Symmetry, and Physics Seminar. Fall 2017.

Symmetries of higher dimensional holomorphic field theories. Montana State University. Mathematics Seminar. Fall 2017

Symmetries of higher dimensional holomorphic field theories. Universit¨atHeidelberg, Mathematisches Institut. Conference ”Flat Connections in Physics and Geometry”. Summer 2017. Invited Talks Bulk-boundary BV-quantization for 2-1 theories. (cont.) Perimeter Institute for Theoretical Physics. Conference “Quantum Field Theory on Manifolds with Boundary and the BV Formalism”. Spring 2017.

Higher Kac–Moody algebras and factorization algebras. University of Berkeley. Topics in Factorization Algebras Seminar. Spring 2017

Higher dimensional chiral differential operators. Institut des Hautes Etudes´ Scientifiques (IHES), Theoretical Physics Seminar. Winter 2017.

Factorization algebras and holomorphic invariants of complex manifolds. University of Aberdeen, Scotland. Mathematics Seminar. Winter 2017.

Universal σ-models in the BV formalism. Montana State University. Mathematics Seminar. Fall 2016.

Observables in the effective BV formalism. Oberwolfach, Germany. Conference “Factorization algebras and Functorial Field Theories”. Summer 2016.

The universal βγ system and CDO’s. Boston University. Geometry and Physics Seminar. Winter 2016.

Chiral differential operators from the curved βγ system. Institute for Basic Science (IBS) Center for Geometry and Physics. Pohang, South Korea. Conference “Homotopical Methods in Quantum Field Theory”. Winter 2016.

Holomorphic factorization algebras and the Virasoro. Notre Dame. Topology Seminar. Fall 2015.

Fully extended two-dimensional TFT’s. University of British Columbia. Conference “West Coast Algebraic Topology Seminar”. Summer 2014.

Visiting Montana State University, August–September 2017. Appointments Research Visitor in the Mathematics Department. Hosted by David Ayala and Ryan Grady.

Perimeter Institute for Theoretical Physics, August–December 2015. Visiting Fellow. Organizational RTG Graduate Research Seminar: The Yangian and 4d gauge theory; Activities Coorganizer with Pavel Etingof and Valerio Toledano Laredo. Joint seminar between Northeastern University and MIT on the mathematics related to 4-dimensional gauge theory.

Lecture series at Oberwolfach; invited to give a joint 10 hour lecture series (with Si Li and Ryan Grady) on “Observables of QFT in the BV-formalism” during the conference “Factorization Algebras and Functorial Field Theory” at Oberwolfach, Germany. May 2016.

Student seminars at Northwestern University; organized and participated in various seminars on quantum field theory and homotopy theory aimed at graduate students in the math department. “ Learning seminar on string topology”, Fall 2013. “Topics in conformal field theory”, Fall 2014. “Instantons and the Nekrasov partition function”, Spring 2015.

Teaching Northeastern University Experience Calculus 1 (Honors) (Fall 2018). Topics class on “Derived deformation theory and Koszul duality” (Spring 2019).

Northwestern University Calculus, Linear Algebra (MENU/Honors), Complex Variables, Partial Differential Equations.

References Prof. Kevin Costello, Perimeter Institute [email protected] Prof. Mikhail Kapranov, Kavli IPMU [email protected] Prof. Si Li, Tsinghua University [email protected] Prof. Stephan Stolz, University of Notre Dame [email protected].