Calvin McPhail-Snyder, Assistant Research Professor

"Quantum topology" applies ideas from mathematical physics and representation theory to the study of topological objects like knots and manifolds. The study of the Chern-Simons topological quantum field theory has been a major unifying theme, in particular its realization in terms of quantum groups.

Recently a number of researchers have worked to extend the Chern-Simons construction by passing to noncompact gauge groups. This process is still somewhat mysterious from a mathematical point of view, but seems to require using "non-semisimple" algebraic objects in place of semisimple ones. It also brings into play extra geometric structure that previously was not relevant. The resulting invariants of knots and manifolds are more complicated but also more powerful than in the compact/semisimple case. I am interested in several aspects of this problem, in particular its consequences for the study of hyperbolic knots.

Contact Info:

Office Location:
Office Phone:	(919) 660-2800
Email Address:
Web Page:	http://esselltwo.com

Teaching (Spring 2023):

• MATH 401.01, INTRO ABSTRACT ALGEBRA Synopsis

  Physics 154, WF 08:30 AM-09:45 AM

• MATH 701.01, INTRO ABSTRACT ALGEBRA Synopsis

  Physics 154, WF 08:30 AM-09:45 AM

Education:

Ph.D.

University of California - Berkeley

2021

Recent Publications

1. McPhail-Snyder, C, Hyperbolic structures on link complements, octahedral decompositions, and quantum SL₂ (March, 2022) [doi]
2. Kai-Chieh, C; McPhail-Snyder, C; Morrison, S; Snyder, N, Kashaev-Reshetikhin Invariants of Links (August, 2021) [doi]
3. McPhail-Snyder, C, Holonomy invariants of links and nonabelian Reidemeister torsion, Quantum Topology, vol. 13 no. 1 (March, 2020), pp. 55-135, European Mathematical Society [doi]
4. McPhail-Snyder, C; Miller, KA, Planar diagrams for local invariants of graphs in surfaces, Journal of Knot Theory and Its Ramifications, vol. 29 no. 01 (January, 2020), pp. 1950093-1950093, World Scientific Pub Co Pte Lt [doi]  [abs]