Stephen Sawin (Fairfield University)
Research Page
I am interested in Quantum Field Theory, and its relationship
to Geometry, Link and Three-Manifold Invariants
and Quantum Groups and Their Representation Theory.
My papers appearing in the Arxiv mathematical preprint
server:
- South Pointing
Chariot: An Invitation to Differential Geometry.
- Efficient
Computation
of the Kauffman Bracket, with Lauren Ellenberg, Gabriella Newman, and Jonathan Shi.J. Knot Theory Ramifications 23 (2014), no. 5, 11 pp.
- A Rigorous Path Integral for N=1 Supersymmetic Quantum Mechanics on a Riemannian Manifold , with Dana Fine
- A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel, with Dana Fine. Comm. Math. Phys. 284 (2008), no. 1, 79--91.
- Witten's Nonabelian Localization for Noncompact Hamiltonian Spaces. Differential Geom. Appl. 25 (2007), no. 2, 191--206.
- Quantum Groups at Roots of Unity and Modularity. J. Knot Theory Ramifications 15 (2006), no. 10, 1245--1277.
- Closed subsets of the Weyl alcove and TQFTs.Pacific J. Math. 228 (2006), no. 2, 305--324.
- Three-Dimensional 2-Framed TQFTs and Surgery. J. Knot Theory Ramifications 13 (2004), no. 7, 947--963.
- Invariants of Spin Three-Manifolds From Chern-Simons Theory and Finite-Dimensional Hopf Algebras. Adv. Math. 165 (2002), no. 1, 35--70.
- Jones-Witten Invariants for Nonsimply-Connected Lie Groups and The Geometry of the Weyl Alcove. Adv. Math. 165 (2002), no. 1, 1--34.
-
Diffeomorphism-Invariant Spin Network States, with John C. Baez. J. Funct. Anal. 158 (1998), no. 2, 253--266.
- On Finiteness of
Certain Vassiliev Invariants, with Louis H. Kauffman and
Masahico Saito. J. Knot Theory Ramifications 6 (1997), no. 2, 291--297.
- Functional Integration
on Spaces of Connections, with John C. Baez. J. Funct. Anal.,
150 (1997), 1-26. J. Funct. Anal. 150 (1997), no. 1, 1--26.
- Links, Quantum Groups, and TQFT's. Bull. Amer. Math. Soc. (N.S.) 33 (1996), no. 4, 413--445.
- Path Integration in
Two-Dimensional Toplogical Quantum Field Theory. J. Math. Phys.
36 (1995), no. 11, 6130--6136.
- Direct Sum Decompositions and Indecomposable TQFT's. J. Math. Phys. 36 (1995), no. 12, 6673--6680.
My papers not appearing in the Arxiv:
- Kauffman, Louis H. ; Radford, David ; Sawin, Stephen . Centrality and the KRH invariant.
J. Knot Theory Ramifications 7 (1998), no. 5, 571--624.
- Sawin, Steve . Finite-degree link invariants and connectivity.
J. Knot Theory Ramifications 5 (1996), no. 1, 117--136.
- Sawin, Stephen . Subfactors constructed from quantum groups.
Amer. J. Math. 117 (1995), no. 6, 1349--1369.
- Sawin, S. Relative commutants of Hecke algebra subfactors.
Amer. J. Math. 116 (1994), no. 3, 591--604.
- Sawin, Stephen French . Subfactors from quantum groups.
Thesis (Ph.D.) - University of California, Berkeley.
ProQuest LLC, Ann Arbor, MI, 1991. 45 pp.
Other Stuff: