Department of Mathematics

University of Massachusetts Dartmouth

North Dartmouth, MA 02747-2300

Tel: (508) 910-6905

Fax: (508) 910-6917

dfine@umassd.edu

- Professor of Mathematics
- Ph.D. in Applied Mathematics, MIT (1989)
- B.S. with Distinction in Mathematics, Stanford University (1983)

**Courses this term:**

- MTH182 Discrete Mathematics II Syllabus Course Policies
- MTH212 Differential Equations Syllabus Course Policies
- MTH451/551 Differential Geometry Syllabus Course Policies

- Rigorous path integrals for supersymmetric quantum mechanics: completing the path integral proof of the index theorem
- Path integrals, SUSY QM and the Atiyah-Singer index theorem for twisted Dirac
- A Rigorous Path Integral for N=1 Supersymmetic Quantum Mechanics on a Riemannian Manifold
- A Rigorous Path Integral for Supersymmetric Quantum Mechanics and the Heat Kernel
- Topological Sectors and Measures on Moduli Space in Quantum Yang-Mills on a Riemann Surface
- Energy in Yang-Mills on a Riemann Surface

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