Division of Natural Science
New College of Florida
5700 N. Tamiami Trail
Sarasota, FL 34243		 960 Indian Beach Drive
Sarasota, FL 34234
Phone: (941)-955-4072 (Home)
Phone: (941)-359-4375 (Office)

Research Interests:

Education:
 
9/86 - 6/90  Massachusetts Institute of Technology
Phd in Mathematics, Thesis Advisor: R. B. Melrose
Thesis: The Laplacian on Spaces with Cone-Like Singularity
9/82- 6/86 The Ohio State University
B.S., M.S. in Mathematics with Honors and Distinction, Battelle Scholar, Phi Beta Kappa

Employment:
 
2005-present  New College of Florida
Division of Natural Science
Professor of Mathematics
2000-2005 New College of Florida
Division of Natural Science
Associate Professor of Mathematics
1995-2000  New College of USF
Division of Natural Science
Assistant Professor of Mathematics
1994 The Ohio State University
Department of Mathematics
Instructor
1993 Denison University
Department of Mathematics
Visiting Professor
1990-1993 The Ohio State University
Department of Mathematics
Research Instructor

Membership and Visiting Positions:
 
9/01-9/02 Massachusetts Institute of Technology 
6/98-7/98 New College, Oxford University (Visiting Fellow)
2/98-3/98 Mathematical Science Research Institute, Berkeley
10/97-11/97 Fields Institute, Toronto
6/96-7/96 Institute for Advanced Study (IAS/PCMI Program)

Publications:

1.  The Laplacian on Spaces with Cone-Like Singularities, MIT Thesis, 1990.
2.  On the functional logdet and related flows on the space of closed embedded curves on S2 - (with D. Burghelea, L. Friedlander, and T. Kappeler),  Jour. Func. Anal. (1994) vol 120, pgs 440-466.
3.  Analytic and Reidemeister torsion for representations in finite type Hilbert modules - (with D. Burghelea, L. Friedlander, T. Kappeler), GAFA (1996) vol 6, pgs 751-859.
4.  The extended generalized lambda distribution system for fitting distributions to data: history, completion (theory and tables) and applications - the final word on moment fits  (with Z. Karian and E. Dudewics), Comm. Stat.: Simulation and Computation, (1996) vol 25, pgs 611-642.
5.  Brownian functionals on hypersurfaces in Rn  (with K. Kinateder), Proc. A.M.S. (1997) vol 125, pgs 1815-1822.
6.  Hypersurfaces in Rn  and the variance of exit times for Brownian motion (with K. Kinateder) Proc. A.M.S. (1997) vol 125, pgs 2453-2462.
7.  Symmetry problems arising in probability (with S. Fromm) Proc. A.M.S. (1997) vol 125, pgs 3293-3298.
8.  Exit time moments, boundary value problems, and the geometry of domains in Euclidean space  (with K. Kinateder, D. Miller) Prob. Th. and Rel. (1998) vol 111, pgs 469-487.
9.  Variational principles for average exit time moments for diffusions in Euclidean space  (with K. Kinateder) Proc. A.M.S. (1999) vol 127, pgs 2767-2772.
10.  Isoperimetric conditions, Poisson problems and diffusions in Riemannian manifolds,  Potential Analysis (2002) vol 16, pgs 115-138.
11.  An Ito formula for domain-valued processes driven by stochastic flows  (with K. Kinateder) Prob. Th. and Rel. (2002) vol 124, pgs 73-99.
12.  Diffusions on graphs, Poisson problems, and spectral geometry   (with R. Meyers) Trans. AMS (2002) vol 347, pgs 5111-5136.
13.  Spectral geometry, the Polya conjecture, and diffusions   Proceedings of the 34th Annual Florida MAA meeting, http://www.spcollege.edu/central/maa/proceedings/2001/default.htm (electronic).
14.  Redefining spinors in Lorentz violating QED   (with D. Colladay) Jour. Math. Physics (2002) vol 43, pgs 3554-3564.
15.  Dirichlet spectrum and heat content   (with R. Meyers) Jour. Funct. Analysis (2003) vol 200, pgs 150-159.
16.  Isospectral polygons, planar graphs and heat content   (with R. Meyers) Proc. AMS (2003) vol 131, pgs  3589- 3599.
17.  Diffusions, exit time moments and Weierstrass theorems   (with V. de la Pena)  Proc. AMS (2004)  vol 132,  pgs 2465-2474.
18.  Moment problems and the causal set approach to quantum gravity  (with A. Ash) Jour. Math. Physics (2003) vol 44, pgs 1666-1678.
19.  Recent results in geometric analysis involving probability   In: Recent Advances in Applied Probability, ed. H.  Gzyl, Kluwer,  Dodrecht (2005),  pgs 351--395.
20.  Yang-Mill instantons with Lorentz violations (with D. Colladay)  Jour. Math. Physics (2004) vol 45, pgs 3228-3238.
21.  Deformed instantons (with D. Colladay)  In:  Proceedings of the  Third Meeting on CPT and Lorentz Symmetry, ed V. A. Kostelecky, World Scientific, Singapore (2005) pgs 312--317.
22.  Nonrelativistic ideal gasses with Lorentz violations (with D. Colladay)  In:  Proceedings of the  Third Meeting on CPT and Lorentz Symmetry, ed V. A. Kostelecky, World Scientific, Singapore (2005) pgs 264--269.
23.  Random graphs and an approach to discrete quantum gravity Proceedings of the 37th Annual Florida MAA meeting (To Appear).
24.  Statistical mechanics and Lorentz violation (with D. Colladay)  Phys Rev D (2004) vol 70, 125007.
25.  Random partial orders, posts and the causal set approach to discrete quantum gravity  (with A. Ash)  Jour. Math. Physics (2005) vol 46,  062502.
26.  Zeta regularized determinants for conic manifolds   (with P. Loya and J. Park)  Jour. Funct. Analysis (in press).
27.  Hitting time and inverse problems for Markov chains  (with V. de la Pena and H. Gzyl)  (submitted).
28.  Eta invariants for quantum graphs  (with P. Loya)  (in preparation).
29.  Bose-Einstein condensation and Lorentz violation  (with D.Colladay)  Phys Rev D (2006) vol 73, 105006.
30.  One-loop renormalization of Yang-Mills with Lorentz violation  (with D.Colladay)  Phys Rev D (2007) vol 75 105002.
31.  Renormalization of gauge theories with Lorentz violation  (with D.Colladay)  (to appear).
32.  Bose-Einstein condensates and Lorentz violation   (with D.Colladay)  (to appear).
33.  Dynamic regulation of cytoskeletal organization: a monte-carlo approach   (with E. Humphris) (In preparation).