## Patrick McDonald

### Professor of Mathematics; Director of Data Science Program - Data Science Program - Mathematics - Natural Sciences

- Phone: (941) 487-4375
- Email: mcdonald@ncf.edu
- Office Location: HNS 103
- Mail Location: HNS 111

Director of Data Science, Professor of Mathematics

Ph.D., Massachusetts Institute of Technology

B.S., M.S., The Ohio State University

**Interests:** Probability and Stochastic Analysis, PDE, Optimization.

Go to Dr. McDonald’s personal homepage

Professor McDonald’s research centers on partial differential equations, microlocal analysis, and geometry. His published work includes results concerning analytic surgery, analytic torsion, infinite dimensional Morse theory, statistics, geometric aspects of Brownian motion, spectral geometry and over determined boundary value problems.

His most recent results are in mathematical physics, where he works on Lorentz violating field theories and quantum gravity, and mathematical biology, where his work centers on microtubule dynamics. He enjoys teaching analysis, probability, geometry and Brazilian jiu-jitsu.

**Recent Courses
**Partial Differential Equations

Real Analysis II

Probability

Number Theory ISP

**Selected Publications**

Ash, A., & **McDonald, P. **(2005 ). Random partial orders, posts, and the causal set approach to discrete quantum gravity. Journal of Mathematical Physics, 46(6), 062502.

Ash, A., & **McDonald, P.** (2003) . Moment problems and the causal set approach to quantum gravity. Journal of Mathematical Physics, 44(4), 1666-1678.

Colladay, D., & **McDonald, P.** (2002). Redefining Spinors in Lorentz-violating quantum electrodynamics. Journal of Mathematical Physics, 43(7), 3554-3564. Retrieved March 30, 2007, from AIP database.

Colladay, D., & **McDonald, P.** (2004). Deformed Instantons. Proceedings of the Third Meeting on CPT and Lorentz Symmetry, Bloomington, IN, 6 pages. Arxiv preprint hep-ph/0409251, 2004 – arxiv.org

Colladay, D., &** McDonald, P.** (2004). Nonrelativistic ideal gasses with Lorentz Violations. Proceedings of the Third Meeting on CPT and Lorentz Symmetry, Bloomington, IN, 264-269. Arxiv preprint hep-ph/0409252, 2004 – arxiv.org

Colladay, D., & **McDonald, P.** (2004). Statistical mechanics and Lorentz violation. Physical Review D, 70(12), 125007.

Colladay, D., & **McDonald, P.** (2004). Yang-Mills instantons with Lorentz violation. Journal of Mathematical Physics, 45(8), 3228-3238.

Colladay, D., & **McDonald, P.** (2006). Bose-Einstein condensates as a probe for Lorentz violation. Physical Review D, 73(10), 2007-105006 . Retrieved February 7, 2007, from http://link.aps.org/abstract/PRD/v73/e105006

Colladay, D., & **McDonald, P.** (2006). One-loop renormalization of pure Yang-Mills with Lorentz violation. High Energy Physics – Phenomenology, 1(14 pp.). Arxiv preprint hep-ph/0609084. Retrieved April 10, 2007, from http://arxiv.org/abs/

hep-ph/0609084

de la Pena, V. H., & **McDonald, P.** (2004). Diffusions, exit time moments and Weierstrass theorems. Proceedings of the American Mathematical Society, 132(8), 2465-2474.

Kinateder, K., & **McDonald, P.** (2002 September). An Ito formula for domain-valued processes driven by Stochastic flows. Probability Theory and Related Fields, 124(1), 73-99.

Loya, P., **McDonald, P.**, & Park, J. (2007 January 1). Zeta regularized determinants for Conic manifolds. Journal of Functional Analysis, 242(1), 195-229.

**McDonald, P.** (2001) Spectral Geometry, the Polya conjecture, and diffusions. Paper presented at the Proceedings of the 34th Annual Florida MAA meeting. Retrieved February 5, 2007

**McDonald, P. **(2002). Isoperimetric conditions, Poisson problems, and diffusions in Riemannian Manifolds. Potential Analysis, 16(2), 115-138.

**McDonald, P.** (2005). Recent results in Geometric analysis involving probability . In H. Gzyl (Ed.), Recent Advances in Applied Probability (pp. 351-395). Dodrecht: Kluwer.

**McDonald, P.**, & Meyers, R. (2002). Diffusions on graphs, Poisson problems and spectral geometry. Transactions of the American Mathematical Society, 3354(12), 5111-5136.

**McDonald, P.**, & Meyers, R. (2003). Dirichlet spectrum and heat content. Journal of Functional Analysis, 200(1), 150-159.

**McDonald, P.**, & Meyers, R. (2003). Isospectral polygons, planar graphs and heat content. Proceedings of the American Mathematical Society, 131(11), 3589-3599.