帕特里克·麦克唐纳
数学教授
教育
Ph.D., Massachusetts Institute of Technology
B.S., M.S.他来自俄亥俄州立大学
Professor McDonald’s mathematical research centers on partial differential equations, 微局部分析, 和几何. His published work includes results concerning analytic surgery, 分析扭, 无限维莫尔斯理论, 统计数据, geometric aspects of Brownian motion, spectral geometry and over determined boundary value problems. He has published extensively in physics where his interests lie primarily in understanding the effects of symmetry breaking on the Standard Model. He is currently engaged in several projects involving health records.
He enjoys teaching analysis, probability, data visualization and Brazilian jiu-jitsu.
最近的课程
偏微分方程
真实分析II
概率
Visualization, Reporting and Reproducible Research
选定的出版物
1. The Laplacian on Spaces With Cone-Like Singularities, MIT Thesis, (1990), 71 pages.
2. On the functional logdet and related flows on the space of closed embedded curves on S2 -with D. Burghelea L. 弗里德兰德T. 卡柏,日记账. 函数. 分析的. 120(1994)， 440-466页.
3. 分析的ytic and Reidemeister torsion for representations in finite type Hilbert modules -with D. Burghelea L. 弗里德兰德T. Kappeler, GAFA, 6 (1996), pages 751-859.
4. The extended generalized lambda distribution system for fitting distribution to data: history, completion (theory and tables) and applications – the final word on moment fits -with Z. Karian E. Dudewicz,通讯. 统计.: Simulation and Computation, 25 (1996), pages 611-642.
5. Brownian functionals on hypersurfaces in Rn -with K. Kinateder, Proc. AMS, 125(1997)，第1815-1822页.
6. Hypersurfaces in Rn and the variance of exit times for Brownian motion -with K. Kinateder, Proc. AMS 125(1997)， 2453-2462页.
7. Symmetry problems arising in probability -with S. 弗洛姆,Proc. 美国医学杂志，125(1997)，3293-3298页
8. Exit times for diffusions in Euclidean Space -with K. Kinateder和D. 米勒:《赌城平台网站》.， 111(1998)，第469-487页.
9. Variational principles for average exit time moments for diffusions in Euclidean space -with K. Kinateder, Proc. AMS, 127(1999)，第2767-2772页.
10. 等周的条件, 泊松问题, and diffusions in Riemannian manifolds, Potential 分析的ysis (2002) 16 pages 115-138.
11. Diffusions on graphs, 泊松问题 and spectral geometry -with R. 迈耶斯,反式. AMS, 354(2002)，第5111-5136页.
12. An Ito formula for domain valued process driven by stochastic flows -with K. Kinateder, 概率 Theory and Rel.，(2002) 124页73-99.
13. Redefining spinors in Lorentz violating QED -with D. Colladay,日记账. 数学. 物理(2002)43，页3554-3564.
14. Dirichlet spectrum and heat content -with R. 迈耶斯,日记账. 功能. 分析(2003)200页，150-159页.
15. Isospectral polygons, planar graphs and heat content -with R. 迈耶斯,Proc. AMS(2003) 131，页3589-3599.
16. Moment problems and the causal set approach to quantum gravity -with A. 灰,日记账. 数学. 物理(2003)44，第1666-1678页.
17. Brownian motion, exit time moments and Weierstrass theorems -with V. de la Pena，检察官. AMS(2004) 132，页2465-2474.
18. Yang-Mills instantons with Lorentz violations -with D. Colladay,日记账. 数学. 物理(2004)45，页3228-3238.
19. 统计istical mechanics and Lorentz violation -with D. Colladay、phy. 牧师. D (2004) 70, 125007.
20. Recent results in geometric analysis involving probability, In: Recent Advances in Applied 概率a- bility, ed. R. Baez-Yates J. Glaz H. Gzyl J. Hussler J.L. Palacio, Springer (2005) pp 351-395.
21. Random partial orders, posts and discrete quantum gravity -with A. 灰,日记账. 数学. 物理学报(2005)46,062502.
22. 变形瞬态-与D. Colladay, In: Proceeding of the Third Meeting on CPT and Lorentz Sym- metry, ed. V. Alan Kostelecky, World Scientific (2005) pp 312–318.
23. Nonrelativistic ideal gasses and Lorentz violation -with D. Colladay, In: Proceeding of the Third Meeting on CPT and Lorentz Symmetry, ed. V. Alan Kostelecky, World Scientific (2005) pp 264–269.
24. Zeta regularized determinants for conic manifolds -with. P. Loya和J. 公园的. 函数. 分析(2007)242，第195-229页.
25. Hitting times and inverse problems for Markov Chains -with V. de la Pena和H. Gzyl，你的App. 概率. (2008) 45 pp 640–649.
26. Bose-Einstein condensation and Lorentz violation -with D. Colladay、phy. 牧师. D. (2006) 73 105006.
27. One loop renormalization of pure Yang-Mills theory with Lorentz violation -with D. 科拉迪，物理牧师. D. (2007) 75 105002.
28. Inverse problems for random walks on trees: network tomography, -with V. de la Pen, a和H. Gzyl,统计. 和概率. 书信(2008)78页3176-3183.
29. One loop renormalization of QCD with Lorentz violation -with D. 科拉迪，物理牧师. D. (2008) 77 085006.
30. Renormalization of gauge theories with Lorentz violation -with D. Colladay, In: Proceeding of the Fourth Meeting on CPT and Lorentz Symmetry, ed. V. Alan Kostelecky, World Scientific (2008) pp 224–229.
31. Bose Einstein condensates and Lorentz violation -with D. Colladay, In: Proceeding of the Fourth Meeting on CPT and Lorentz Symmetry, ed. V. Alan Kostelecky, World Scientific (2008) pp 255–260.
32. One loop renormalization of the electroweak sector with Lorentz violation -with D. 科拉迪，物理牧师. D. (2009) 79 125019.
33. Factoring the dispersion relation in the presence of Lorentz violation -with D. Colladay和D. 马林斯J. 今天一个. (2010) 43 275202.
34. Quaternion formulation of the Lorentz-violating Dirac equation -with D. Colladay和D. Mullins, In: Proceeding of the Fifth Meeting on CPT and Lorentz Symmetry, ed. V. Alan Kostelecky, World Scientific (2011) pp 199–204.
35. Lorentz violation and extended supersymmetry -with D. Colladay, In: Proceeding of the Fifth Meeting on CPT and Lorentz Symmetry, ed. V. Alan Kostelecky, World Scientific (2011) pp 234–239.
36. Vector superfields and Lorentz violation -with D. 科拉迪，物理牧师. D. (2011) 83 025021.
37. Classical lagrangians for momentum dependent Lorentz violation -with D. Colladay、phy. 牧师. D (2012) 83 044042.
38. Exit time, moment problems and comparison geometry Potential 分析的ysis (2012) DOI 10.1007/s11118-012-9318-5.
39. Gupta-Bleuler photon quantization in the Standard Model Extension -with D. Colladay和R. 盆栽、phy. 牧师. D (2014) 89 085014.
40. Singular Lorentz-violating Lagrangians and associated Finsler structures -with D. Colladay、phy. 牧师. D92(2015)号.[j] .地球科学进展[j] .北京:北京大学.01018 (hep-ph).
41. Cherenkov Radiation with Massive, CPT-violating Photons -with D. Colladay和R. 盆栽、phy. 牧师. D (2016) 93 125007.
42. Quantum graphs, torsional rigidity and isospectrality -with D. Colladay和L. Kaganovskiy(提交).
43. Heat content determines planar triangles -with R. 迈尔(提交).