Publications

51. With Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko, Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators, preprint: https://arxiv.org/abs/2312.14883

50. With Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko, Zeros of random polynomials undergoing the heat flow, preprint https://arxiv.org/abs/2308.11685

49. With Ching-Wei Ho, Jonas Jalowy, and Zakhar Kabluchko, The heat flow, GAF, and SL(2;R), Indiana Univ. Math. J., to appear: https://arxiv.org/abs/2304.06665

48. With Ching-Wei Ho, The heat flow conjecture for random matrices, preprint https://arxiv.org/abs/2202.09660

47. With Ching-Wei Ho, The Brown measure of a family of free multiplicative Brownian motions, Prob. Theory Related Fields, 186 (2023),1081–1166. https://doi.org/10.1007/s00440-022-01166-5 .

46. With Ching-Wei Ho, The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element, Lett. Math. Phys. 112 (2022), Paper No. 19, 61 pages.

45. PDE methods in random matrix theory, in “Harmonic Analysis and Applications” (M. Th. Rassias, Ed.), pp. 77-124, Springer, 2022.

44. With B. Driver and T. Kemp, The Brown measure of the free multiplicative Brownian motion, Prob. Theory Related Fields 184 (2022), pp. 209-273.
Note: A Mathematica notebook containing all the plots and simulations appearing in the above paper is available at this link: https://www.notebookarchive.org/id/2019-05-bjnnq2h . There you can either view the notebook directly on the web or download the file (52 MB!) so that you can run your own simulations. Please note that even when viewing on the web, it will take a few minutes for the file to load.

43. With B. Driver and T. Kemp, The complex-time Segal-Bargmann transform, J. Funct. Anal. 278 (2020), Article 10830 (42 pages)

42. With T. Kemp, Brown measure support and the free multiplicative Brownian motion, Advances in Math. 355 (2019), Article106771 (36 pages)

41. The eigenvalue process for Brownian motion in U(N), unpublished notes. eigenvalue.pdf

40. With Benjamin Lewis, A unitary “quantization commutes with reduction” map for the adjoint action of a compact Lie group, Quarterly Journal of Math. 69 (2018), 1387-1421.

39. Coherent states for compact Lie groups and their large-N limits, in “Coherent states and their applications: a contemporary panorama” (J.-P. Antoine, F. Bagarello, and J.-P. Gazeau, eds.), Springer, 2018.

38. The large-N limit for two-dimensional Yang-Mills theory, Comm. Math. Phys363 (2018), 789-828. Available from the journal’s website here (read only). 

37. With B. Driver, F. Gabriel, and T. Kemp, The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces, Comm. Math. Phys. 352 (2017), 967-978. Available from the journal’s website here (read only)

36. With B. Driver and T. Kemp, Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane,Comm. Math. Phys. 351 (2017), 741-774. Available from the journal’s website here (read only).

35. With J. Mitchell, The Segal-Bargmann transform for odd-dimensional hyperbolic spaces, Mathematics 3 (2015), 758-780. Open access.

34. The Segal-Bargmann transform for unitary groups in the large-N limit, expository article on the material in joint paper (Ref. 32) with Driver and Kemp. Large-N

33. With M. Cecil, Dimension-independent estimates for heat operators and harmonic functions, Potential Anal. 40 (2014), 363–389. 

32. With B. K. Driver and T. Kemp, The large-N limit of the Segal-Bargmann transform on U(N)J. Funct. Anal. 265(2013), 2585-2644.

31. With W. Kirwin, Complex structures adapted to magnetic flows, J. Geom. Phys. 90 (2015), 111-131.

30. With J. Mitchell, Coherent states for a particle on a 2-sphere with a magnetic field, J. Physics A45 (2012), 18 pages. (Special issue on coherent states). JPhysA.pdf

29. With K. Chailuek, Toeplitz operators on generalized Bergman spaces. Integral Eq. Operator Theory 66 (2010), 53-77. 

28. With W. Kirwin, Adapted complex structures and the geodesic flow. Mathematische Annalen 350 (2011), 455-474. MathAnn350

27. Berezin-Toeplitz quantization on Lie groups, J. Funct. Anal. 255 (2008), 2488-2506 (Special issue in honor of Paul Malliavin). Jfa255

26. Leonard Gross’s work in infinite-dimensional analysis and heat kernel analysis,  Comm. on Stochastic Analysis (special volume in honor of Leonard Gross), 2 (2008), 1-9. GrossCosa.pdf

25. The heat operator in infinite dimensions, in “Infinite Dimensional Analysis in Honor of H.-H. Kuo,” edited by A. N. Sengupta and P. Sundar, World Scientific 2008, pp. 161-174.

24. With J. Mitchell, The Segal-Bargmann transform for compact quotients of symmetric spaces of the complex type. Taiwanese J. Math. 16 (2012), 13-45. Link to TJM Volume 16

23. With J. Mitchell, Isometry theorem for the Segal-Bargmann transform on a noncompact symmetric space of the complex type, J. Functional Analysis 254 (2008), 1575-1600. jfa254

22. With W. Kirwin, Unitarity in “quantization commutes with reduction,”  Comm. Math. Phys. 275 (2007), 401-442. cmp275

21. With J. J. Mitchell, The Segal-Bargmann transform for noncompact symmetric spaces of the complex type, J. Functional Analysis 227 (2005), 338-371. jfa227.pdf

20. The range of the heat operator, in “The Ubiquitous Heat Kernel,” edited by Jay Jorgensen and Lynne Walling, AMS 2006, pp. 203-231. range.pdf

19. With W. Lewkeeratiyutkul, Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform, J. Functional Analysis 217 (2004), 192-220. jfa217.pdf

18. With M. B. Stenzel, Sharp bounds for the heat kernel on certain symmetric spaces of non-compact type. In, “Finite and Infinite Dimensional Analysis in Honor of Leonard Gross” (H.-H. Kuo and A. N. Sengupta, Eds.) 117-135, Contemp. Math. 317, Amer. Math. Soc., 2003. gross2.pdf

17. The Segal-Bargmann transform and the Gross ergodicity theorem. In, “Finite and Infinite Dimensional Analysis in Honor of Leonard Gross” (H.-H. Kuo and A. N. Sengupta, Eds.), 99-116, Contemp. Math. 317, Amer. Math. Soc., 2003. gross1.pdf

16. With J. J. Mitchell, The large radius limit for coherent states on spheres. In, “Mathematical Results in Quantum Mechanics” (R. Weder, et al., Eds.), 155-162, Contemp. Math. 307, Amer. Math. Soc., 2002. qmath.pdf

15. Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type, Comm. Math. Phys. 226 (2002), 233-268. cmp226.pdf

14. With J. J. Mitchell, Coherent states on spheres, J. Math. Phys. 43 (2002), 1211-1236. jmp43.pdf

13. Bounds on the Segal-Bargmann transform of Lp functions, J. Fourier Analysis Applications 7 (2001), 553-569. jfaa7.pdf

12. Coherent states and the quantization of (1+1)-dimensional Yang-Mills theory, Rev. Math. Phys. 13 (2001), 1281–1305. rmp13.pdf

11. Harmonic analysis with respect to heat kernel measure, Bull. Amer. Math. Soc. (N.S.) 38 (2001), 43-78. bull38.pdf

10. With B. K. Driver, The energy representation has no non-zero fixed vectors. In, “Stochastic Processes, Physics and Geometry: New Interplays, II” (Leipzig, 1999), 143-155, CMS Conf. Proc., 29, Amer. Math. Soc., Providence, RI, 2000.

9. Holomorphic methods in analysis and mathematical physics. In, “First Summer School in Analysis and Mathematical Physics” (S. Pérez-Esteva and C. Villegas-Blas, Eds.), 1-59, Contemp. Math. 260, Amer. Math. Soc., 2000. holomorphic_methods.pdf

8. With S. Albeverio and A. N. Sengupta, The Segal-Bargmann transform for two-dimensional Euclidean quantum Yang-Mills, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2 (1999), 27-49. idaqp2.pdf

7. A new form of the Segal-Bargmann transform for Lie groups of compact type, Canad. J. Math. 51 (1999), 816-834.

6. With B. K. Driver, Yang-Mills theory and the Segal-Bargmann transform, Comm. Math. Phys. 201 (1999), 249-290. cmp201.pdf

5. With A. N. Sengpupta, The Segal-Bargmann transform for path-groups, J. Functional. Analysis 152 (1998), 220-254. jfa152.pdf

4. Quantum mechanics in phase space. In, “Perspectives on Quantization” (L. Coburn and M. Rieffel, Eds.), 47-62, Contemp. Math., 214, Amer. Math. Soc., Providence, RI, 1998

3. Phase space bounds for quantum mechanics on a compact Lie group, Comm. Math. Phys. 184 (1997), 233-250. cmp184.pdf

2. The inverse Segal-Bargmann transform for compact Lie groups, J. Functional Analysis 143 (1997), 98-116. jfa143.pdf

1. The Segal-Bargmann “coherent state” transform for compact Lie groups, J. Functional Analysis 122 (1994), 103-151. jfa122.pdf