Department of Mathematics, Michigan State University
Office: C327 Wells Hall
Education: Ph.D. California Institute of Technology, 2004
Teaching in Spring, 2020
MTH 992: Brownian motion and stochastic analysis. [Notes, completed]
Teaching in Fall, 2019
MTH 320: Analysis I. [Website]
MTH 925: Random Variables and Stochastic Processes. [Notes] (completed).
Office hours: Mon: 2 每 3 pm, Tue: 9 每 10 am, Thu: 1 每 2 pm, or by email appointment.
Teaching in Spring, 2019
MTH 992: Random Variables and Stochastic Processes, II. [Notes] (Completed).
Probability Theory, Schramm-Loewner evolution (SLE), Statistical lattice models
Click here to see my [CV].
Click here to see my research statement [Research Statement].
I gave a lecture on Schramm-Loewner evolution. Click here to see the lecture notes [lecture]
Professor Michigan State University 2017 - present
Associate Professor Michigan State University 2012 - 2017
Assistant Professor Michigan State University 2009 - 2012
Gibbs Assistant Professor Yale University 2007 - 2009
Morrey Assistant Professor UC Berkeley 2004 - 2007
Awards and Grants
Simons Fellowship (2016)
Salem Prize (2012)
Sloan Research Fellowship (2011-2015)
NSF CAREER award: DMS 1056840 (2011-2018)
NSF Grant: DMS 0963733 (2009-2013)
0. Random Loewner Chains in Riemann Surfaces, PhD dissertation at Caltech, 2004.
1. Stochastic Loewner evolution in doubly connected domains, Probability Theory and Related Fields, 129:340-380, 2004
2. Some properties of annulus SLE. Electronic Journal of Probability, 11:1069-1093, 2006.
3. The scaling limits of planar LERW in finitely connected domains. Annals of Probability, 36(2):467-529, 2008.
4. Reversibility of chordal SLE. Annals of Probability, 36(4):1472-1494, 2008.
5. Duality of chordal SLE. Inventiones Mathematicae, 174(2):309-353, 2008.
6. Continuous LERW started from interior points. Stochastic Processes and their Applications, 120:1267-1316, 2010.
7. Reversibility of some chordal SLE(百;老) traces. Journal of Statistical Physics, 139(6):1013-1032, 2010.
8. Duality of chordal SLE, II. Ann. I. H. Poincare-Pr., 46(3):740-759, 2010.
9. Loop-erasure of planar Brownian motion. Communications in Mathematical Physics, 133(3):709-720, 2011.
10. Restriction properties of annulus SLE. Journal of Statistical Physics, 146(5):1026-1058, 2012.
11. Reversibility of Whole-Plane SLE. Probability Theory and Related Fields, 161(3):561-618, 2015.
12. Ergodicity of the tip of an SLE curve. Probability Theory and Related Fields, 164(1):333-360, 2016.
13. Backward SLE and symmetry of welding. (with Steffen Rohde) Probability Theory and Related Fields, 164(3):815-863, 2016.
14. Higher moments of the natural parameterization for SLE curves. (with Mohammad A. Rezaei) Ann. I. H. Poincare-Pr., 53(1):182-199, 2017.
15. Boundary arm exponents for SLE. (with Hao Wu) Electronic Journal of Probability, 22, Paper no. 89, 26 pp, 2017.
16. Green's function for chordal SLE curves. (with Mohammad A. Rezaei) To appear in Probability Theory and Related Fields.
17. Decomposition of Schramm-Loewner evolution along its curve. To appear in Stochastic Processes and their Applications.
18. Decomposition of backward SLE in the capacity parameterization. (with Benjamin Mackey) To appear in Stat. Probab. Lett.
19. Optimal Hölder continuity and dimension properties for SLE with Minkowski content parametrization. To appear in Probability Theory and Related Fields.
20. Multipoint estimates for radial and whole-plane SLE. (with Benjamin Mackey) In preprint, to appear in Journal of Statistical Physics.
1. SLE loop measures, arXiv:1702.08026, 2017.
2. Two-curve Green's function for $2$-SLE: the interior case. In preprint, arXiv:1806.09663, 2018.
3. Two-curve Green's function for $2$-SLE: the boundary case. In preprint, arXiv:1901.00254, 2019.
4. Time-reversal of multiple-force-point SLE$_\kappa(\rho)$ with all force points lying on the same side, In preprint, arXiv:1906.06005, 2019.