Department of Mathematics, Michigan State University
Office: C327 Wells Hall
Education: Ph.D. California Institute of Technology, 2004
Probability Theory, Schramm-Loewner evolution (SLE), Statistical lattice models
Click here to see my [CV].
Click here to see my research statement [Research Statement].
Associate Professor Michigan State University 2012 - present
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(κ;ρ) 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. (with Steffen Rohde) Backward SLE and Symmetry of Welding. Probability Theory and Related Fields, 164(3):815-863, 2016.
14. (with Mohammad A. Rezaei) Higher moments of the natural parameterization for SLE curves. Accepted by Ann. I. H. Poincare-Pr.
1. Decomposition of Schramm-Loewner evolution along its curve. In preprint, arXiv:1509.05015.
In this paper, it is proved that if one samples a point on an SLE curve using natural parametrization, then he sees a two-sided radial SLE near that point; and if one samples a point on the SLE curve using capacity parametrization, then he sees an SLE(κ,-8) curve near that point.
2. (with Hao Wu) Boundary Arm Exponents for SLE. In preprint, arXiv:1606.05998.
In this paper, we derive boundary arm exponents for SLE. Combining with the convergence of critical lattice models to SLE, these exponents would give the alternating half-plane arm exponents for the corresponding lattice models.
3. (with Mohammad A. Rezaei) Green's function for chordal SLE curves. In preprint, arXiv:1607.03840.
In this paper, we prove the existence of Green’s function for chordal SLE for any finite number of points, i.e., the rescaled probability that a chordal SLE curve (κ<8) passes through given points in the domain (expressed in terms of a limit), and provide the convergence rates and up to constant sharp bounds for these Green’s functions.
Teaching in Fall, 2016
MTH 428H: Honors Complex Analysis I [Course Website]
MTH 992-002: Random Variables and Stochastic Processes
Office hours: MWF: 11:15-12:15 or by appointment.