Ph.D., MathematicsThesis: "Rotational spectrum of planar domains"
Advisor: Dr. Nikolai G. Makarov
B.Sc., M.S., Mathematics (with honors)Thesis: "A theorem on correction up to gradients of harmonic functions."
Advisor: Dr. Alexei B. Aleksandrov
Assistant Professor Visiting Assistant Professor Visitor Assistant Professor Member Benjamin Peirce Assistant Professor "Weak convergence of charges ". Vestnik Leningrad Univ. Math. 24 (1991), no. 1, 13 - 18.
"A theorem on correction up to gradients of harmonic functions ". St.-Petersburg Math. Journal 5 (1994), no. 2, 91 - 107.
"Rotational spectrum of planar domains". PhD Thesis, 1997.
"Harmonic measure and rotation of planar domains". Preprint
"Phase transition for the universal bounds on the integral means spectrum". Preprint
"Asymptotic for the integral mixed spectrum of the basin of attraction of infinity for the polynomials z(z+δ)". Preprint
(With N. Makarov and S. Smirnov) "Harmonic measure and polynomial Julia sets". Duke Mathematical Journal 117 (2003), no. 2, 343--365
(With L. De Marco) "Dimension of pluriharmonic measure for Julia sets ". International Math Research Notes 2003:11 (2003) 613 - 625
(With B. Duplantier) "Harmonic Measure and Winding of Conformally Invariant Curves ". Physical Review Letters 89, 264101 (2002)
(With P. Jones) "Harmonic measure and polynomial Julia sets: strong fractal approximation ". In preparation
(With L. De Marco) "Dimension of pluriharmonic measure and endomorphisms of CPn ". In preparation
(With D. Beliaev) "Correcton theorem for Riesz potentials ". In preparation
NSERC DISCOVER grant 5810-2004-298433 Research Board Award, University of Illinois, Urbana-Champaign NSF grant DMS-9970283, Principal Investigator Clark and Cooke grants, Harvard Tozier grant, Harvard Alfred P. Sloan foundation Fellowship Bohnenblust Travel Prize, Caltech Special Institute Fellowship, Caltech Tchebyshev fellowship, St. Petersburg State University All-Soviet Mathematical Olympiad for college students, Special prize International Mathematical Olympiad, Silver Medal Stochastic Loewner Evolution Differential Equations and Orthogonal Functions Advanced Calculus Multivariable Calculus Introductory Real Analysis Undergraduate course in Complex Analysis and Applications Graduate course in Harmonic Measure Undergraduate course in Sets, Groups and Topology Graduate course in Complex Analysis Undergraduate course in Complex Analysis Graduate course in Real Analysis Freshman Calculus Teaching Assistant for Undergraduate Calculus Teaching Assistant for graduate courses in Differential Equations, Dynamical Systems, Statistics, and Classical Analysis Instructor for Undergraduate Mathematical Analysis Instructor in Mathematical High School 1st Joint CMS-SFR Meeting " AMS Meeting", Columbus, Ohio "Scaling in Probability and PDE", Strobl, Austria "Probability and Conformal Mappings", Tenerife, Spain Euroconference in Geometric Function Theory Barrett Memorial Lectures, University of Tennessee "Ergodic theory and dynamical systems", Warsaw, Poland Semi-annual Workshop in Dynamical Systems, Penn State Texas A&M University University oif Geneva Yale University, Hahn Lecture University of Connecticut University of Toronto Instititute Henri Poincare University of Chicago Yale University University of Toronto University Paris-Sud Mittag-Leffler Institut University of Indiana University of Toronto University of Illinois, Urbana-Champaign SUNY, Stony Brook Cornell University UIPUI Northwestern University University of Washington Brown University Kansas State University Florida State University McGill University