Preprints and publications
Recent
Positive curvature
Random geometry
Function theory in the unit disk
Critical sets of inner functions
Makarov's principle and related topics
 Sparse Beltrami coefficients, integral means of conformal mappings and the FeynmanKac formula
Potential Analysis 48 (2018), no. 4, 437457.
 Makarov's principle for the Bloch unit ball
with Ilgiz Kayumov
Sbornik: Mathematics 208 (2017), no. 3, 399412
 On Makarov's principle in conformal mapping
Int. Math. Res. Not. 2019 (2019), no. 5, 15431567
 Quasicircles of dimension 1+k^2 do not exist
updated March 29, 2017
 Asymptotic variance of the Beurling transform
with Kari Astala, Antti Perälä and István Prause
Geom. Funct. Anal.
25 (2015), no. 6, 16471687
WeilPetersson geometry
Curious things
Slides
 Critical values of inner functions
Harmonic and Complex Analysis: Modern and Classical, Ramat Gan, Israel, June 20, 2023
 Entropy of universal covering maps
Constructive Aspects of Complex Analysis, Honolulu, Hawaii, March 22, 2019
 Describing Blaschke Products by their critical points
Knoxville, Tennessee, January 22, 2019
 Dimension of sparse quasicircles
Analysis and dynamics conference, Oaxaca, Mexico, Sept. 20, 2016
 Makarov's principle
Everything is complex, Saas Fee, Switzerland, Mar. 9, 2016
 WeilPetersson geometry
PhD Defense, Harvard University, Apr. 23, 2014
Some notes on various topics – not for publication
Expositions from my undergraduate studies

Centaurs: Here, There, Everywhere!
with Dimitri Dziabenko
College
Mathematical Journal 39 (September 2008), 267272
 My notes from Prof. Edward Bierstone's class on Complex Analysis