Here are some various versions of my CV (updated Sept 2022):
long CV includes a list of publiations with brief abstracts
short CV lists publications without abstracts
CV only does not include publication list
publication list with abstracts
publication list without abstracts
Links to most of my pulished papers are posted here in reverse chronological order, and unpublished preprints are listed at the end.
My research interests and plans, describes some problems I am currently interested in. This is a more expository version of my recent NSF proposals, given below, which contain more precise definitions and added technicalities.
Teaching statement and evaluations:
Here is teaching portfolio that includes a brief statement on teaching philosophy, a list of recently taught courses, some letters from former students, and comments from recent student evaluations.
Recordings of my online classes:
MAT 126, Fall 2020: Calculus B; about 200 students.
MAT 638, Fall 2020: Topics in Real Analysis: Weil-Petersson curves, traveling salesman theorems and minimal surfaces; about 10 graduate students and 20 outside auditors.
Video recordings of some recent lectures:
Harmonic measure: algorithms and applications video recording of my 2018 ICM lecture.
Mappings and Meshes: using computational and hyperbolic geometry to give a fast conformal mapping algorithm
Trees, Triangles and Tracts, I and II : Part I covers harmonic measure, dessins d'enfants and triangulations of Riemann surfaces. Part II gives a version of dessins d'enfants for infinite trees and applications to transcendental dynamics. These was given as part of workshop in Barcelona, so there are variety of local references.
Random Thoughts on Random Sets : brief introduction to open problems related to DLA (diffusion limited aggregation), Brownian motions and flows related to random triangulations.
Weil-Petersson curves, traveling salesman theorems, and minimal surfaces : I outline several equivalent definitions of the Weil-Petersson class, a collection of closed curves that has connections to string theory, pattern recognition, SLE, geometric measure theory, knot theory, mininal surfaces and other topics.
Slides for some recent lectures are posted at lectures .
My 2018 ICM article, describes central role of harmonic measure in my work.
A random walk in analysis is an expository article that describes a chain of ideas starting from harmonic measure on fractals and leading to optimal meshing algorithms.
NSF Proposal and Reviews:
This is my 2018 NSF proposal, which describes some of my current interests in greater detail.
Some previous NSF proposals, written in: 2015, 2012, 2009, 2006, 2003, 2000,
The corresponding proposal reviews from: 2018, 2015, 2012, 2009, 2006, 2003 , 2000.
Books and lecture notes:
Fractals in Probability and Analysis by Christopher Bishop and Yuval Peres. Cambridge Studies in Advanced Mathematics, vol 162, 2017. Math Reviews , MAA Review , endorsements.
Introduction to transcedental dynamics , lecture notes on hyperbolic geometry, quasiconformal mappings and application to dynamics, (in preparation).
The Riemann mapping theorem , lecture notes on numerical conformal mapping, (in preparation).
Experimental and computational math Math 331, Fall 2018 , webpage for class in mathematical experimenting via MATLAB. We cover the simplest cases of various topics like root finding, graph theory, simply cryptography, image compression, random walks, ... using 'hand-made' methods , rather than pre-existing software.