** Here are some various versions of my CV (updated October 2023): **

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order, and unpublished preprints are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.

** Research description: **

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 638, Fall 2020: Topics in Real Analysis:
Weil-Petersson curves, traveling salesman theorems
and minimal surfaces; about 10 graduate students and 20 outside auditors.

MAT 627, Spring 2022: Topics in Complex Analysis: Conformal fractals . Introduction
to Brownian motion and diffusion limited aggregation (DLA) and the tools from complex analysis
used to study them.

MAT 670, Fall 2023: Topics in Complex Analysis: Dessins and Dynamics. Connections between
Grothendieck's theory of dessins d'enfants, quasiconformal constructions and holomoprhic dynamics.

** 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 .

** Expository articles: **

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
2022 NSF proposal, which describes
some of my current interests in greater detail.

Some previous NSF proposals, written in:
2018,
2015,
2012,
2009,
2006,
2003,
2000,

The corresponding proposal reviews from:
2022,
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.