Yevgeny Vilensky
Ph.D. Student
Department of Mathematics
Courant Institute of Mathematical Sciences
New York University
251 Mercer Street, Office #1109 (8-3289)
New York, NY 10012


Current Endeavors
My research is in probability theory under the direction of Prof. S.R.S. Varadhan. Currently, I am studying the large deviation properties of interacting particle systems, in particular simple exclusion processes. My thesis project is to extended the current results on lower bounds for the Totally Asymmetric Simple Exclusion Process to a wider class of non- entropy solutions. What does this all mean? It means I'm dealing with lots of nasty (or beautiful! depending on whether you're still writing a thesis or if it's already written) hyperbolic PDE issues having to do with entropicity.

Past Endeavors
Functional Analysis Notes (Updated 3/13/2006)
Oral Examination Outline

Future Endeavors
You mean, I have a future?

Useful Links

Mathematics

Probability and Stochastic Processes
Yuval Peres' and Peter Morters' Book on Brownian Motion (very thorough with a good balance of theory and examples)
Harry Van Zanten's Continuous Time Stochastic Processes Notes (good for Levy Processes and general Markov Process theory)
Amir Dembo's Stochastic Processes Lecture Notes (good coverage of Poisson Processes and branching processes)
Richard Bass' Stochastic Calculus Notes (good overall coverage of subject... excellent as a first intro)
Richard Bass' notes on probabilistic aspects of PDE's (excellent coverage of Martingale problems, Feynman-Kac, etc.).
Prof. Varadhan's lecture notes on Stochastic Processes (takes a rather different approach from most books, from the viewpoint of Martingale Problems)
Prof. Varadhan's book on Probability and Limit Theorems (nice book that requires you to work hard... superb for weak convergence).

Real Analysis (esp. Measure Theory)
David Sattinger's notes on Measure Theory (very nice notes)
Richard Bass' lecture notes on Measure Theory (a quick and easy intro to Measure Theory)
Bruce Driver's Analysis notes (extremely thorough, too thorough... not all of it is important for a first intro in the field).

Harmonic Analysis
Thomas Wolff's graduate course on Fourier Analysis from Caltech. (Nice intro that goes into modern topics such as Kakeya problems)

PDE
There are very few good lecture notes online in this area.
Bruce Driver's notes from a PDE course at UCSD (they're not bad... a bit daunting for an introduction)
David Sattinger's PDE for Applied Mathematics course at Yale (Good coverage of the usual topics)


Big Media (a.k.a. MSM)

Wall Street Journal Editorial Page
Washington Post
The New Republic
Reason Magazine

Blogs (a.k.a. guys in pajamas)

Academic Infractions (my seldomly-updated blog)
The Volokh Conspiracy (Libertarianish Law Profs)
Instapundit (the grand-daddy of blogging, U of Tenn Law Prof Glenn Reynolds)
Becker-Posner Blog (awesome Law and Economics blog by Circuit Court judge Richard Posner and Nobel Laureate in Econ, Gary Becker... this blog will make you smarter)
Asymmetrical Information (libertarian blog by a business writer for The Economist)
Ann Althouse (moderate law prof at U of Wisconsin... a lot of pop-culture blogging)
Virginia Postrel (former Reason magazine editor Virginia Postrel on technology, pop culture, style, and freedom)
Hit and Run (libertarian blog by those crazy cats at Reason)
Kira's Gulch (quasi-pseudo-ex-Objectivist libertarian blogger)
Crescat Sententia (former U of Chicago students... the best one on there is Will Baude, definitely check out his posts)
OxBlog (Americans in Oxford... international relations)
Eve Tushnet (libertarian/right Catholic writer)
Overlawyered (blog by Walter Olson and Ted Frank documenting everything that is wrong with our tort system).

Miscellania

New York Magazine's Restaurant Guide (the indespensable source for dining in NYC)
Make a restaurant reservation online!