Shiri Artstein-Avidan ùéøé àøèùèééï-àáéãï

I am an associate professor at the School of Mathematical Science at Tel Aviv University.

I received my Ph.D. from Tel Aviv University in 2004.

My thesis was titled Entropy Methods, you can view it here.

My Ph.D. advisor was Vitali Milman.

Here is my cv in Pdf format.

My publication list (and most online available papers) can be viewed here: papers.

In Pdf format my publication list is here: publist (with slightly different numbering than above, because of some TAU regulations).

An on-line lecture of mine is available here: Entropy increases at every step.

M.Sc.: Liran Tuchman (jointly with E. Blumenfeld-Liberthal),

Keshet Gutman,

Yoav Nir (jointly with Y. Ostrover).

Ph.D.:  D. Florentin (jointly with V. Milman),

B. Slomka.

M.Sc.: T. Weisblatt (jointly with V. Milman), O. Raz.

Courses:

This fall (2012-13) I am teaching Chedva I for math. Also a seminar for MSc.

Some past courses:   Chedva II and  CHEDVA III for mathematics students,  the course HILBERT SPACES, also for math students. An undergrad course called convex bodies in high dimensions.

Research: [Please note: this part is not updated very frequently, and may be somewhat outdated]

I worked mainly in the following directions:

(keywords: geometric functional analysis, the geometry of high dimensions, probability theory applied to geometry, convex geometry, functional inequalities, Shannon entropy, geometric entropy, explicit geometric constructions, asymptotic symplectic geometry and abstract duality).

1.     Shannon Entropy and Fisher information: We solved a long standing problem of Shannon on the monotonicity of entropy, in a project joint with K. Ball, F. Barthe and A. Naor (paper [2] in the publication list) and also got optimal rates for the rate of convergence in the Central Limit Theorem under a spectral gap assumption (paper [3]).

2.     Metric Entropy and Duality: In a project joint with V. Milman and S. Szarek, we proved a conjecture of Pietsch from 1972 called 'duality of metric entropy' in its most central and well studied case, where one of the spaces in Hilbert (papers [5], [6] and [7] in the publication list). Jointly also with N. Tomczak-Jaegermann (paper [8]) we showed that the conjecture holds for a much wider class of spaces, and introduced a new notion of packing.

3.     Using Chernoff bounds in geometry: Together with O. Friedland, V. Milman (papers [10], [15] in the publication list) and in another paper joint also with S. Sodin (paper [14]), we show how the classical Chernoff bound can be effectively used for geometric problems.

4.     Symplectic Geometry: In a joint project with Y. Ostrover we successfully apply methods from asymptotic geometric analysis to symplectic geometry. Together also with V. Milman, we proved a conjecture of Viterbo for capacities of convex sets up to a universal constant (papers [13] and [17] in the publication list, and another paper under preparation).

5.     Derandomization: The question of decreasing (or eliminating) randomness in algorithms and other constructions is central in computer science. We investigate this question for certain geometric constructions, and in the most studied case of sections of the cross polytope were able to decrease randomness from square of the dimension to a near-linear number of bits (n times log n). (Paper [12] in the publication list, joint with V. Milman). This was later improved to linear by S. Sodin and S. Lovett. More randomness decreasing results we found in [16].

6.     Concentration: Computing neighborhoods of proportional sections of the sphere (paper [1] in the publication list) computing certain ("Rademacher") projections of convex bodies (paper [4]) and proving concentration inequalities for some abstract (and closed under perturbations) families of random variables (paper [11]).

7.     Functional Inequalities: We proved, together with B. Klartag and V. Milman, a functional form of the Santaló inequality on the non-symmetric case (paper [9]). This naturally led to the question of justifying the definition of duality for functions, which led to:

8.     The concept of duality: A very novel direction which we pursued lately, jointly with V. Milman, is understanding the abstract characterization of duality for different classes of functions. We discovered very surprising results which show how little is needed in order to characterize, essentially uniquely, duality for many classes of functions (see papers [18,20,21] in the publication list). This general ideology led also to a characterization of Fourier transform and other related result, work in preparation jointly also with S. Alesker.

Contact Info:

shiri at post dot tau dot ac dot il

Office: Schreiber 306

Phone:  972 (0) 3 640 7614