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
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.
Current graduate students:
M.Sc.: Liran Tuchman (jointly with E.
Blumenfeld-Liberthal) and O. Raz.
Ph.D.: D. Florentin (jointly with V. Milman) and B.
Slomka.
Courses:
In the fall semester 2010 I
taught CHEDVA
III for mathematics students, and the course HILBERT
SPACES, also for math students. Spring and fall semester 2011 I am hosting
an advanced SEMINAR
for M.Sc.: Asymptotic Geometric Analysis. I am teaching an advanced
undergrad course called
convex bodies in high dimensions. Webpages for older courses around the
same topic can be found here and here.
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and may be somewhat outdated]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
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