Shiri Artstein-Avidan
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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),
Keshet Gutman,
Yoav Nir (jointly with Y. Ostrover).
Ph.D.: D. Florentin
(jointly with V. Milman),
B. Slomka.
Past graduate students:
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frequently, and may be somewhat outdated]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
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