# Mathematical Sciences Research Institute

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# Workshop

Probabilistic Reasoning in Quantitative Geometry September 19, 2011 - September 23, 2011
 Registration Deadline: September 19, 2011 over 3 years ago June 19, 2011 almost 4 years ago
Parent Program: Quantitative Geometry Mathematical Sciences Research Institute, Berkeley CA
Organizers Anna Erschler* (Université Paris-Sud), Assaf Naor (Courant Institute), and Yuval Peres (Microsoft Research)
Speaker(s)

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Description

"Probabilistic Reasoning in Quantitative Geometry" refers to the use of probabilistic techniques to prove geometric theorems that do not have any a priori probabilistic content. A classical instance of this approach is the probabilistic method to prove existence of geometric objects (examples include Dvoretzky's theorem, the Johnson-Lindenstrauss lemma, and the use of expanders and random graphs for geometric constructions). Other examples are the use of probabilistic geometric invariants in the local theory of Banach spaces (sums of independent random variables in the context of type and cotype, and martingale-based invariants), the more recent use of such invariants in metric geometry (e.g., Markov type in the context of embedding and extension problems), probabilistic tools in group theory, the use of probabilistic methods to prove geometric inequalities (e.g., maximal inequalities, singular integrals, Grothendieck inequalities), the use of probabilistic reasoning to prove metric embedding results such as Bourgain's embedding theorem (where the embedding is deterministic, but its analysis benefits from a probabilistic interpretation), probabilistic interpretations of curvature and their applications, and the use of probabilistic arguments in the context of isoperimetric problems (e.g., Gaussian, rearrangement, and transportation cost methods).

Accommodation:

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Please mention MSRI and the workshop name when making reservations via phone, fax or e-mail. If you are making your reservations on line, please go to Hotel Durant website, choose your dates of stay and enter the "123MSRI" promo code in the box. The cut-off date for reservations is Midnight on the day of Friday, August 19, 2011. The rate is $110 per night plus tax. New, completely renovated Hotel Shattuck Plaza has rooms available for you! MSRI’s preferred rate is$135. Guests can either call the hotel’s main line, 510-845-7300, and ask for the MSRI rate or go to http://www.hotelshattuckplaza.com, click on "Corporate Rates" in the reservation screen and type the code “msri11”.

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is \$129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

## Show Visa/Immigration

Schedule
Sep 19, 2011
Monday
 09:15 AM - 09:30 AM Welcome 09:30 AM - 10:20 AM Gaussian Surface Area and Noise Sensitivity Keith Ball (University College) 10:30 AM - 11:00 AM Tea 11:00 AM - 11:50 AM Uniform Isoperimetric Constants via Random Forests Russell Lyons 12:00 PM - 12:40 PM Markov Type and Embedding Obstructions Yuval Peres (University of California, Berkeley) 12:40 PM - 02:00 PM Lunch 02:00 PM - 02:50 PM Fine Estimates in Dvoretzky\'s Theorem Gideon Schechtman (Weizmann Institute of Science) 03:00 PM - 03:30 PM Tea 03:30 PM - 04:20 PM Random Cubes in a Metric Space with Application to Singular Integrals with Non-doubling Measures Tuomas Hytönen
Sep 20, 2011
Tuesday
 09:30 AM - 10:20 AM Random Matrices, Exact Operator Spaces and Non-commutative Grothendieck Theorem Gilles Pisier (Texas A&M International University) 10:30 AM - 11:00 AM Tea 11:00 AM - 11:50 AM Random Sequences of Simple Rearrangements Almut Burchard (University of Toronto) 12:00 PM - 12:40 PM New Applications of Rearrangement Inequalities Perla Sousi 12:40 PM - 02:00 PM Lunch 02:00 PM - 02:50 PM Near-equivalence of the Restricted Isometry Property and the Johnson-Lindenstrauss Lemma Rachel Ward 03:00 PM - 03:30 PM Tea 03:30 PM - 04:20 PM Speed exponents for random walks on groups Balint Virag 04:30 PM - 06:30 PM Reception
Sep 21, 2011
Wednesday
 09:30 AM - 10:20 AM Random Cayley Graphs and Expanders for Finite Simple Groups Emmanuel Breuillard (Université de Paris XI) 10:30 AM - 11:00 AM Tea 11:00 AM - 11:50 AM Calculus for Nonlinear Spectral Gaps Manor Mendel (Open University of Israel) 12:00 PM - 12:45 PM Problem Session
Sep 22, 2011
Thursday
 09:30 AM - 10:20 AM Optimal Gaussian Partitions Elchanan Mossel (University of California, Berkeley) 10:30 AM - 11:00 AM Tea 11:00 AM - 11:50 AM Entropies for Covers of Compact Manifolds François Ledrappier (University of Notre Dame) 12:00 PM - 12:40 PM Probabilistic Tools in Nonlinear Dvoretzky Theory Assaf Naor (New York University, Courant Institute) 12:40 PM - 02:00 PM Lunch 02:00 PM - 02:50 PM Homogeneous Finite-Simensional Banach Spaces and Random Projections of Convex Bodies Nicole Tomczak Jaegermann (University of Alberta) 03:00 PM - 03:30 PM Tea 03:30 PM - 04:20 PM Random Geometric Constructions for the Sharp Estimates of Singular Operators Alexander Volberg
Sep 23, 2011
Friday
 09:30 AM - 10:20 AM Homomorphisms from Random Walks Anders Karlsson 10:30 AM - 11:00 AM Tea 11:00 AM - 11:50 AM Near-Linear Lower Bound for Dimension Reduction in L1 Alexandr Andoni 12:00 PM - 02:00 PM Lunch 02:00 PM - 02:40 PM The effect of dimensionality on the stability in the Brunn-Minkowski inequality: A blessing or a curse? A joint work with Bo'az Klartag Ronen Eldan 02:50 PM - 03:20 PM Tea