Organizing Committee
Abstract

Probabilistic methods have long played an important role in various areas of geometry and analysis. Notable applications of probabilistic methods appear, for example, in geometric functional analysis, in harmonic analysis, and in discrete mathematics. Conversely, mathematical phenomena of fundamentally geometric and analytic origin, such as the concentration of measure phenomenon, play a central role in modern probability theory. Novel interactions between probability, geometry and analysis continue to drive important innovations in these fields.

The aim of this workshop is to bring together a diverse range of experts from probability, geometry, and analysis, in order to promote further dialogue between these fields and to catalyze the creation of new interactions.

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Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, October 17, 2022
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Session Chair
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:45 am EDT
    Upper bounds for the Fisher information
    11th Floor Lecture Hall
    • Sergey Bobkov, University of Minnesota
    Abstract
    We discuss upper bounds for the Fisher information in high dimensions in terms of the total variation and norms in Sobolev spaces.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The convex hull of space curves with totally positive torsion
    11th Floor Lecture Hall
    • Virtual Speaker
    • Paata Ivanishvili, University of California, Irvine
    Abstract
    Finding a simple description of a convex hull of a set K in n-dimensional Euclidean space is a basic problem in mathematics. When K has some additional geometric structures one may hope to give an explicit construction of its convex hull. A good starting point is when K is a space curve. In this talk I will describe convex hulls of space curves which have a "very" positive torsion. In particular, we obtain a parametric representation of the boundary of the convex hull, different formulas for their Euclidean volumes and the surface areas, and the solution to a general moment problem corresponding to such curves.
  • 11:30 am - 12:15 pm EDT
    How curved are level surfaces of eigenfunctions?
    11th Floor Lecture Hall
    • Virtual Speaker
    • David Jerison, MIT
    Abstract
    I will discuss several conjectures about level sets of eigenfunctions in convex domains.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Approximation of convex bodies in Hausdorff distance by random polytopes
    11th Floor Lecture Hall
    • Elisabeth Werner, Case Western Reserve University
    Abstract
    While there is extensive literature on approximation, deterministic as well as random, of general convex bodies in the symmetric difference metric, or other metrics coming from intrinsic volumes, very little is known for corresponding random results in the Hausdorff distance. For a polygon Q in the plane, the convex hull of n points chosen at random on the boundary of Q gives a random polygon Q_n. We determine the exact limiting behavior of the expected Hausdorff distance between Q and a random polygon Q_n as the number n of points chosen on the boundary of Q goes to infinity. Based on joint work with J. Prochno, C. Schuett and M. Sonnleitner.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Stanislaw Szarek, Case Western Reserve U.
  • 5:00 - 6:30 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, October 18, 2022
  • 9:00 - 9:45 am EDT
    TBA
    11th Floor Lecture Hall
    • Kavita Ramanan, Brown University
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    TBA
    11th Floor Lecture Hall
    • Jelani Nelson, UC Berkeley
  • 11:30 am - 12:15 pm EDT
    Spectral hypergraph sparsification via chaining
    11th Floor Lecture Hall
    • James Lee, University of Washington
    Abstract
    Using aspects of Talagrand's generic chaining theory, we show how to construct spectral hypergraph eps-sparsifiers with only O(eps^{-2} log(r) n log n) hyperedges, where n is the number of vertices and r is the rank of the hypergraph.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Embedding the hypercube into dense bipartite graphs
    11th Floor Lecture Hall
    • Konstantin Tikhomirov, Carnegie Mellon University
    Abstract
    A well known conjecture of Burr and Erdos asserts that the Ramsey number of the hypercube on 2^n vertices is of the order O(2^n). Motivated by this problem, we construct randomized embeddings of the hypercube into dense bipartite graphs and, as a corollary, show that the Ramsey number of the hypercube is of order O(2^{2n−cn}) for a universal constant c>0. This improves upon the previous best known bound O(2^{2n}), due to Conlon, Fox and Sudakov.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Volume growth of groups and random walks
    11th Floor Lecture Hall
    • Tianyi Zheng, UCSD
Wednesday, October 19, 2022
  • 9:00 - 9:45 am EDT
    Regularity for weighted convex isoperimetric problems
    11th Floor Lecture Hall
    • Alexandros Eskenazis, University of Cambridge
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    TBA
    11th Floor Lecture Hall
    • Han Huang, Georgia Institute of Technology
  • 11:30 am - 12:15 pm EDT
    TBA
    11th Floor Lecture Hall
    • Alexander Litvak, University of Alberta
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Limit laws and hypoellipticity
    11th Floor Lecture Hall
    • Maria (Masha) Gordina, University of Connecticut
    Abstract
    We will consider several classical problems for hypoelliptic diffusions and random walks: the large deviations principle (LDP), the small ball problem (SBP), Chung’s law of iterated logarithm (LIL), and finding the Onsager-Machlup functional. As two very different examples we will look at hypoelliptic Brownian motion and the corresponding random walk on the Heisenberg group, and the Kolmogorov diffusion. We will explore the role of space-time scaling property, Gaussianity, and spectral properties via Dirichlet forms in these settings. The Onsager-Machlup functional is used to describe the dynamics of a continuous stochastic process, and it is closely related to the SBP and LIL, as well as the rate functional in the LDP. Unlike in the elliptic (Riemannian) case we do not rely on the tools from differential geometry such as comparison theorems or curvature bounds as these are not always available in the hypoelliptic (sub-Riemannian) setting. The talk is based on the joint work with Marco Carfagnini, Tai Melcher and Jing Wang.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Oanh Nguyen, Brown University
Thursday, October 20, 2022
  • 9:00 - 9:45 am EDT
    Transportation of measures via Langevin flows
    11th Floor Lecture Hall
    • Yair Shenfeld, MIT
    Abstract
    A basic problem in probability theory and engineering is finding a way of representing a complicated probability measure as a simpler probability measure under some transformation. A desirable property of such transformations is that it is Lipschitz, since it allows for information from the simpler probability measure to be transferred to the complicated measure. While various transformations (optimal transport, Knothe-Rosenblatt rearrangement) exist, establishing their regularity is a difficult problem. In this talk, I will discuss the Lipschitz properties of the Langevin transport map which is constructed infinitesimally along the Langevin dynamics. I will show that this map is Lipschitz in many settings where no other Lipschitz transport maps are known to exist. I will conclude the talk by introducing a new connection between the Langevin transport map and renormalization groups methods from quantum and statistical field theories.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Horocyclic Brunn-Minkowksi inequality
    11th Floor Lecture Hall
    • Rotem Assouline, Weizmann Institute of Science
  • 11:30 am - 12:15 pm EDT
    The estimate for the Dimensional Brunn-Minkowski conjecture for all log-concave measures
    11th Floor Lecture Hall
    • Galyna Livshyts, Georgia Tech
    Abstract
    We will show that for any even log-concave measure \mu and any pair of symmetric convex sets K and L, and any t between 0 and 1, one has the inequality: \mu(tK+(1-t)L)^{c(n)}\geq t\mu(K)^{c(n)}+(1-t)\mu(L)^{c(n)}, Where c(n)=n^{-4-o(1)}. This constitutes progress towards the Dimensional Brunn-Minkowski conjecture.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Bounding suprema of canonical processes via convex hull
    11th Floor Lecture Hall
    • Rafał Latała, University of Warsaw
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    A Gaussian correlation inequality for p.s.h. functions
    11th Floor Lecture Hall
    • Dario Cordero-Erausquin, Sorbonne University
    Abstract
    A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural semigroup associated to the Gaussian dbar-Laplacian. Joint work with Franck Barthe.
Friday, October 21, 2022
  • 9:00 - 9:45 am EDT
    A quick estimate for the volume of a polyhedron
    11th Floor Lecture Hall
    • Virtual Speaker
    • Alexander Barvinok, University of Michigan
    Abstract
    Let P be a bounded polyhedron, defined as the intersection of the non-negative orthant in R^n and an affine subspace of codimension m. I present a simple and computationally efficient formula that approximates the volume of P within a factor c^m, where c > 0 is an absolute constant. This is joint work with Mark Rudelson.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Bourgain’s slicing problem and KLS isoperimetry up to polylog
    11th Floor Lecture Hall
    • Joseph Lehec, Université Paris-Dauphine
    Abstract
    We prove that Bourgain’s hyperplane conjecture and the Kannan-Lovasz-Simonovits isoperimetric conjecture hold true up to a factor that is polylogarithmic in the dimension.
  • 11:30 am - 12:15 pm EDT
    A *Slightly* Improved Bound for the KLS Constant (or The Fashion Wars: LV vs L-dan)
    11th Floor Lecture Hall
    • Santosh Vempala, Georgia Tech College of Computing
    Abstract
    We refine the recent breakthrough technique of Klartag and Lehec to obtain an improved polylogarithmic bound for the KLS constant.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    TBA
    11th Floor Lecture Hall
    • Dan Mikulincer, MIT
    Abstract
    TBA
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .

Application Information

ICERM welcomes applications from faculty, postdocs, graduate students, industry scientists, and other researchers who wish to participate. Some funding may be available for travel and lodging. Graduate students who apply must have their advisor submit a statement of support in order to be considered.

Your Visit to ICERM

ICERM Facilities
ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am - 5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
Traveling to ICERM
ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. In-depth directions and transportation information are available on our travel page.
Lodging
ICERM's special rate will soon be made available via this page for our preferred hotel, the Hampton Inn & Suites Providence Downtown. ICERM also regularly works with the Graduate Hotel and Hilton Garden Inn who both have discounted rates available. Contact housing@icerm.brown.edu before booking anything.
The only way ICERM participants should book a room is through the hotel reservation links located on this page or through links emailed to them from an ICERM email address (first_last@icerm.brown.edu). ICERM never works with any conference booking vendors and never collects credit card information.
Childcare/Schools
Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
Technology Resources
Wireless internet access ("Brown-Guest") and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
Accessibility
To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
Discrimination and Harassment Policy
ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Brown University's "Code of Conduct", "Discrimination and Workplace Harassment Policy", "Sexual and Gender-based Misconduct Policy", and "Title IX Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director of Finance & Administration; they are the responsible employees at ICERM under this policy.
Exploring Providence
Providence's world-renowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.

Visa Information

Contact visa@icerm.brown.edu for assistance.

Eligible to be reimbursed
B-1 or Visa Waiver Business (WB)
Ineligible to be reimbursed
B-2 or Visa Waiver Tourist (WT)
Already in the US?

F-1 and J-1 not sponsored by ICERM: need to obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.

H-1B holders do not need letter of approval.

All other visas: alert ICERM staff immediately about your situation.

ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.

Financial Support

This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.

ORCID iD
As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Travel Maximum Contributions
  • New England: $250
  • Other contiguous US: $750
  • Asia & Oceania: $2,000
  • All other locations: $1,500
  • Note these rates were updated in Spring 2022 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
Reimbursement Requests

Request Reimbursement with Cube

Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Associated Semester Workshops

Harmonic Analysis and Convexity
Image for "Harmonic Analysis and Convexity"
Opening Event: Harmonic Analysis and Convexity
Image for "Opening Event: Harmonic Analysis and Convexity"