Universität Bonn

Dual Trimester Program: "Synergies between modern probability, geometric analysis and stochastic geometry"


January 8 - April 19, 2024

Organizers: Ronen Eldan, Assaf Naor, Kavita Ramanan, Matthias Reitzner, Christoph Thäle, Elisabeth M. Werner

Description: The connection between probability and geometry is an emerging research area. It includes log-Brunn Minkowski inequality, large deviations and asymptotic geometric analysis, concentration phenomena and random spatial systems. It has numerous applications, ranging from material science and theoretical computer science to high dimensional statistics.

In the last decade these connections turned out to be extremely fruitful. Ideas and techniques from geometry strongly influenced probability theory and vice versa, leading to several breakthrough results.

The program aims to stimulate substantial progress at the crossroads of these disciplines by bringing together researchers from asymptotic geometric analysis, stochastics and stochastic geometry, and high dimensional convex geometry.

 The trimester program will include an introductory winter school
"Interaction between probability and geometry" (January 22 - 26, 2024)

two workshops
"Asymptotics of (random) convex sets: fluctuations and large deviations" (February 19 - 23, 2024)
"High dimensional phenomena: geometric and probabilistic aspects" (March 11 - 15, 2024)

and three thematic weeks
Interaction between convexity and discrete structures (February 5 - 9, 2024)
Asymptotic properties of random sets (February 26 - March 1, 2024)
Large deviations in asymptotic functional analysis (March 18 - 22, 2024)

The application for the trimester program has been closed.


Participants

PERSON
AFFILIATION
PERIOD OF STAY
Shiri Artstein Tel Aviv University
Imre Barany Renyi Institute of Mathematics 18.02.2024 – 19.04.2024
Franck Barthe Université Toulouse III - Paul Sabatier
Dominik Beck Charles University 14.01.2024 – 27.01.2024
Andreas Bernig Goethe University Frankfurt am Main 10.03.2024 – 23.03.2024
Florian Besau Technische Universität Wien 21.01.2024 – 19.04.2024
Leo Brauner TU Wien 25.02.2024 – 15.03.2024
Pierre Calka Universite de Rouen Normandie 11.02.2024 – 24.02.2024
Alan Chang Washington University in St. Louis 08.01.2024 – 09.02.2024
Cecilia D'Errico Université Paris-Saclay 11.02.2024 – 24.02.2024
Jaume de Dios Pont ETHZ 08.01.2024 – 31.01.2024
Nina Gantert Technische Universität München 04.03.2024 – 15.03.2024
Miriam Gordin Princeton University 03.03.2024 – 16.03.2024
Daniel Hug Karlsruhe Institute of Technology (KIT) 26.02.2024 – 24.03.2024
Benjamin Jaye Georgia Tech 03.03.2024 – 29.03.2024
Michael Juhos University of Passau 19.02.2024 – 01.03.2024
Zakhar Kabluchko University of Münster 08.01.2024 – 19.04.2024
Kirill Kashkan University of Toronto 08.01.2024 – 19.04.2024
Jonas Knoerr TU Wien 03.03.2024 – 22.03.2024
Alexander Koldobsky University of Missouri-Columbia 03.03.2024 – 19.04.2024
Dylan Langharst Sorbonne University 08.01.2024 – 19.04.2024
Rafal Latala University of Warsaw 11.02.2024 – 01.03.2024
Anna Lytova Opole University 16.03.2024 - 29.03.2024
Alexander Litvak University of Alberta 21.01.2024 – 19.04.2024
Galyna Livshyts Georgia Institute of Technology 03.03.2024 – 29.03.2024
Monika Ludwig TU Wien 14.01.2024 – 15.03.2024
Francisco Marín Sola University of Murcia 21.01.2024 – 15.03.2024
Sergii Myroshnychenko University of the Fraser Valley 17.02.2024 – 02.03.2024
Assaf Naor Princeton 17.03.2024 – 23.03.2024
Paul Navas Alban TU Dortmund 08.01.2024 – 27.01.2024
Oscar Ortega Moreno Technische Universität Wien 25.02.2024 – 15.03.2024
Grigorios Paouris Texas A&M University
Eli Putterman Tel Aviv University 08.01.2024 – 19.04.2024
Yaozhong Qiu Imperial College London 08.01.2024 – 19.04.2024
Kavita Ramanan Brown University 29.02.2024 – 22.03.2024
Matthias Reitzner Universität Osnabrück 28.01.2024 – 19.04.2024
Mark Rudelson University of Michigan 10.03.2024 – 19.04.2024
Carsten Schuett Christian-Albrechts-Universitaet 08.01.2024 – 19.04.2024
Matthias Schulte Hamburg University of Technology 11.02.2024 – 23.02.2024
Hui-An Shen University of Bern 21.01.2024 – 22.03.2024
Mathias Sonnleitner University of Passau 14.01.2024 – 27.01.2024
Mathias Sonnleitner University of Passau 18.02.2024 – 23.02.2024
Anna Strotmann University of Osnabrück 21.01.2024 – 27.01.2024
Anna Strotmann University of Osnabrück 03.03.2024 – 22.03.2024
Rui Sun University of Alberta 03.02.2024 – 25.02.2024
Stanislaw Szarek Case Western Reserve University 18.02.2024 – 22.03.2024
Maud Szusterman Tel Aviv University 21.01.2024 – 15.03.2024
Christoph Thäle Ruhr University Bochum 19.02.2024 – 22.03.2024
Tara Trauthwein University of Oxford 25.02.2024 – 15.03.2024
Hiroshi Tsuji Osaka university 25.02.2024 – 16.03.2024
Philipp Tuchel Ruhr University Bochum 21.01.2024 – 23.02.2024
Jacopo Ulivelli TU Wien 21.01.2024 – 23.02.2024
Santosh Vempala Georgia Tech 01.03.2024 – 16.03.2024
Beatrice-Helen (Veatriki Eleni) Vritsiou University of Alberta 08.01.2024 – 29.03.2024
Vladislav Vysotskiy University of Sussex 11.02.2024 – 23.02.2024
Elisabeth M. Werner Case Western Reserve University 08.01.2024 – 19.04.2024
Bartlomiej Zawalski Polish Academy of Sciences 09.03.2024 – 23.03.2024
Ning Zhang Huazhong University of Science and Technology 17.01.2024 – 20.04.2024
PERSON
AFFILIATION
Dominik Beck Charles University
Florian Besau Technische Universität Wien
Xiaxing Cai Vienna University of Technology
Alan Chang Washington University in St. Louis
Jaume de Dios Pont ETHZ
Mathias in Wolde-Lübke University of Münster
Zakhar Kabluchko University of Münster
Kirill Kashkan University of Toronto
Dominik Kutek University of Warsaw
Dylan Langharst Sorbonne University
Matthias Lienau Hamburg University of Technology
Alexander Litvak University of Alberta
Monika Ludwig TU Wien
Andreas Malliaris IMT
Francisco Marín Sola University of Murcia
Taisiia Morozova Uppsala University
Paul Navas Alban TU Dortmund
Eli Putterman Tel Aviv University
Yaozhong Qiu Imperial College London
Benedikt Rednoß Ruhr University Bochum
Daniel Rosen Technische Universität Dortmund
Carsten Schuett Christian-Albrechts-Universitaet
Hui-An Shen University of Bern
Mathias Sonnleitner University of Passau
Clara Stegehuis University of Twente
David Steigenberger University of Münster
Anna Strotmann University of Osnabrück
Kateryna Tatarko University of Waterloo
Vanessa Trapp Hamburg University of Technology
Philipp Tuchel Ruhr University Bochum
Jacopo Ulivelli TU Wien
Beatrice-Helen (Veatriki Eleni) Vritsiou University of Alberta
Elisabeth M. Werner Case Western Reserve University
Xiaohan Zhu Universität Zürich
PERSON
AFFILIATION
PERIOD OF STAY
Gusakova Anna
 University of Münster
 
Kur Gil
ETH Zurich
 
Navas Alban Paul
Technical University of Dortmund
 
O'Reilly Eliza
Johns Hopkins University
 
Rednoß Benedikt
Ruhr University Bochum
 
Rotem Liran
Technion -- Israel Institute of Technology
 
Sambale Holger
Ruhr University Bochum, Faculty of Mathematics
 
Sonnleitner Mathias
University of Passau
 
Tkocz Tomasz
 Carnegie Mellon University
 
Trapp Vanessa
 Hamburg University of Technology
 
PERSON
AFFILIATION
PERIOD OF STAY
Alfonseca Cubero Maria de los Angeles
 North Dakota State University
 
Assouline Rotem
Weizmann Institute of Science
 
Bartl Daniel
University of Vienna
 
Bilyk Dmitriy
University of Minnesota
 
Colesanti Andrea
University of Florence
 
Faifman Dmitry
Tel Aviv University
 
Fradelizi Matthieu
Gustave Eiffel University
 
Haddad Julián Eduardo
University of Sevilla
 
Herscovici Orli
St. John's University, NY
 
König Hermann
University of Kiel
 
Ludwig Monika
University of Vienna
 
Navas Alban Paul
Technical University of Dortmund
 
Peccati Giovanni
University of Luxembourg
 
Sambale Holger
Ruhr University Bochum
 
Yaskin Vladyslav
University of Alberta
 
Zhang Ning
 Huazhong University of Science and Technology
 

Trimester Seminar Series

Tuesday February 27, 2024

10:00 - 11:00 am, Ning Zhang (Huazhong University of Science and Technology)

Title: The Aleksandrov projection theorem for convex lattice polygons

Abstract: In this talk, we will show that the examples given in Gardner-Gronchi-Zong's work are only counterexamples for the discrete analogue of the Aleksandrov projection theorem in Z^2.

YouTube

Thursday February 29, 2024 

10:00 - 11:00 am, HIM lecture hall, Poppelsdorfer Allee 45,  Bram Petri (University of Sorbonne)

Title: Probabilistic methods in hyperbolic geometry

Abstract:Hyperbolic manifolds are Riemannian manifolds whose metric is complete and has constant sectional curvature equal to -1. Another way to phrase the latter property is to say that they are locally isometric to hyperbolic space (of the right dimension). The geometry and topology of such manifolds plays a role in various domains of mathematics. I will talk about how probabilistic methods can help to solve questions on the geometry and topology of hyperbolic manifolds.

YouTube

Tuesday March 5, 2024

10:00 - 11:00 am, HIM lecture hall, Poppelsdorfer Allee 45, Mascha Gordina (University of Connecticut)

Title: Large deviations principle for sub-Riemannian random walks

Abstract: In this talk we consider large deviations for sub-Riemannian random walks on homogeneous Carnot groups. In addition to proving a LDP we can identify a natural rate function for such sub-Riemannian random walks, namely, as an energy functional. The diffusion processes corresponding to such random walks are hypoelliptic Brownian motions. The focus will be on a standard Brownian motion compared to the Brownian motion in the Heisenberg group.  The talk is based on the joint work with Tai Melcher and Jing Wang et al.

YouTube

Thursday March 7, 2024

10:00 - 11:00 am, HIM Lecture Hall, Poppelsdorfer Allee 45, Mira Gordin (Princeton)

Title: Vector-Valued Concentration on the Symmetric Group

Abstract:Concentration inequalities for real-valued functions are well understood in many settings and are classical probabilistic tools in theory and applications -- however, much less is known about concentration phenomena for vector-valued functions. We present a novel vector-valued concentration inequality for the uniform measure on the symmetric group. Furthermore, we discuss the implications of this result regarding the distortion of embeddings of the symmetric group into Banach spaces, a question which is of interest in metric geometry and algorithmic applications. We build on prior work of Ivanisvili, van Handel, and Volberg (2020) who proved a vector-valued inequality on the discrete hypercube, resolving a question of Enflo in the metric theory of Banach spaces. This talk is based on joint work with Ramon van Handel.

YouTube

Tuesday March 19, 2024 

10:00 - 11:00 am, HIM lecture hall, Poppelsdorfer Allee 45, Hermann Koenig (University of Kiel)

Title: Hyperplane sections of l_p^n for 2 < p < ∞

Abstract: tba

Tuesday March 26, 2024

10:00-11:00 am, HIM lecture hall, Poppelsdorfer Allee 45, Anna Lytova (Opole University)

Title: On the  fluctuations  of the linear eigenvalue statistics  of the sample covariance matrices corresponding to data with a tensor product structure

Abstract:Consider a vector that is a tensor product of two n-dimensional copies of a  random vector Y, and the corresponding sample covariance matrix with the number of data points proportional to n. Under some additional moment conditions, we study the fluctuations of the linear eigenvalue statistics of such matrices as n goes to infinity.  In particular, we show that taking Y from the normal distribution or from the uniform distribution on the unit sphere results in different orders of fluctuations of the resolvent traces. We use this result to prove the CLT for the corresponding, properly normalized and centralized, linear eigenvalue statistics. The talk is based on the joint work with Alicja Dembczak-Kolodziejczyk.

Thursday  April 4, 2024

Thursday, April 4, 10 - 11 am Imre Barany (Budapest and London)

Title: The Steinitz lemma, its matrix version, and balancing vectors

Abstract: The Steinitz lemma, a classic from 1913, states that a sequence a_1,...,a_n of (at most) unit vectors in R^d whose sum is the origin, can be rearranged so that every partial sum of the rearranged sequence has norm at most 2d. It is an important result with several applications. I plan to mention a few. I also explain its connection to vector balancing. 

In the matrix version of the Steinitz lemma A is a k by n matrix whose entries unit vectors in R^d and their sum is the origin. Oertel, Paat, Weismantel have proved recently that there is a rearrangement of row j of A (for every j) such that the sum of the entries in the first m columns of the rearranged matrix has norm at most 40d^5 (for every m). We improve this bound to 4d-2.

Thursday April 11, 2024

10:00 - 11:00 am Imre Barany (Budapest and London)

Title: The Steinitz lemma, its matrix version, and balancing vectors II

Abstract: The Steinitz lemma, a classic from 1913, states that a sequence a_1,...,a_n of (at most) unit vectors in R^d whose sum is the origin, can be rearranged so that every partial sum of the rearranged sequence has norm at most 2d. It is an important result with several applications. I plan to mention a few. I also explain its connection to vector balancing. 

In the matrix version of the Steinitz lemma A is a k by n matrix whose entries unit vectors in R^d and their sum is the origin. Oertel, Paat, Weismantel have proved recently that there is a rearrangement of row j of A (for every j) such that the sum of the entries in the first m columns of the rearranged matrix has norm at most 40d^5 (for every m). We improve this bound to 4d-2.


  Publications & Preprints


Winter School on Geometry and Probability

January 22 - 26, 2024

Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)

Organizers: Ronen Eldan, Assaf Naor, Kavita Ramanan, Matthias Reitzner, Christoph Thäle, Elisabeth M. Werner

Lecturers:

  • Daniel Rosen
  • Clara Stegehuis
  • Kateryna Tatarko

Description: The aim of this school is to introduce junior researchers to different angles of the program. Courses will be given on large deviation theory and its applications, on geometric analysis, and on the connections between probability theory and geometry. In addition to the courses, a poster session accompanied by blitz talks will be organized.

 The application is closed.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


Workshop: Asymptotics of (random) convex sets: fluctuations and large deviations

February 19-23, 2024

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Kavita Ramanan, Matthias Reitzner and Christoph Thäle

Lecturers:

  • Radek Adamczak
  • Pierre Calka
  • Anna Gusakova
  • Zakhar Kabluchko
  • Gil Kur
  • Rafal Latala
  • Alexander Litvak
  • Sergii Myroschnychenko
  • Eliza O’Reilly
  • Liran Rotem
  • Holger Sambale
  • Matthias Schulte
  • Carsten Schütt
  • Maud Szusterman
  • Tomasz Tkocz
  • Jacopo Ulivelli
  • Beatrice Vritsiou
  • Vladislav Vysotskiy

Description: Asymptotic geometric analysis is concerned with geometric and linear properties of finite dimensional objects, when the dimension and other relevant parameters, grow to infinity. Stochastic geometry deals with randomly constructed sets and asks for fundamental functionals like volume, curvature or combinatorial and topological properties of the resulting set when some underlying parameters tend to infinity.

Breakthrough results within the last years are, for example, strong concentration inequalities for volumes of convex bodies and more general log-concave measures, and a large number of limit laws for random sets.

This workshop brings together experts from asymptotic geometric analysis and stochastic geometry in order to build new bridges between these areas and to stimulate mutual exchange.


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


Workshop: High dimensional phenomena: geometric and probabilistic aspects

March 11-15, 2024

Venue: HIM lecture hall, Poppelsdorfer Allee 45, Bonn

Organizers: Ronen Eldan, Assaf Naor and Elisabeth M. Werner

Lecturers:

  • Rotem Assouline
  • Andreas Bernig
  • Florian Besau
  • Leo Brauner
  • Andrea Colesanti
  • Maria Alfonseca Cubero
  • Dima Faifman
  • Matthieu Fradelizi
  • Julian Haddad
  • Orli Herscovici
  • Daniel Hug
  • Jonas Knoerr
  • Alexander Koldobsky
  • Dylan Langharst
  • Galyna Livshyts
  • Monika Ludwig
  • Assaf Naor
  • Eli Putterman
  • Mark Rudelson
  • Lisa Sauermann
  • Maud Szusterman
  • Tara Trauthwein
  • Hiroshi Tsuji
  • Santosh Vempala
  • Vlad Yaskin

Description: High-dimensional systems, i.e., systems depending on a large number of parameters, are frequent in mathematics and the applied sciences, and so understanding of high-dimensional structures and phenomena have become increasingly important and indispensable.

The workshop “High dimensional phenomena: geometric and probabilistic aspects” is dedicated to these topics with a focus on probabilistic properties in high dimensional convex geometry. 


Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.


Wird geladen