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 logBrunn 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.
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 ParisSaclay  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 MissouriColumbia  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  ChristianAlbrechtsUniversitaet  08.01.2024 – 19.04.2024 
Matthias Schulte  Hamburg University of Technology  11.02.2024 – 23.02.2024 
HuiAn 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 
BeatriceHelen (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 WoldeLübke  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  ChristianAlbrechtsUniversitaet 
HuiAn 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 
BeatriceHelen (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 

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 GardnerGronchiZong's work are only counterexamples for the discrete analogue of the Aleksandrov projection theorem in Z^2.
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.
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 subRiemannian random walks
Abstract: In this talk we consider large deviations for subRiemannian random walks on homogeneous Carnot groups. In addition to proving a LDP we can identify a natural rate function for such subRiemannian 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.
Thursday March 7, 2024
10:00  11:00 am, HIM Lecture Hall, Poppelsdorfer Allee 45, Mira Gordin (Princeton)
Title: VectorValued Concentration on the Symmetric Group
Abstract:Concentration inequalities for realvalued 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 vectorvalued functions. We present a novel vectorvalued 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 vectorvalued 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.
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
10:0011:00 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 ndimensional 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 DembczakKolodziejczyk.
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 4d2.
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 4d2.
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.
February 1923, 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 logconcave 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.
March 1115, 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: Highdimensional systems, i.e., systems depending on a large number of parameters, are frequent in mathematics and the applied sciences, and so understanding of highdimensional 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.