Institute
General information about the institute, such as our mission statement, organizational structure, staff directory, history, directions, etc.

See More
Research
Scientific profile with all research groups, topics, collaborations, as well as columns on research at the institute.

See More
News
News and press releases about the institute, as well as a media archive.

See More
- News Overview
- Press Releases
Events
Overview of all events around the institute, such as talks, seminars, lectures, workshops, conferences and public events.

See More
Publications
Overview of all scientific publications of the institute, as well as our preprint and software repositories.

See More
Career
Information on open positions at the institute, benefits of working with us, graduate school, and postdoctoral supervision.

See More

Events
Mathematical Concepts in the Sciences and Humanities

MPI für Mathematik in den Naturwissenschaften Leipzig (Leipzig) E1 05 (Leibniz-Saal) Live Stream

conference

16.05.22 25.05.22

Mathematical Concepts in the Sciences and Humanities

This conference is dedicated to Jürgen Jost on the occasion of his 65th birthday. His influential work ranges from countless scientific contributions to the creation of a culture of interdisciplinary thinking in which concepts and abstract mathematical structures are identified as the core instrument for integrating knowledge across scientific disciplines. Over the years, Jürgen Jost has shaped a new kind of interdisciplinary science, with mathematics at its heart, and deeply influenced future generations of scientists. The conference brings together experts working with mathematical concepts in a broad spectrum of fields, comprising contributions from friends, former students and colleagues.

It is our deepest regret to announce that the conference will be in-person for speakers and invited guests only, due to the current corona regulations. Despite this situation, it is our greatest wish to share this celebration of excellence with a broad audience and offer online registration to join us via video broadcast.

Speakers

Sergio Albeverio

University of Bonn, Germany

Fatihcan Atay

Bilkent University, Turkey

Nihat Ay

Hamburg University of Technology, Germany and Santa Fe Institute, USA

Nils Bertschinger

Innoplexus, Germany

Klaus Blaum

Vizepräsident MPG

Jean-Pierre Bourguignon

IHÉS, France

David Chavalarias

Centre d'Analyses de Mathématiques Sociales (CAMS), France and École des Hautes Études en Sciences Sociales (EHESS), France

Vincenzo De Risi

CNRS, France

Tobias Elze

Harvard Medical School, USA

Christoph Engel

Max Planck Institute for Collective Goods, Germany

Bernhard Englitz

Radboud University, Netherlands

James Evans

The University of Chicago, USA

Shaoming Fei

Capital Normal University, China

Peter Gärdenfors

Lund University, Sweden

Boris Gutkin

ENS, France

Daniela Horak

AIG, United Kingdom

Jürgen Jost

Max Planck Institute for Mathematics in the Sciences

Holger Kantz

Max Planck Institute for the Physics of Complex Systems, Germany

Enno Kessler

Max Planck Institute for Mathematics, Germany

Thorbjørn Knudsen

University of Southern Denmark, Denmark

Christian Kühn

Technical University Munich, Germany

Manfred Laubichler

Arizona State University, USA

Hông Vân Lê

Czech Academy of Sciences, Czech Republic

Johannes Lenhard

TU Kaiserslautern, Germany

Jiayu Li

University of Science and Technology of China, China

Volker Lindenstruth

Frankfurt Institute for Advanced Studies - FIAS, Germany

Kristian Lindgren

Chalmers University of Technology, Sweden

Shiping Liu

University of Science and Technology of China, China

Joseph Lizier

University of Sydney, Germany

Joachim Lohkamp

University of Münster, Germany

Stephan Luckhaus

University of Leipzig, Germany

Rosemarie Nagel

UPF Barcelona, Spain

Jürgen Renn

Max Planck Institute for the History of Science, Germany

Michael Röckner

University of Bielefeld, Germany

Areejit Samal

The Institute of Mathematical Sciences, India

Klaus Scherrer

Institute Jacques Monod, CNRS, France

Charlotte Schubert

Leipzig University, Germany

Lorenz Schwachhöfer

TU Dortmund University, Germany

Matthias Schwarz

University of Leipzig, Germany

Leonhard Smith

London School of Economics, United Kingdom

Knut Smoczyk

Leibniz University Hannover, Germany

Peter Stadler

University of Leipzig, Germany

Angela Stevens

University of Münster, Germany

Michael Struwe

ETH Zurich, Switzerland

Karl-Theodor Sturm

University of Bonn, Germany

Mina Teicher

Bar-Ilan University, Israel

Wilderich Tuschmann

Karlsruhe Institute of Technology (KIT), Germany

Leo van Hemmen

Technical University Munich, Germany

Guofang Wang

Freiburg University, Germany

Massimo Warglien

Università Ca' Foscari di Venezia, Italy

Anna Wienhard

Heidelberg University, Germany

David Wolpert

Santa Fe Institute, USA

Shing-Tung Yau

Harvard University, USA

Miaomiao Zhu

Jiaotong University, China

Kang Zuo

Johannes Gutenberg University Mainz, Germany

Program

09:30 - 10:00	Welcome Coffee
	Opening session & Philosophy and History of Science: Chair: Bernd Sturmfels
10:00 - 10:15	Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences) Welcome Address Video (720p) Video (1080p)
10:15 - 11:15	Wilderich Tuschmann (Karlsruhe Institute of Technology (KIT)) Laudatio Video (720p) Video (1080p)
11:15 - 11:45	Coffee & Tea
11:45 - 12:30	Vincenzo De Risi (CNRS) Leibniz and Newton on a Geometry of Space The talk considers the evolution of Leibniz's philosophy of space, and the genesis of his famous relational theory that he opposed Newton in the course of the Leibniz-Clarke Correspondence. A detailed analysis of Leibniz' various definitions of space shows that we need to reconsider in depth the chronology of Leibniz's philosophy of space. Finally, the relationship between Leibniz and Newton on the dispute between absolute and relational space is reconsidered in a new light, an unknown source of Leibniz's conception of space is discussed, and the possibility for a different reading of the Leibniz-Clarke Correspondence is opened up. Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
14:30 - 15:15	Johannes Lenhard (TU Kaiserslautern) Created by Prediction. On the history, ontology, and computation of the Lennard-Jones Fluid Video (720p) Video (1080p) Abstract
15:15 - 15:45	Coffee & Tea
15:45 - 16:30	Manfred Laubichler (Arizona State University) Co-evolutionary dynamics from the origin of life to the Anthropocene Video (720p) Video (1080p)

08:30 - 09:00	Welcome Coffee
	Semantic Spaces, Cognition and Strategy Science: Chair: Manfred Laubichler
09:00 - 09:45	James Evans (The University of Chicago) The Curvature of Culture and Society: Analyzing meaning and connection through curved embeddings of text and networks Text and network embedding models have become a powerful tool for the study of culture and society, respectively, in recent years. Word embeddings may be understood as representing semantic relations between words as relationships between vectors in a high-dimensional semantic space, specifying a relational model of meaning consistent with many contemporary theories of culture. Similarly, network embeddings may be understood as representing social relations between persons or collectives as relationships between vectors in a high-dimensional space. In this paper, we theorize the independent ontology and value of discrete textual expressions and network ties and curved manifolds built from them, where linguistic expression trace communicative action and network topologies trace social interaction, while continuous manifolds capture the space of probable actions and interactions. Then we introduce a unified, geometric characterization of system-level structure in textual and social networks that simplifies description while improving prediction of system-level network processes. By viewing words in an expression and nodes in graphs as embedded in a latent manifold, geometric curvature of the manifold shapes action and interaction patterns. Regions embedded in positive curvature manifest dense thickets of words and ties through which information pools and cycles; regions embedded in negative curvature are characterized by infrequent communication and sparse ties representing ridges over which information spreads and flows. In this way, curvature combines local and global perspectives, providing a continuous characterization of semantic and network structure that eliminates the need for discrete distinctions between roles and communities to enable accurate modeling of system-level processes like semantic and network evolution and information diffusion with increased accuracy. We develop statistical tests for network curvature estimation, show how they link and validate emerging approaches to curvature measurement in discrete mathematics and machine learning, and demonstrate the utility of our approach for characterizing semantic and social networks, predicting network evolution and deepening geometric understanding of semantic and social constraint using simulated and observed networks across domains of multi-ethnic community life, adolescent school interactions, and scientific innovation. Video (720p) Video (1080p)
09:45 - 10:30	Peter Gärdenfors (Lund University) Determining cognitive categories by their invariances The world as we perceive it is structured into objects, actions and places. In this talk my aim is to explain why these categories are cognitively primary. From an empiricist and evolutionary standpoint, it is argued that the reduction complexity of sensory signals is based on the brain’s capacity to identify various types of invariances that are evolutionarily relevant for the activities of the organism. The aim of the article is to explain why places, object and actions are primary cognitive categories in our constructions of the external world. Following Breidbach and Jost (2006), it is shown that the invariances that determine these categories have their separate characteristics and that they are, by and large, independent of each other. This separation is supported by what is known about the neural mechanisms. The invariances for the category of numbers is also briefly discussed. Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Charlotte Schubert (Leipzig University) Rethinking Authorship in Classics Authorship as a concept remains controversial: death of the author, return of the author, authorial function, collective authorship, are just a few highlights of the discussion, which continues with undiminished acuteness. In the Classics, the question of the author arises in a very extreme form in view of the numerous fragment editions (text corpora of authors whose works are lost or only fragmentarily preserved) and the almost equally numerous attributions of works to "pseudo" authors. Here, computational approaches, operating on a path independent of the classical hermeneutic method, offer the humanities a completely new perspective. Using a striking example (Pseudo-Xenophon's Athenaion Politeia, which is considered the first completely preserved prose writing of antiquity), it will be shown how a new approach can be gained for the controversial topic of authorship. Video (720p) Video (1080p)
11:45 - 12:30	Massimo Warglien (Università Ca' Foscari di Venezia) Semantics beyond conceptual spaces Video (720p) Video (1080p)
12:30 - 14:35	Lunch Break
14:30 - 15:15	Thorbjørn Knudsen (University of Southern Denmark) Robustness and Complexity: A New Perspective for Strategy. This paper develops a novel approach to analyze the relation between complexity and robustness in social organizations. To this end, we develop a measure of complexity that can be used to quantify organizational complexity from empirical data. From a theoretical perspective, we outline how our complexity measure can be used to identify gains from improving the balance between an organization's differentiation (division of labor) and integration (of the divided effort). Our complexity measure also serves as a stepping-stone for analyzing robustness in complex organizations. We show that complexity not only represents a liability of change, but also enhances the organization’s ability to withstand turbulence in its value network. Surprisingly, perhaps, we can demonstrate that complexity controls robustness: the higher the complexity of a system, the greater its potential robustness. We argue that this insight reconciles literatures on resilience and complexity and opens a new perspective on the drivers of performance in business ecosystems and other complex organizations. Video (720p) Video (1080p)
15:15 - 16:00	Rosemarie Nagel (UPF Barcelona) Behavioral Game Theory and Neuroeconomics in Simple Situations Video (720p) Video (1080p)
16:00 - 16:30	Coffee & Tea
16:30 - 17:15	Christoph Engel (Max Planck Institute for Collective Goods) What the Judge Argues is Not What the Judge Thinks – Eye Tracking Evidence about the Disconnect Between Judicial Decision-Making and Judicial Reasoning Video (720p) Video (1080p)

08:30 - 09:00	Welcome Coffee
	Complexity: Chair: Thorbjørn Knudsen
09:00 - 09:45	Joseph Lizier (University of Sydney) Analytic relationship of information processing and synchronizability to network structure and motifs Video (720p) Video (1080p)
09:45 - 10:30	David Wolpert (Santa Fe Institute) The singularity will arrive soon - but it will be a distributed system Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Nils Bertschinger (Innoplexus) Complexity in financial markets
11:45 - 12:30	David Chavalarias (Centre d'Analyses de Mathématiques Sociales (CAMS)) How social networks modeling can help us understand the inevitable democratic disruption under the impact of Big Tech Digital spaces are increasingly present and influential in contemporary societies, to the point that what happens online can no longer be ignored when it comes to understanding their evolution. From politics to global warming debates, through vaccination debates, what happens online, and in particular on social networks, has more and more influence on what happens offline.This virtualization of social interactions brings as many new research questions as it does major challenges for our democracies. On the one hand, we have never had so much data on social systems, which should be conducive to a better conceptual understanding of their dynamics. On the other hand, the acceleration of information, the amplification of disinformation and misinformation phenomena, as well as the multiplication of digital interference between competing countries, give us the impression of a disruption and a weakening of the social fabric, victim of fragmentation and polarization.We will illustrate these phenomena from the observation of six years of political activism in France within the framework of the Politoscope project, a social macroscope using Twitter data. Then we will analyze what, in a systemic way, can lead to these democratic disruptions and, in order to stop it, the necessary evolutions of the organization of our digital spaces. Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
14:30 - 15:15	Kristian Lindgren (Chalmers University of Technology) Entropy and complexity — microscopic and macroscopic perspectives in physical systems Video (720p) Video (1080p)
15:15 - 16:00	Holger Kantz (Max Planck Institute for the Physics of Complex Systems) Truly finite prediction horizons due to scale dependent error growth rates in toy models, turbulence, and weather forecasts schemes
16:00 - 16:30	Coffee & Tea
16:30 - 17:15	Leonhard Smith (London School of Economics) Predictability Does Not Exist Video (720p) Video (1080p)
17:30 - 18:30	Reception
18:30 - 19:00	Jürgen Jost (Max Planck Institute for Mathematics in the Sciences) Across Fields -- The Intellectual Adventures of a Mathematician Video (720p) Video (1080p)

08:45 - 09:15	Welcome Coffee
09:15 - 09:45	Klaus Blaum (Vizepräsident MPG) Greeting & Congratulatory Message Video (720p) Video (1080p)
	Felix Otto (Max Planck Institute for Mathematics in the Sciences) Greeting & Congratulatory Message Video (720p) Video (1080p)
	Computational Biology and Neuroscience: Chair: Felix Otto
09:45 - 10:30	Angela Stevens (University of Münster) Mathematical models for regeneration in biological model organisms Flatworms are among the biological model organisms for regeneration. Severe cutting and grafting experiments still result in the regeneration of a complete and functioning flatworm. So far, most mathematical models could not account for these basic experiments, without adaptations for each setting. A new model is suggested and analyzed, which covers the central regeneration experiments, while not changing the structure of the equations. Dynamic boundary conditions play a crucial role here.(Joint work with A. Scheel and C. Tenbrock) Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Areejit Samal (The Institute of Mathematical Sciences) Minimum complexity drives regulatory logic in Boolean models of living systems Boolean modeling is an established framework for studying gene regulatory networks. In a Boolean network, different molecular components correspond to the nodes that receive inputs and relay outputs according to node-specific input-output rules, determining how their states change with time. In this talk, I will present our work where we have examined the rules arising in curated Boolean models of diverse regulatory networks. We have studied the complexity of these logic rules using two definitions in computer science: Boolean complexity based on string lengths in formal logic which is yet unexplored in the biological context, and the average sensitivity. We find that an overwhelming majority of the rules in these biological models minimize the two complexities, pointing to complexity as a major force in selecting regulatory logic in living systems. We provide quantitative support for the long-standing hypothesis that logic rules in gene regulatory networks are likely to be ‘simple’, or in other words, possess 'minimum complexity’. These observations have implications for ongoing efforts to build predictive models of biological systems. Video (720p) Video (1080p)
11:45 - 12:15	Klaus Scherrer (Institute Jacques Monod, CNRS) The Working Genome is RNA - Evolution of a Conceptual Challenge Video (720p) Video (1080p) Abstract
12:15 - 12:45	Wiktor Mlynarski (Institute of Science and Technology Austria) Adaptation of large-scale neural populations to natural scene statistics The idea that sensory neurons exploit the statistical structure of natural stimuli to efficiently transmit information has been a guiding principle in neuroscience for over half a century. This conceptual framework, known as the efficient coding hypothesis, has provided successful theoretical accounts of sensory coding across species and sensory systems with the retina being the paramount example. The spatial organisation of the retina has, however been assumed to be uniform and translation invariant. Here we challenge this view. By combining theory and novel experimental approaches, we demonstrate that large populations of retinal neurons exploit the inhomogeneous structure of natural scenes across the visual field to increase the efficiency of neural coding. Video (720p) Video (1080p)
12:45 - 14:30	Lunch Break
14:30 - 15:15	Leo van Hemmen (Technical University Munich) Geometric Perturbation Theory and Sound Localization Geometric perturbation theory is universally needed but not recognized as such yet. A typical example is provided by the three-dimensional wave equation, widely used in acoustics; particularly, in modelling the input to animal hearing and sound localization. We face vibrating eardrums as binaural auditory input stemming from an external sound source. In the setup of internally coupled ears (ICE), which are present in more than half of the land-living vertebrates, the two tympana are coupled by an internal air-filled cavity, whose geometry determines the acoustic properties of the ICE system. The eardrums themselves are described by a two-dimensional, damped, wave equation and are part of the spatial boundary conditions of the three-dimensional Laplacian belonging to the wave equation of the internal cavity that couples and internally drives the eardrums. In animals with ICE the resulting signal is the superposition of external sound arriving at both eardrums and the internal pressure coupling them. This is also the typical setup for geometric perturbation theory. In the context of ICE it boils down to acoustic boundary-condition dynamics (ABCD) for the coupled dynamical system of eardrums and internal cavity. In acoustics, the deviations from equilibrium are extremely small (nm range). Perturbation theory therefore seems natural and is shown to be appropriate. In doing so, we use a time-dependent perturbation theory à la Dirac in the context of Duhamel’s principle. We set the general stage for geometric perturbation theory where (d − 1)-dimensional manifolds as subsets of the boundary of a d-dimensional domain are driven by their own dynamics with e.g. the domain pressure p and an external source term as input, at the same time constituting time-dependent boundary conditions for p. Video (720p) Video (1080p)
15:15 - 16:00	Mina Teicher (Bar-Ilan University) Synchronization in brain activity and application In this talk we will present the first proof that Neurons activations is subject to synchronization and not determined by the firing rate . We show it on behaving animals and up to 3 mili seconds. We will also mention some medical applications . Video (720p) Video (1080p)
16:00 - 16:30	Coffee & Tea
16:30 - 17:15	Bernhard Englitz (Radboud University) Using compositional restricted Boltzmann machines to account for the whole-brain activity of zebrafish larvae. Video (720p) Video (1080p)
17:15 - 18:00	Boris Gutkin (ENS) Inverse stochastic resonance in neurons and in neural circuits Video (720p) Video (1080p)

08:30 - 09:00	Welcome Coffee
	Machine Learning and Data Analysis: Chair: Leo van Hemmen
09:00 - 09:45	Volker Lindenstruth (Frankfurt Institute for Advanced Studies - FIAS) Quarks und Bytes At the Large Hadron Collider (LHC) at CERN in Geneva very large scale experiments are conducted. In these experiments each nucleus-nucleus collision can generate thousands of new elementary particles. For the understanding of the dynamics and the underlying physics it is paramount to identify those particles. They are being measured with a variety of detectors in order to identify their various properties. In addition the particles traverse a large magnetic field in order to determine their momentum. Typically those detectors measure space points, which have to be connected to the particles trajectory, which generates a combinatorial background with makes the computing cost prohibitively expensive. Novel algorithms have been developed which are based on cellular automata and Kalman filters in order to minimize the computational overhead. Those algorithms exhibit a linear dependence of the tracking time on the number of space points. Further the Kalman filter was optimized to equally perform very fast. To date those algorithms are the baseline for many new detector developments. The ALICE experiment at the LHC has undergone a significant upgrade and will start again with beam time in a few weeks. The data rates exceed 600 GB/s and all data of the experiment has to be processed on-line. An appropriate compute farm with 16.000 CPU cores and 2000 GPUs has been deployed, which is capable to handle the task. The presentation will outline the requirements and the algorithms used and the particular solution as an example for this research field. Video (720p) Video (1080p)
09:45 - 10:30	Hông Vân Lê (Czech Academy of Sciences) Categorical language and geometrical methods in Machine Learning In Machine Learning we develop mathematical methods for modeling data structures, which express the dependency between observables, and design efficient algorithms for estimation of such dependency. The most advanced part of Machine Learning is statistical learning theory that takes into account our incomplete information of observables, using measure theory and functional analysis. In this way we not only unveil hidden structure of data but also make a prediction for the future. In my lecture I shall consider basic problems in statistical learning theory and demonstrate the efficiency of categorical language, manifested, in particular, in terms of probabilistic morphisms, and the use of geometric constructions, e.g. diffeological Fisher metric, in solving these problems. Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Tobias Elze (Harvard Medical School) Identifying Disease Subtypes from Complex Medical Data Many contemporary fields of medicine produce increasingly high-dimensional data. "Traditional" data analysis methods trained in clinical research education are insufficient to investigate such highly complex data. Therefore, various machine learning techniques are increasingly finding their way into medical data analysis. However, disease diagnosis itself has traditionally been defined on simple rules based on easily observable low-dimensional data. Traditional clinical diagnoses can therefore be inappropriate as ground truths to train machine learning classifiers. Here, using the eye disease of glaucoma as an example, we demonstrate how patterns identified by unsupervised machine learning on complex medical data can help to refine and quantitatively re-define disease diagnosis. Our patterns of vision loss due to glaucoma enable a whole field of quantitative research which was not available by previously existing diagnostic approaches. Video (720p) Video (1080p)
	Metric Geometry, Graphs and Hypergraphs, Network Analysis
11:45 - 12:30	Peter Stadler (University of Leipzig) Chemical Reaction Networks: idenfication, representation, and generation Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
14:30 - 15:15	Shiping Liu (University of Science and Technology of China) Geometric and spectral theory of signed graphs A signed graph is a graph whose edges are labelled by a signature. It serves as a simple model of discrete vector bundle. The fundamental ideas of balance and switching of signed graphs often lead to more systematic understanding of various parts of graph theory. In this talk, I will explain two such cases: a unification of Cheeger inequality and Bauer-Jost dual Cheeger inequality, and a unification of the discrete nodal domain theorem due to Davis, Galdwell, Leydold and Stadler, and Fiedler's approach on eigenvectors of acyclic matrices. This talk is based on joint works with Fatihcan Atay, Chuanyuan Ge. Video (720p) Video (1080p)
	Dynamical Systems and Stochastic Processes
15:15 - 16:00	Christian Kühn (Technical University Munich) On the Interplay between Network Dynamics and Differential Equations Video (720p) Video (1080p)
16:00 - 16:30	Coffee & Tea
16:05 - 16:45	Daniela Horak (AIG) Stability analysis of intersection graphs and it’s application for hyperparameter tuning in TDA Mapper TDA Mapper (also referred to as topological data visualisation or topological clustering), is a method that yields an approximation of a Reeb graph of a data manifold, and has been used successfully in applications across different fields over several last decades. In spite of TDA Mapper showing great promise, it's wide spread adoption has been limited. This is primarily due to practioners' ad-hoc approach to parameter tuning. This is unsurprising, since all unsupervised learning algorithms face the same issue due to absence of ground truth labels, and TDA Mapper even more so, due to existence of hyper parameters along with parameters. Model selection is, therefore, highly non-trivial. In this talk I will present stability analysis as a systematic tool for hyper-parameter tuning on Mapper Graphs, discuss appropriate distance metrics on these mathematical structures, and conclude with few applications. Attention: this event is cancelled.

08:30 - 09:00	Welcome Coffee
	Geometric Analysis
09:00 - 09:45	Shing-Tung Yau (Harvard University) Quasi local mass and angular momentum in general relativity Video (720p) Video (1080p)
	Dynamical Systems and Stochastic Processes
09:45 - 10:30	Michael Röckner (University of Bielefeld) Equilibria of nonlinear distorted Brownian motions Joint work with: Viorel Barbu (Romanian Academy, Iasi) This talk will review the connection of nonlinear Fokker-Planck-Kolmogorov (FPK) equations and McKean-Vlasov SDEs, with special emphasis on the case where the coefficients depend Nemytskii-type on the time marginal laws. A class of examples are nonlinear distorted Brownian motions. Recent results on their asymptotic behaviour, obtained through their corresponding nonlinear FPK equations, will be presented both in the non-degenerate and degenerate case.ReferencesBarbu, Viorel; Röckner, Michael Probabilistic representation for solutions to nonlinear Fokker-Planck equations. SIAM J. Math. Anal. 50 (2018), no. 4, 4246–4260.Barbu, Viorel; Röckner, Michael From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE. Ann. Probab. 48 (2020), no. 4, 1902–1920.Barbu, Viorel; Röckner, Michael Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. J. Funct. Anal. 280 (2021), no. 7, 108926, 35 pp.Barbu, Viorel; Röckner, Michael The invariance principle for nonlinear Fokker-Planck equations. J. Differential Equations 315 (2022), 200–221.Barbu, Viorel, Röckner, Michael Uniqueness for nonlinear Fokker-Planck equations and for McKean-Vlasov SDEs: The degenerate case arXiv:2203.00122Barbu, Viorel, Röckner, Michael The evolution to equilibrium of solutions to nonlinear Fokker-Planck equations arXiv:1904.08291 , to appear in Indiana Univ. Math. J., 36 pp.   Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Fatihcan Atay (Bilkent University) Anticipation and delay effects in network dynamics Video (720p) Video (1080p)
	Philosophy and History of Science
11:45 - 12:30	Jürgen Renn (Max Planck Institute for the History of Science) What drives the Great Acceleration Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
	Geometric Analysis: Chair: Michael Röckner
14:30 - 15:15	Jiayu Li (University of Science and Technology of China) Recent progress on the mean field equation
15:15 - 16:00	Jean-Pierre Bourguignon (IHÉS) Spinors in 2022 Video (720p) Video (1080p)
16:00 - 16:30	Coffee & Tea
16:30 - 17:15	Guofang Wang (Freiburg University) Optimal geometric inequalities for hypersurfaces with or without boundary Video (720p) Video (1080p)
	Dynamical Systems and Stochastic Processes
17:15 - 18:00	Sergio Albeverio (University of Bonn), Francesco De Vecchi (University of Bonn) On relations between functional integrals, quantum fields, singular pde's and stochastic analysis We first recall some basic historic relations between the areas of the title as an introduction to new developments in constructing models of relativistic quantum fields via singular stochastic pde's.We then illustrate the methods for the case of models involving exponential interactions (that occurr also in geometric contexts). Video (720p) Video (1080p)
19:00 - 22:00	Dinner

08:30 - 09:00	Welcome Coffee
	Geometric Analysis
09:00 - 09:45	Miaomiao Zhu (Jiaotong University) Quantization for geometric PDEs over 4-manifolds with varying geometric structures
	Dynamical Systems and Stochastic Processes
09:45 - 10:30	Karl-Theodor Sturm (University of Bonn) Conformally Invariant Random Geometry on Riemannian Manifolds of Even Dimension We construct and analyze conformally invariant, log-correlated Gaussian random fields on compact Riemannian manifolds of general even dimension defined through its covariance kernel given as inverse of the Graham-Jenne-Mason-Sparkling (GJMS) operator. The corresponding Gaussian multiplicative chaos is a generalization to the n-dimensional case of the celebrated Liouville quantum gravity measure in dimension two. Finally, we study the Polyakov-Liouville measure on the space of distributions on M induced by the copolyharmonic Gaussian field, provide explicit conditions for its finiteness and compute the conformal anomaly. Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
	Geometric Analysis
11:00 - 11:45	Michael Struwe (ETH Zurich) Plateau flow Using the Millot-Sire interpretation of the half-Laplacian on $S^1$ as the Dirichlet-to-Neumann operator for the Laplace equation on the ball $B$, we devise a classical approach to the heat flow for half-harmonic maps from $S^1$ to a closed target manifold $N\subset\R^n$, recently studied by Wettstein, and for arbitrary finite-energy data we obtain a result fully analogous to the classical results for the harmonic map heat flow of surfaces and in similar generality. When $N$ is a smoothly embedded, oriented closed curve $\Gamma\subset\R^n$ the half-harmonic map heat flow may be viewed as an alternative gradient flow for the Plateau problem of disc-type minimal surfaces. Video (720p) Video (1080p)
11:45 - 12:30	Joachim Lohkamp (University of Münster) The Geometry of Positive Mass Theorems We give an overview over geometric tools and methods we developed to solve problems in higher dimensional scalar curvature geometry and general relativity. Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
14:30 - 15:15	Knut Smoczyk (Leibniz University Hannover) Graphical mean curvature flow with bounded bi-Ricci curvature
15:15 - 16:00	Stephan Luckhaus (University of Leipzig) Data Models and the use of Invariants for the Covid 19 Pandemic Video (720p) Video (1080p)
16:00 - 16:30	Coffee & Tea
	Geometry and Mathematical Physics
16:30 - 17:15	Kang Zuo (Johannes Gutenberg University Mainz) Higgs bundles in arithmetic geometry I shall report the recent development of Higgs bundles in arithmetic geometry, in particular, constructing rank-2 motivic local systems on the projective line with 4 punctures via p-adic nonabelian Hodge theory and Drinfeld’ work on global Langlands correspondence over function fields of characteristic p. This is a joint program with Raju Krishnamoorthy, Mao Sheng, and Jinbang Yang. Video (720p) Video (1080p)

08:30 - 09:00	Welcome Coffee
	Geometry and Mathematical Physics: Chair: Karl-Theodor Sturm
09:00 - 09:45	Shaoming Fei (Capital Normal University) Geometry in quantum computation and information processing We introduce the geometry of quantum computation and some related researches in quantum information processing, including quantum coherence, quantum entanglement, quantum nonlocality, quantum information masking, quantum uncertainty relations, as well as tensor network compressed sensing and machine learning. Video (720p) Video (1080p)
09:45 - 10:30	Enno Kessler (Max Planck Institute for Mathematics) Super J-holomorphic curves J-holomorphic curves or pseudoholomorphic curves are maps from Riemann surfaces to symplectic manifolds satisfying the Cauchy-Riemann equations. J-holomorphic curves are of great interest because they allow to construct invariants of symplectic manifolds and those invariants are deeply related to topological superstring theory. A crucial step towards Gromov–Witten invariants is the compactification of the moduli space of J-holomorphic curves via stable maps which was first proposed by Kontsevich and Manin. In this talk, I want to report on a supergeometric generalization of J-holomorphic curves and stable maps where the domain is a super Riemann surface. Super Riemann surfaces have first appeared as generalizations of Riemann surfaces with anti-commutative variables in superstring theory. Super J-holomorphic curves couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and are critical points of the superconformal action. The compactification of the moduli space of super J-holomorphic curves via super stable maps might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.Based on arXiv:2010.15634 [math.DG] and arXiv:1911.05607 [math.DG], joint with Artan Sheshmani and Shing-Tung Yau. Video (720p) Video (1080p)
10:30 - 11:00	Coffee & Tea
11:00 - 11:45	Lorenz Schwachhöfer (TU Dortmund University) Parametrized measure models in classical and quantum information geometry. In this talk, we shall give an account of the geometrization of the space of probability measures on a given measure space, and report on recent progress to generalize this to quantum models as well. Video (720p) Video (1080p)
11:45 - 12:30	Matthias Schwarz (University of Leipzig) String ideas in symplectic geometry Video (720p) Video (1080p)
12:30 - 14:30	Lunch Break
14:30 - 15:15	Wilderich Tuschmann (Karlsruhe Institute of Technology (KIT)) Manifolds and Moduli Spaces of Positive Ricci Curvature Metrics I will report on joint ongoing work with Philipp Reiser on the construction of new metrics of positive Ricci curvature and its applications to the topology of corresponding moduli spaces of metrics. Video (720p) Video (1080p)
15:15 - 16:00	Anna Wienhard (Heidelberg University) On and around (higher) Teichmüller spaces Video (720p) Video (1080p)
16:00 - 16:15	Closing & Good Bye

Participants

Wanjun Ai

Southwest university, China

Sergio Albeverio

University of Bonn, Germany

Natalia Albizu

Freie Universität Berlin, Germany

Renan Assimos Martins

Leibniz University Hannover

Fatihcan Atay

Bilkent University, Turkey

Nihat Ay

Hamburg University of Technology, Germany

Jumana Baghabra

NDU, Saudi Arabia

Ruhit Bardhan

Tripura University (A Central University) Agartala,Tripura India, India

Lukas Barth

MPI for Mathematics in the Sciences, Germany

Robert Baumgarth

Leipzig University, Germany

Christian Becker

Universität Greifswald, Germany

Ulrich Behn

Leipzig University, Germany

Antonio Bellon

Czech Technical University in Prague, Italy

Nils Bertschinger

Innoplexus, Germany

Klaus Blaum

Vizepräsident MPG

Tobias Boege

Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany

Tobias Boege

MPI-MiS, Germany

Paul Bourgine

UNESCO UniTwin CS-DC, France

Jean-Pierre Bourguignon

IHÉS, France

Sebastian Bürger

Leipzig University, Germany

David Chavalarias

Centre d'Analyses de Mathématiques Sociales (CAMS), France

Qun Chen

Wuhan University, China

Hua Chen

Wuhan University, China

wenyi Chen

Wuhan University, China

Pavel Chvykov

General Motors, USA

Florio Maria Ciaglia

Universidad Carlos III de Madrid

Christian da Silva Rodrigues

Universidad Estadual de Campinas/ MPI MiS

PEDRO ROMERO DE CARVALHO

Ernst Strüngmann Institute (ESI) for Neuroscience, Germany

Vincenzo De Risi

CNRS, France

Jean-Marie DEGBO

Université d'Abomey Calavi, Benin

Elena Derunova

Max Planck Institute of Microstructure Physics, Germany

Fabio Di Nocera

Max Planck Institute for Mathematics in the Sciences, Germany

Ulrich Dierkes

University of Duisburg -Essen

Qi Ding

Fudan University, China

César Augusto Duque Sánchez

Universidad del Rosario, Colombia

Felix Effenberger

Ernst Strüngmann Institute, Germany

masud ehsani

MPI for mathematics in sciences, Germany

Marzieh Eidi

MPI, Germany

Tobias Elze

Harvard Medical School, USA

Christoph Engel

Max Planck Institute for Collective Goods, Germany

Bernhard Englitz

Radboud University, Netherlands

James Evans

The University of Chicago, USA

Fatemeh Fahimi

MPI MiS, Germany

Rifaldy Fajar

InterMaths DD, University of L'Aquila, Italy, Italy

Shaoming Fei

Capital Normal University, China

Conor Finn

MPI MiS, Germany

Mohsen Forghani

University of Vienna, Poland

Stephen Forrest

Maplesoft Europe GmbH, Germany

Matthias Frenzl

Adjacent Possible Network, Austria

Erick Galinkin

Rapid7, USA

Peter Gärdenfors

Lund University, Sweden

Chuanyuan Ge

University of Science and Technology of China;, China

Fekadu Tolessa Gedefa

Eötvös Loránd University, Institute of Mathematics, Hungary

Elena Griniari

Springer, Germany

Yaoting GUI

MPI MiS, Germany

Boris Gutkin

ENS, France

Xiaoli Han

Tsinghua University, China

Md Mehedi Hasan

Shahjalal University Of science and Technology, Bangladesh

Lukas Hauger

University of Leipzig, Germany

Zunwu He

Fudan university, China

Jules Hedges

University of Strathclyde, United Kingdom

Paul Heine

MiS, Germany

Joachim Heinze

SpringerNature, Germany

Michael Herrmann

University of Tübingen, Germany

Michael Herrmann

University of Tübingen, Germany

Daniela Horak

AIG, United Kingdom

David Hruska

Leipzig University, Germany

zhi hu

USTC, China

Chunyang Hu

University of Science and Technology of China, China

Bobo Hua

Fudan University, China

Bobo Hua

Fudan University, China

Sanjay Jain

University of Delhi, India

Sarika Jalan

Indian Institute of Technology Indore, India

Lizhen Ji

Univ of Michigan, USA

Shuhan Jiang

Max Planck Institute for Mathematics in the Sciences, Germany

Shuhan Jiang

Max Planck Institute for Mathematics in the Sciences, Germany

Parvaneh Joharinad

MIS.MPG, Germany

Jürgen Jost

Max Planck Institute for Mathematics in the Sciences

Holger Kantz

Max Planck Institute for the Physics of Complex Systems, Germany

Janis Keck

MPI MIS, Germany

Enno Kessler

Max Planck Institute for Mathematics, Germany

Moritz Ketzer

IPU Berlin | Charité | UKE, Germany

Venera Khoromskaia

Max-Planck Institute for Mathematics in the Sciences, Germany

Boris Khoromski

Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany, Germany

Bernd Kirchheim

Universität Leipzig, Germany

Mark Kirstein

MPI MIS, Germany

Thorbjørn Knudsen

University of Southern Denmark, Denmark

Kiran Murlidhar Kolwankar

Ramniranjan Jhunjhunwala College, India

Milan Kroemer

University of Bonn, Germany

Christian Kühn

Technical University Munich, Germany

Michael Lachmann

Santa Fe Institute, USA

Carlotta Langer

Technische Universität Hamburg, Germany

Manfred Laubichler

Arizona State University, USA

Tim Laux

University of Bonn, Germany

Hông Vân Lê

Czech Academy of Sciences, Czech Republic

Wilmer Leal

Max Planck Institute for Mathematics in the Sciences, Germany

Kang-Ju Lee

Seoul Natioanl University, South Korea

Marco Lehmann-Waffenschmidt

TU Dresden, Germany

Johannes Lenhard

TU Kaiserslautern, Germany

Anna Levina

Tübingen University, Germany

Ruowei Li

Fudan University, China

Chao Li

ICTP, Italy

Jiayu Li

University of Science and Technology of China, China

Wei Li

Hua-Zhong Normal University, China

Sunhyuk Lim

MPI MiS, Germany

Volker Lindenstruth

Frankfurt Institute for Advanced Studies - FIAS, Germany

Kristian Lindgren

Chalmers University of Technology, Sweden

Shiping Liu

University of Science and Technology of China, China

Lei Liu

Central China Normal University, China

Shiping Liu

University of Science and Technology of China, China

Joseph Lizier

University of Sydney, Germany

Joachim Lohkamp

University of Münster, Germany

Gabriele Lohmann

MPI for Biological Cybernetics

Wenlian Lu

Fudan University, China

Stephan Luckhaus

University of Leipzig, Germany

Duc Luu

MIS, Germany

Kawa MANMI

University of Birmingham, United Kingdom

Dimitra Maoutsa

Technical University of Berlin, Germany

Pablo Marquet

Universidad CAtolica de Chile/Santa Fe Institute, Chile

Uriel Martínez León

Universidad Nacional Autónoma de México, Mexico

Andres Marulanda

MiS-MPG, Colombia

Robert Marx

TU Dresden, Germany

Rostislav Matveev

MPI MiS, Germany

Onofrio Mazzarisi

MPI MiS, Leipzig, Germany

Aurélien MEKUKO

UNIVERSITY OF YAOUNDE I, Cameroon

Fábio Meneghetti

University of Campinas, Brazil

Wiktor Mlynarski

Institute of Science and Technology Austria, Austria

Guido Montufar

UCLA / MPI MiS, USA

Raffaella Mulas

MPI MiS, Germany

Olaf Müller

Humboldt-Universität zu Berlin, Germany

Fenna Müller

Leipzig University/MPI MIS, Germany

Rosemarie Nagel

UPF Barcelona, Spain

Jiaxi Nie

MPI MIS, Germany

Vasilis Oikonomou

Aristotle University of Thessaloniki

Rasaki Olawale Olanrewaju

Pan African University, Institute for Basic Sciences, Technology and Innovation (PAUSTI), Kenya

Eckehard Olbrich

Max Planck Institute for Mathematics in the Sciences, Germany

Felix Otto

Max Planck Institute for Mathematics in the Sciences, Germany

Vicent Pallardó

Universitat de València, Spain

John Pepper

US National Cancer Institute, USA

Paolo Perrone

University of Oxford

Hoàng Xuân Phú

Vietnam Academy of Science and Technology

Felix Pogorzelski

Leipzig University, Germany

Hongbing QIU

Wuhan University, China

Hans-Bert Rademacher

Universität Leipzig, Germany

Veljko Radic

University of Belgrade, Serbia

Maria Alejandra Ramirez

MPI Mathematics in the Sciences, Germany

Johannes Rauh

IQTIG, Germany

Jürgen Renn

Max Planck Institute for the History of Science, Germany

Guillermo Restrepo

MPI-MiS, Germany

Sharwin Rezagholi

University of Applied Sciences Technikum Wien

Sandra Ried

Leipzig University, Germany

Tobias Ried

MPI MiS + Leipzig University, Germany

Michael Röckner

University of Bielefeld, Germany

Christian Rose

University of Potsdam, Germany

Areejit Samal

The Institute of Mathematical Sciences, India

CHALLA K S N M SANKAR

VERENYA CENTRE OF AI & NANOTECHNOLOGY, India

Artem Sapozhnikov

Leipzig University, Germany

Dhiman Sarkar

JGEC, India

Emil Saucan

ORT Braude College of Engineering

Friedrich Sauvigny

Brandenburg University of Technology Cottbus-Senftenberg

Andreas Savas-Halilaj

University of Ioannina, Greece

Klaus Scherrer

Institute Jacques Monod, CNRS, France

Armin Schikorra

University of Pittsburgh, USA

Charlotte Schubert

Leipzig University, Germany

Gregor Schuldt

HTWK Leipzig, Germany

Leonard Schulz

Uni Leipzig, RSC4earth, Germany

Lorenz Schwachhöfer

TU Dortmund University, Germany

Matthias Schwarz

University of Leipzig, Germany

Alice Schwarze

Dartmouth College, USA

Akram Sharif

TU Dresden, Germany

Shafie Shokrani

Universität Siegen, Germany

Bik Soon Sia

University of Leipzig, Malaysia

Fatma Muazzez Şimşir

Selçuk University, Turkey

Leonhard Smith

London School of Economics, United Kingdom

Knut Smoczyk

Leibniz University Hannover, Germany

Gerardo Sosa

--, Mexico

Peter Stadler

University of Leipzig, Germany

Maximilian Stegemeyer

MPI MiS Leipzig, Germany

Friedrich Steinle

Technische Universität Berlin, Germany

Angela Stevens

University of Münster, Germany

Michael Struwe

ETH Zurich, Switzerland

Alina Studenova

CBS MPG, Germany

Karl-Theodor Sturm

University of Bonn, Germany

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences, Germany

Ajay Subbaroyan

The Institute of Mathematical Sciences, India

Linlin Sun

Wuhan University, China

Jun Sun

Wuhan University, China

Tamara Tal

UFZ, Germany

Chester Tan

Julius-Maximilians-Universität Würzburg, Germany

Tamer Taskiran

Bilkent University, Turkey

Marie Teich

MIS, Germany

Mina Teicher

Bar-Ilan University, Israel

Léonard TODJIHOUNDE

Institut de Mathématiques et de Sciences Physiques, Benin

Arne Traulsen

MPI for Evolutionary Biology, Germany

Wilderich Tuschmann

Karlsruhe Institute of Technology (KIT), Germany

Leo van Hemmen

Technical University Munich, Germany

Jesse van Oostrum

Hamburg University of Technology, Germany

Nicola Vassena

Freie Universitaet Berlin, Germany

Peter Vouzas

Australian National University, Australia

Tao Wang

Fudan University, China

Guofang Wang

Freiburg University, Germany

Massimo Warglien

Università Ca' Foscari di Venezia, Italy

Stephen J. Watson

University of Glasgow, Scotland

Anna Wienhard

Heidelberg University, Germany

David Wolpert

Santa Fe Institute, USA

Ruijun WU

SISSA, Italy

Yuanlong Xin

Fudan University, China

wendi xu

Fudan University, China

Yasharth Yadav

The Institute of Mathematical Sciences, India

Marius Yamakou

University of Erlangen-Nuremberg, Germany

Marius Yamakou

Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)

Yi-Hu YANG

Shanghai Jiao Tong University, China </

Mathematical Concepts in the Sciences and Humanities

Links

Speakers

Sergio Albeverio

Fatihcan Atay

Nihat Ay

Nils Bertschinger

Klaus Blaum

Jean-Pierre Bourguignon

David Chavalarias

Vincenzo De Risi

Tobias Elze

Christoph Engel

Bernhard Englitz

James Evans

Shaoming Fei

Peter Gärdenfors

Boris Gutkin

Daniela Horak

Jürgen Jost

Holger Kantz

Enno Kessler

Thorbjørn Knudsen

Christian Kühn

Manfred Laubichler

Hông Vân Lê

Johannes Lenhard

Jiayu Li

Volker Lindenstruth

Kristian Lindgren

Shiping Liu

Joseph Lizier

Joachim Lohkamp

Stephan Luckhaus

Rosemarie Nagel

Jürgen Renn

Michael Röckner

Areejit Samal

Klaus Scherrer

Charlotte Schubert

Lorenz Schwachhöfer

Matthias Schwarz

Leonhard Smith

Knut Smoczyk

Peter Stadler

Angela Stevens

Michael Struwe

Karl-Theodor Sturm

Mina Teicher

Wilderich Tuschmann

Leo van Hemmen

Guofang Wang

Massimo Warglien

Anna Wienhard

David Wolpert

Shing-Tung Yau

Miaomiao Zhu

Kang Zuo

Program

Participants

Wanjun Ai

Sergio Albeverio

Natalia Albizu

Renan Assimos Martins

Fatihcan Atay

Nihat Ay

Jumana Baghabra

Ruhit Bardhan

Lukas Barth

Robert Baumgarth

Christian Becker

Ulrich Behn

Antonio Bellon

Nils Bertschinger

Klaus Blaum

Tobias Boege

Tobias Boege

Paul Bourgine

Jean-Pierre Bourguignon

Sebastian Bürger