**Prof. Stefan Hollands, PhD (Leipzig University)**

Title: Quantum Effects Inside Black Holes

Abstract: Hidden behind their event horizons, black holes harbour singularities of spacetime.

It has long been debated what is the actual nature of these singularities. Recent theoretical developments suggest that quantum effects strongly influence their macroscopic nature. I will outline some of this findings in this colloquium and provide glimpses at the mathematical structures that underlie these theoretical developments.

*The talk will take place in Lecture Hall 5 in the Main University Building at 2pm ct. eKVV*

**Prof. Christiane Fuchs (Bielefeld University & Helmholtz Munich)**

Title: Integrative modelling of infections in a corona virus cohort study

Abstract: Research on statistical modelling holds various potentials: on the one hand, it enables the further development of methodologically sophisticated models and inference; on the other hand, models may be applied to real data and lead to relevant knowledge gains in the applied domain. In practice, compromises must be made if approaches other than the theoretical ideals prove to be the most expedient.

Since the outbreak of the corona pandemic, many mathematical and statistical approaches have been used to identify drivers of infection and disease, to advise decision makers, and to predict the further course. However, models that worked well in idealized contexts often encountered limitations in real-world situations; these include unreliable information on numbers of infected individuals, and a rapidly changing environment regarding control measures, varying testing and vaccination capacities and strategies, weather conditions, and new virus variants.

I will report from our work in the KoCo19 Consortium, which has established a representative cohort for the Munich population in private households and has collected and analyzed laboratory and questionnaire data in several rounds since April 2020. We estimate the prevalence of SARS-CoV-2 in the population and combine different data sources to reliably estimate the effectiveness of non-pharmaceutical intervention methods. This is done using a variety of statistical methods, not least differential equations and Bayesian modelling. Ultimately, the project reveals synergies between the methods and application, despite or perhaps because of the compromises made.

*The talk will take place in UHG V2-210/16 at 3pm.*

**Prof. Viola Priesemann (Georg-August-Universität Göttingen)**

Title: Network dynamics, learning and self-organization: from neural information flow to COVID-19

Abstract: Spreading dynamics is ubiquitous: activity spreads in neural networks, news and fake news in social networks, and just recently the spread of a novel virus has disrupted the daily lives of people around the globe. Interestingly, in all these networks, the connections are not static, but change systematically over time. In neural networks, this is essential to implement learning, for the pandemic it was key to mitigating the spread of SARS-CoV-2. We derive the principles of self-organization in these diverse networks, show under which conditions phase transitions and critical phenomena occur, and how these can help to optimize information flow. We then put these theoretical results to the test in living real-world networks. Overall, our work contributes to our understanding of the learning and self-stabilization of living systems, from emergent information flow in neural networks to the infodemics-pandemics interaction in social networks.

The talk took place in hybrid form in H6 + online via Zoom.

**Prof. Xin Guo (UC Berkeley)**

Title: Generative Adversarial Networks (GANs): an analytical perspective

Abstract: Generative Adversarial Networks (Gans) have attracted intense interest lately in computer vision, image generation, and simulation of financial time series data. In this talk, I will first provide a gentle review of the mathematics framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.

The talk took place as Zoom video conference.

**Prof. Nihat Ay (Hamburg University of Technology)**

Title: Information Geometry for Data Science

Abstract:

Data, in its many forms and across various disciplines, is becoming an essential source for research in the 21st century. In fact, data driven knowledge extraction nowadays constitutes one of the core paradigms for scientific discovery. This paradigm is supported by the many successes with universal architectures and algorithms, such as deep neural networks, which can explain observed data and, at the same time, generalise extremely well to unobserved new data. Thus, such systems are capable of revealing the intrinsic structure of the data, as an important step within the process of knowledge extraction.

Structure is coupled with geometry at various levels. Traditionally, information geometry has been concerned with the identification of natural geometric structures of statistical models. These structures turn out to be crucial within statistical methods and learning algorithms. One instance of this is given by the natural gradient method, which improves the learning simply by utilising the natural geometry induced by the Fisher-Rao metric. The talk will outline the general perspective of information geometry and highlight its geometric structures. This perspective had already a great influence on machine learning and is expected to further influence the general field of data science.

The talk took place as Zoom video conference.

**Prof. Jens Südekum (Heinrich Heine Universität Düsseldorf)**

Title: Economic policies in Germany in times of COVID 19

Abstract: This talk reflects on economic policies that the German government has designed in the course of the Corona pandemic, and on the role of economists in advising and influencing those decisions.

The talk took place as Zoom video conference.

**Prof. Lloyd Hollenberg (The University of Melbourne)**

Title: Quantum computing: past, present, future

Abstract: Quantum computers represent an exciting new information processing paradigm. While we do not fully comprehend the strangeness of quantum mechanics (and possibly cannot), one can exploit quantum dynamics to encode and process information in quantum versions of bits (qubits). After decades of fundamental theoretical and experimental research, programmable quantum computer devices have arrived. State-of-the-art Noisy Intermediate Scale Quantum (NISQ) systems are approaching the 100 qubit level and beyond. Complimenting the developments in hardware, is a rush on the “quantum software” front to exploit the NISQ technology in various applications areas as an era of heuristic and approximate quantum computing (“HAQC”) takes hold. In this talk I’ll present a high-level overview, from qubit basics to the status and outlook for practical quantum computing in the short term, and universal quantum computing in the long term.

The talk took place as Zoom video conference.

**Prof. Luciano Rezzolla (Goethe University Frankfurt)**

Title: Modelling binary neutron stars: Einstein's richest laboratory

Abstract: I will argue that if black holes represent one the most fascinating implications of Einstein's theory of gravity, neutron stars in binary system are arguably its richest laboratory, where gravity blends with astrophysics and particle physics. I will discuss the rapid recent progress made in modelling these systems and show how the inspiral and merger of a binary system of neutron stars is more than a strong source of gravitational waves. Indeed, while the gravitational signal can provide tight constraints on the equation of state for matter at nuclear densities, the formation of a black-hole--torus system can explain much of the phenomenology of short gamma-ray bursts, while the ejection of matter during the merger can shed light on the chemical enrichment of the universe. The talk took place as Zoom video conference.

**Prof. Huyên PHAM (University Paris Diderot)**

Title: Mean field control/games. A survey

Abstract: The optimal control of McKean-Vlasov equation, also called mean-field type control (MFC), has become one of the most exciting and tremendous source of development in the general field of stochastic control since the emergence of the mean-field game (MFG) theory, initiated about a decade ago by Lasry/Lions, and Huang/Caines/Malhamé. MFG and MFC have generated crucial advances in the study and understanding of equilibrium behavior of large population of agents in strategic or cooperative interaction. They have known a surge of interest, which is explained by the range of potential applications in various fields (economics, social sciences, biology or electrical engineering), as well as the diversity of used mathematical tools in control, analysis and probability.

The aim of the talk is to present a survey of the topic, with emphasis on the dynamic programming approach and the recent mathematical tools that have been developed in this context: differentiability in the Wasserstein space of probability measures, Itô formula along a flow of probability measures and Master Bellman equation. We shall also discuss some current issues in connection with reinforcement learning with many agents, and deep neural networks techniques for numerical approximationof MFC.

**Prof. Peter Imkeller (HU Berlin)**

Title: Paleoclimatic time series: dynamics and statistics

Abstract: Simple models of the earth's energy balance are instrumental forinterpreting some qualitative aspects of the dynamics of paleo-climatic data. In the 1980s this led to the investigation of periodically forced dynamical systems of the reaction-diffusion type with small Gaussian noise, and a rough explanation of glacial cycles by Gaussian meta-stability.

A spectral analysis of Greenland ice time series performed at the end of the 1990s representing average temperatures during the last ice age suggest an α-stable noise component with an α ~ 1.75. Based on this observation, papers in the physics literature attempted an interpretation featuring dynamical systems perturbed by small Lévy noise.

In terms of statistics of stochastic processes, this leads to a model selection problem. As an example of a possible low dimensional model class we describe the time series as a simple dynamical system perturbed by α-stable noise. One needs an efficient test for the best fitting α. We discuss a statistical testing method based on the p-variation of the solution trajectories ofSDE with Lévy noise.

(joint work with J. Gairing, C. Hein, M. Högele, I. Pavlyukevich)

**Prof. Sabine Jansen (LMU München)**

Title: Condensation, big jump and heavy tails: from phase transitions to probability

Abstract: Ice melts, water evaporates - these are everyday experiences of phase transitions. The explanation of this macroscopic phenomenon from microscopic laws belongs to the realm of statistical physics, which treats matter as a composite system made up of many individual "agents" with random behavior. From a mathematician's point of view, a fully rigorous understanding still eludes us. The search for it leads to questions in probability that open up surprising connections: toy models for surface tension of liquid droplets build on heavy-tailed variables used in insurance mathematics; a big jump made by a random walker is a condensation phenomenon in disguise. The talk explains some of these connections and presents open problems and partial answers.

**Prof. Jon Keating (University of Bristol)**

Title: The Riemann Hypothesis: recent perspectives on a grand mathematical challenge

Abstract: The Riemann Hypothesis, formulated by Riemann in 1859, is one of the great unsolved problems in mathematics. It relates to the distribution of the prime numbers and many other fundamental problems in the subject. Remarkably, it seems also to be connected to problems that arise in other areas of science, in particular in Physics. I will explain what the Riemann Hypothesis is, why it is so important and mysterious, and how it appears to connect with phenomena found in other disciplines. Furthermore, I hope to do this without assuming any significant mathematical knowledge.

**Prof. Jean-Philippe Bouchaud (École polytechnique)**

Title: Tipping points and crises: from statistical physics to macroeconomic modelling

Abstract: Using the methodology of statistical physics, which characterizes a model through its ``phase diagram", we explore the possible types of phenomena that ``agent-based" macroeconomic models with interactions, frictions and heterogeneities can reproduce. Through this looking glass, we will discuss three stylized models (interacting firms networks, agent based models of firms and households and dynamical trust networks). In each case one finds generic phase transitions (or tipping points) between a ``good economy" state where unemployment/volatility are low and confidence is high, and a ``bad economy" state where unemployment/volatility are high and confidence is low. If the parameters are such that the system is close to such transitions, any small fluctuation may be amplified, leading to a large level of endogenous volatility. This can cause the monetary policy itself to trigger instabilities and be counter-productive. We identify several theoretical scenarios for synchronization and instabilities in large economies that can generate aggregate volatility and acute crises without any identifiable idiosyncratic shocks. This suggests an interesting explanation for the unexpected outbursts of endogenous economic or financial crises, also known as the ``small shocks, large business cycles" puzzle.

**Prof. Dr. Jan Plefka (Humboldt University of Berlin)**

Title: The world as a hologram: News from String Theory

Abstract: We are all familiar with holograms: Two dimensional optical structures which - when suitably lit - create the illusion of a three-dimensional object. In fact the light waves emerging from holograms are identical to the ones one would preceive from the three-dimensional object - a distant observer cannot distinguish the two. Recent research in fundamental physics has revealed that the gravitational force of nature might in fact be a holographic illusion in this sense. It is replacable by a lower dimensional structure, known as gauge field theory. The latter is the theoretical framework to describe all the non-gravitational forces in nature which reign elementary particle physics. Our lecture will begin with reviewing the basic concepts of gravitation, quantum mechanics and quantum fields. Then the holographic concept and its relation to superstrings will be presented. Finally, current insights on how to exploit this duality to answer questions in gauge field theory, which had not been accessible so far, will be presented.

**Prof. Eiichiro Komatsu (Max-Planck-Institute for Astrophysics)**

Title: Critical Tests of Theory of the Early Universe using the Cosmic Microwave Background

Abstract: The Cosmic Microwave Background (CMB), the fossil light of the Big Bang, is the oldest light that one can ever hope to observe in our Universe. The CMB provides us with a direct image of the Universe when it was still an “infant” - 380,000 years old - and has enabled us to obtain a wealth of cosmological information, such as the composition, age, geometry, and history of the Universe. Yet, can we go further and learn about the primordial universe, when it was much younger than 380,000 years old, perhaps as young as a tiny fraction of a second? If so, this gives us a hope to test competing theories about the origin of the Universe at ultra high energies. In this talk I present the results from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite that I contributed, and then discuss the recent results from the Planck satellite (in which I am not involved). Finally, I discuss future prospects on our quest to probe the physical condition of the very early Universe.