Bielefeld Graduate School in Theoretical Sciences

Prof. Huyên PHAM (University Paris Diderot):

Mean field control/games. A survey.

16:15, lecture hall: H5

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 approximation of MFC.

Prof. Peter Imkeller (HU Berlin):

Paleoclimatic time series: dynamics and statistics

16:15, lecture hall: H6

Abstract:
Simple models of the earth's energy balance are instrumental for
interpreting 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 of
SDE with Lévy noise.

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

Prof. Sabine Jansen (LMU München):

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

16:15, lecture hall H5

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):

The Riemann Hypothesis: recent perspectives on a grand mathematical challenge

16:15, lecture hall H3

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) :

Tipping points and crises: from statistical physics to macroeconomic modelling

16:15, lecture hall H6

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):

The world as a hologram: News from String Theory

16:15, lecture hall H6

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):

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

16:15, lecture hall H6

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

Prof. Dr. Ulrich Horst (Humboldt University of Berlin ):

Optimal Order Display in Limit Order Markets,

18:15, lecture hall H8

Prof. Chris Shannon (University of California, Berkeley):

Risk, Uncertainty and Ambiuity in Markets,

16:15, seminar room V2.210

PD Dr. Ulf Hashagen (Forschungsinstitut für Technik- und Wissenschaftsgeschichte, Deutsches Museum München):

Kein Platz für das "Genie": Der ungarisch-jüdische Mathematiker Johann von Neumann in Deutschland,

16:15, lecture hall H6