IGDK Compact Course: Concentration inequalities and matrix computationsOnline (Boltzmannstr. 3, 85748 Garching)

This live online course gives an introduction to the theory of concentration inequalities with some basic applications to matrix computations. The course assumes only a basic level of experience with probability, linear algebra, and matrix computations. It does not assume exposure to high-dimensional probability or randomized matrix computations. The course will consist of four 90-minute lectures on scalar concentration, matrix concentration, subspace embeddings and randomized SVD. Each lecture takes place online from 18:30-20:00 from Modal 3rd to Thursday 6th May 2021.

Further Information and registration under: https://igdk1754.ma.tum.de/IGDK1754/CC_Tropp

Modelling human crowds from first principles and through machine learning methodsvia ZOOM (Boltzmannstr. 3, 85748 Garching)

Large human crowds constitute a fascinating research area for mathematical modelling. Even though the individuals forming the crowd are extremely complex, dominant emergent behaviors like density-velocity profiles and lane formation can be captured with relatively simple models. In this talk, we discuss recent "first principle", agent-based approaches, coarser cellular automatons, as well as modelling ideas from fluid dynamics. We also show how machine learning methods can provide a separate path to understanding crowds, with both strengths and shortcomings compared to the traditional approach.

Stability analysis of cluster synchronization patterns in generalized networks: Is symmetry really your friend?Virtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

Many biological and technological networks show intricate synchronization patterns, where several internally coherent but mutually independent clusters coexist. Which synchronization patterns we can ultimately observe are determined by their stabilities. It is widely believed that utilizing symmetries in the network structure is crucial to the characterization of a pattern’s stability. However, symmetry-based methods are limited in the types of synchronization patterns they can directly treat and can be computationally expensive. In this talk, I will show that when symmetry information is discarded, the stability problem becomes easier, not harder. By forgoing symmetry, we not only can analyze all synchronization patterns in a unified fashion but also develop algorithms that are orders of magnitude faster than symmetry-based ones. Our symmetry-independent method is based on finding the finest simultaneous block diagonalization of noncommuting matrices in the variational equation. This framework can be naturally extended to networks with generalized interactions, including hypergraphs and temporal networks.

The *-Edge Reinforced random walk, bayesian statistics and statistical physics(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

We will introduce recent non-reversible generalizations of the Edge-Reinforced Random Walk and its motivation in Bayesian statistics for variable order Markov Chains. The process is again partially exchangeable in the sense of Diaconis and Freedman (1982), and its mixing measure can be explicitly computed. It can also be associated to a continuous process called the *-Vertex Reinforced Random Walk, which itself is in general not exchangeable. If time allows, we will also discuss some properties of that process.Based on joint work with S. Bacallado and C. Sabo.

Using full genome (and epigenome) data to infer past species history and ecological/life-history traitsMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)

The field of evolutionary genetics is profoundly rooted in stochastic mathematical theory and since several years the theory has been extended to model the evolution of full genomes. Indeed, large amount of full genome data are becoming available for human but also non-model organisms. Several methods based on the Sequential Markovian coalescent (SMC) have been developed to use sequence data to uncover population demographic history. While these methods can be applied in principle to all possible species, they have been developed based on the human biological characteristics and have main limitations such as assuming sexual reproduction and no overlap of generations. However, in many plants, invertebrates, fungi and other taxa, these assumptions are often violated due to different ecological and life history traits, such as self-fertilization, long term dormant structures (seed or egg-banking) or large variance in offspring production. I will first describe a novel SMC-based method which we developed to infer 1) the rates of seed/egg-bank and of self-fertilization, and 2) the populations' past demographic history. We also apply our method to Arabidopsis thaliana, Daphnia pulex and to detect seed banking in different populations of the wild tomato species Solanum chilense. Finally, I will show that we can even extend this method to detect and to date the changes of selfing / seed banking in time. I will conclude by discussing more general class of mathematical stochastic models and methods which should be developed for applicability to all species.

Link and Passcode: https://tum-conf.zoom.us/j/96536097137 Code 101816

The virtual percentage strip – an intervention study in grade 6via ZOOM (Theresienstraße 39, 80333 München)

Link: https://lmu-munich.zoom.us/j/581970248?pwd=SkdUZS8yWE53Ri9MVnBBMzMrb3RrQT09

Meeting-ID: 581 970 248, Kenncode: 062401

Differentiability of the speed of biased random walks on Galton-Watson trees(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

We prove that the speed of a $\lambda$-biased random walk on a supercritical Galton-Watson tree (with/without leaves) is differentiable for $\lambda$ such that the walk is ballistic and obeys a central limit theorem. We also give an expression of the derivative using a certain 2-dimensional Gaussian random variable, which naturally arise as limits of functionals of a biased random walk. The proof heavily uses the renewal structure of Galton-Watson trees that was introduced by Lyons-Pemantle-Peres. In particular, an important role is played by moment estimates of regeneration times, which are locally uniform in $\lambda$. This talk is based on a joint work with Adam Bowditch (University College Dublin).

A dynamical Theory for rough singular equations with delayVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

The Multiplicative Ergodic Theorem (MET) forms the theoretical foundation for many areas of dynamical systems research, notably smooth ergodic theory and the theory of SRB measures for both finite-dimensional systems (ODE and SDE) as well as infinite-dimensional systems (PDE, SPDE, and SDDE). MET is particularly important to study the invariant manifolds, bifurcations, computing the Entropy, and investigating the chaotic behavior. In this talk, we propose a new version of this theorem with full generality and apply it to provide a comprehensive dynamical analysis of stochastic singular delay equations. Indeed we prove the Oseledets splitting for the linear case and the existence of invariant manifolds in non-linear case. The main tools here are MET, Rough path theory, and Hopf Algebra, this dynamical theory can also be applied to the singular delay equations driven with FBM with low regularity. This talk is mainly based on the following paper https://link.springer.com/article/10.1007/s10884-021-09969-1 Joint work with Sebastian Riedel

The Future of Mathematics in the Age of Artificial Intelligence via ZOOM (Boltzmannstr. 3, 85748 Garching)

‘Maths in Society’ is a lecture series started by the graduate students of the Mathematics Department at the Technical University of Munich. We are conducting our first event on 12th May 2021 (Wednesday) at 18:00 CET. A lecture on ‘The Future of Mathematics in the Age of Artificial Intelligence’ will be delivered by Prof Gitta Kutyniok (from LMU Munich).

Abstract: We currently witness the impressive success of artificial intelligence (AI) in real-world applications, ranging from science to public life. Such type of approaches often outperforms classical model-based and mathematically founded approaches. At the same time, AI methods such as deep learning still lack a profound theoretical understanding, sometimes even being referred to as "alchemy". This poses an enormous challenge to, but also a tremendous chance for mathematics as a field.

The goal of this lecture is to first provide an introduction into this research area. We will then focus on two aspects. We first ask: What is the future of areas such as inverse problems or partial differential equations, whose change can already by now be observed, and why are hybrid methods such important? We will discuss this also based on several examples. Second, we will show to which extent mathematics can contribute to this new world of artificial intelligence, and how in turn this might also change mathematics.

To register for the event, please fill this form: https://forms.gle/LMzC9QGkkNmCT4nE6

For more information, please check out this website: https://www.ma.tum.de/en/news-events/studies-information/maths-in-society.html

Universal dynamics of pulled frontsVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

The formation of structure in spatially extended systems is often mediated by an invasion process, in which a pointwise stable state invades a pointwise unstable state. A fundamental goal is then to predict the speed of this invasion. The marginal stability conjecture postulates that, absent a mechanism through which the nonlinearity enhances propagation, the invasion speed is predicted by marginal linear stability of the pointwise unstable background state in a suitable norm. We introduce a set of largely model-independent conceptual assumptions under which we establish nonlinear propagation at the linear spreading speed for open classes of steep initial data, thereby resolving the marginal stability conjecture in the general case of stationary invasion. Our assumptions hold for open classes of parabolic equations, including higher order equations without comparison principles, while previous results rely on special structure of the equation and the presence of a comparison principle. Our result also establishes universality of the logarithmic in time delay in the position of the front, compared with propagation strictly at the linear speed, as predicted in generality by Ebert and van Saarloos and first established in the special case of the Fisher-KPP equation by Bramson. Our proof describes the invasion process through the interaction of a Gaussian leading edge with the pulled front in the wake. Technically, we rely on sharp linear decay estimates to control errors from this matching procedure and corrections from the initial data

Interacting Pólya urns with removals as linear competition process(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

A linear competition process is a continuous time Markov chain defined as follows. The process has N (N\ge 1) non-negative integer components. Each component increases with the linear birth rate or decreases with a rate given by some linear function of other components. A zero value is an absorbing state for each component: should a component become zero ("extinct"), it would stay zero for good. For all possible interactions we show that a.s. eventually only a (possibly, random) subset of non-interacting components can survive. A similar result holds for the relevant generalized Pólya urn model with removals.(Based on a joint work with Serguei Popov and Vadim Shcherbakov.)