Munich Mathematical CalendarCalendar with mathematical talks near Munich2024-07-17T06:46:39Ztag:mathcal.ma.tum.de,2013-04-10:/feed/filter2/year2024/month701.07.2024 14:15 Michael Kupper (University of Konstanz): Discrete approximation of risk-based pricing under volatility uncertainty2024-05-06T08:38:42ZMichael Kupper (University of Konstanz)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240506103649We discuss the limit of risk-based prices of European contingent claims in discrete-time financial markets under volatility uncertainty when the number of intermediate trading periods goes to infinity. The limiting dynamics are obtained using recently developed results for the construction of strongly continuous convex monotone semigroups. We connect the resulting dynamics to the semigroups associated to G-Brownian motion, showing in particular that the worst-case bounds always give rise to a larger bid-ask spread than the risk-based bounds. Moreover, the worst-case bounds are achieved as limit of the risk-based bounds as the agent’s risk aversion tends to infinity. The talk is based on joint work with Jonas Blessing and Alessandro Sgarabottolo.
01.07.2024 15:00 Swann Marx: Stability and controllability analysis of infinite-dimensional singularly perturbed systems2024-06-20T04:48:14ZSwann Marxtag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240620064632This talk is devoted to infinite-dimensional singularly perturbed systems, namely, partial differential equations. To be more precise, such systems admit two different time-scales, i.e. one can see them as the coupling between a fast system and a slow system. This may lead to several technical issues - for example, in numerical analysis, where the time steps have to be adapted according to the ratio between the time scales. Another way is to compute approximated and decoupled systems, called the reduced order and the boundary layer systems, for which the analysis is easier. This talk focuses on control theory. In particular, the singular perturbation allows, at least in finite dimension, to deduce the stability of the full-system thanks to the stability analysis of the approximated systems (if the fast system is sufficiently fast). In infinite-dimension, this analysis might be not possible, and this talk proposes some counter-examples together with examples for which such property holds. It is a joint work with Gonzalo Arias, Eduardo Cerpa and Guilherme Mazanti.
01.07.2024 16:30 Apolline Louvet: Modelling populations expanding in a spatial continuum2024-06-25T11:07:46ZApolline Louvettag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240507074847Understanding the emergence of genetic diversity patterns in expanding populations is of longstanding interest in population genetics. In this talk, I will introduce a model that can be used to gain some insight on the evolution of genetic diversity patterns at the front edge of an expanding population. This model, called the ∞-parent spatial Λ-Fleming Viot process (or ∞-parent SLFV), is characterized by an "event-based" reproduction dynamics that makes it possible to control local reproduction rates and to study populations living in unbounded regions. I will present what is currently known of the growth properties of this process, and what are the implications of these results in terms of genetic diversity at the front edge.
Based on a joint work with Amandine Véber (MAP5, Univ. Paris Cité) and Matt Roberts (Univ. Bath).
02.07.2024 14:00 Thomas Richardson (University of Washington, Seattle): Short Course on “Graphical causal modeling” (Lecture 3/3)2024-06-21T07:16:49ZThomas Richardson (University of Washington, Seattle)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240621091224This short course covers recent developments in graphical and causal modeling in Statistics/Machine Learning. It is comprised of the following three lectures, each two hours long.
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June 25, 2024; Lecture 1: “Learning from conditional independence when not all variables are measured: Ancestral graphs and the FCI algorithm”
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June 27, 2024; Lecture 2: “Identification of causal effects: A reformulation of the ID algorithm via the fixing operation”
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July 2, 2024; Lecture 3: “Nested Markov models”
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The course targets an audience with exposure to basic concepts in graphical and causal modeling (e.g., conditional independence, DAGs, d-separation, Markov equivalence, definition of causal effects/the do-operator).
08.07.2024 16:30 Peter Mörters: Metastability of the contact process on evolving scale-free networks2024-06-04T06:19:12ZPeter Mörterstag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240603082310We study the contact process on scale-free inhomogeneous random graphs evolving
according to a stationary dynamics, where the neighbourhood of each vertex is updated
with a rate depending on its strength. We identify the full phase diagram of metastability
exponents in dependence on the tail exponent of the degree distribution and the rate of updating.
The talk is based on joint work with Emmanuel Jacob (Lyon) and Amitai Linker (Santiago de Chile).
09.07.2024 16:15 Prof. Dr. Sven Bachmann (UBC Vancouver) : A new bulk Z_2 invariant for interacting phases2024-06-20T10:14:06ZProf. Dr. Sven Bachmann (UBC Vancouver) tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240620121107The stability of topological indices of condensed matter systems in the presence of interactions is not expected to hold universally. In this colloquium, I will first discuss the mathematical setup of the classification of interacting phases. I will then focus on a new Z_2-valued index for time-reversal invariant interacting fermions on infinite lattices and prove its topological stability. I will show that it generalizes the well-known Fu-Kane-Mele index of topological insulators, thereby proving its stability under large perturbations. This is joint work with Alex Bols and Mahsa Rahnama.
11.07.2024 12:15 Dr. Yahya Saleh (University of Hamburg): Augmenting Spectral Methods with Normalizing Flows and Application to Computing Molecular Excited States2024-06-06T08:43:57ZDr. Yahya Saleh (University of Hamburg)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240527125236(Pseudo)spectral methods are popular for solving a wide variety of differential equations and generic optimization problems. Due to favourable approximation properties, such as rapid con-vergence for smooth functions, they are particularly popular and effective for solving time-independent Schrödinger equations. For example, in the domain of molecular quantum phy-sics, spectral and pseudospectral methods are the building blocks for a variety of variational techniques to solve nuclear Schrödinger equations. Despite their many favourable approxima-tion properties, these methods suffer from the curse of dimensionality and have slow conver-gence rates for highly-oscillatory functions. This limits their applicability in a wide variety of fields. Moreover, their effectiveness is highly dependent on the initial choice of the basis.
In this talk I propose increasing the expressivity of (pseudo)spectral methods by composing a chosen orthonormal basis with an optimizable measurable mapping. This gives rise to an in-duced sequence. I characterize necessary and sufficient conditions for this sequence to inherit the completeness of the underlying orthonormal basis. Here, it is shown that the invertibility of the mapping is a necessary condition. Subsequently, I discuss the approximation of Schwartz functions in the linear span of Hermite functions that are composed with invertible mappings. To this end, I derive convergence guarantees and characterise the convergence order. Finally, I show numerical simulations for computing the vibrational spectra of polyatomic molecules. In these simulations, the invertible mapping was modelled using a normalizing flow, i.e., an inver-tible neural network to augment the expressivity of a given basis. Comparisons against the use of standard bases demonstrate orders-of-magnitude increased accuracy when using normali-zing flows.
12.07.2024 14:15 Vivian Haller: Presentation of a Master's Thesis on "Development of a software tool facilitating exam staff allocation"2024-07-09T09:39:40ZVivian Hallertag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240709113759Assigning supervisors and correctors to exams is a recurrent task handled at the TUM-CIT Department of Mathematics. The current practice of determining a suitable allocation has several drawbacks leading to increased time consumption, which the implemented tool should help mitigate.
15.07.2024 14:15 Xunyu Zhou, Columbia University: Reinforcement Learning for Diffusion Processes2024-06-26T12:35:21ZXunyu Zhou, Columbia Universitytag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240626143225Reinforcement learning (RL) is a version of stochastic control in which the system dynamics are unknown (up to the type of dynamics such as Markov chains or diffusion processes). There has been an upsurge of interest in RL for (continuous-time) controlled diffusions in recent years. In this talk I will highlight the latest developments on theory and algorithms arising from this study, including entropy regularized exploratory formulation, policy evaluation, policy gradient, q-learning, and regret analysis. Time permitting, I will also discuss applications to mathematical finance and generative AI.
15.07.2024 15:00 Gianmarco del Sarto: A non-autonomous framework for climate change and extreme weather events increase in a stochastic energy balance model2024-06-25T08:36:31ZGianmarco del Sartotag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240625103423 We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the super-greenhouse effect in tropical regions, fits within the setting of stochastic reaction-diffusion equations. Our results show how both mean and variance of temperature increase, without the system going through a bifurcation point. This study aims to advance the conceptual understanding of the extreme weather events frequency increase due to climate change. This is a joint work with Prof. F. Flandoli.
15.07.2024 16:00 Alexander Drewitz: Branching Brownian motion, branching random walks, and the Fisher-KPP equation in spatially random environment2024-07-09T06:08:40ZAlexander Drewitztag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240611134959Branching Brownian motion, branching random walks, and the F-KPP equation have been the subject of intensive research during the last couple of decades. By means of Feynman-Kac and McKean formulas, the understanding of the maximal particles of the former two Markov processes is related to insights into the position of the front of the solution to the F-KPP equation.
We will discuss some recent result on extensions of the above models to spatially random branching rates and random nonlinearities. Interestingly, the introduction of such inhomogeneities leads to a richer and much more nuanced picture when compared to the homogeneous setting.
15.07.2024 17:30 Matthias Löwe: Fluctuations in the dilute Curie-Weiss model2024-07-08T09:09:47ZMatthias Löwetag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240611135142The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the level of laws of large numbers the magnetization as well as the free energy behave as they do in the usual Curie-Weiuss model (i.e. mean-field Ising model). We analyze CLTs for the these quantities and give several critical values for p at which these fluctuaions change. This is joint work with Zakhar Kabluchko and Kristina Schubert.
16.07.2024 16:30 Maximilian Fels: The BRW subject to a hard-wall constraint2024-07-09T10:36:40ZMaximilian Felstag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240522092531We study the (binary) branching random walk when the heights of all
particles in the most recent generation are conditioned to be positive.
We obtain sharp asymptotics for the probability of this event and for
various statistics, conditional on its occurrence. In particular, we
identify the repulsion profile followed by the conditional field, and
derive limits in law for its maximum, minimum and associated additive
martingales.
These results show, among other things, that the laws of the conditional
and unconditional fields are mutually singular in the limit.
18.07.2024 12:15 Dr. Loic Joubert-Doriol (Univ Eiffel, Paris) and Dr. Benjamin Lasorne (Univ Montpellier): Introduction to Modelling Molecular Observables and Spectral Responses2024-07-15T08:33:28ZDr. Loic Joubert-Doriol (Univ Eiffel, Paris) and Dr. Benjamin Lasorne (Univ Montpellier)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240715103019This talk will provide a partial overview of how to model molecular observables and spectral responses.
We shall start with the essential quantum mechanical concepts and formalisms that are used in theoretical chemistry and molecular physics.
This will be followed by an illustration of the tools that are involved in numerical simulations in this context.
22.07.2024 15:00 Erik Mau: Phase reduction explains chimera shape: when multi-body interaction matters2024-07-05T07:22:05ZErik Mautag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240705091818Networks of weakly coupled oscillators can display complex phenomena of partial synchrony, e.g., chimera states. While some features of the model are conserved in its respective phase-reduced model up to first order in the coupling strength, others require the usage of terms of higher order to be present. Recently, we used the concept of phase-isostable coordinates to derive those terms for coupled two-dimensional limit-cycle oscillators. Here, we use this approach on an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely via an arbitrary adjacency matrix. Ultimately, we arrive at a second-order extension of the paradigmatic Kuramoto-Sakaguchi model for networks and explicitly demonstrate how the adjacency matrix translates into the multi-body coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of non-locally coupled oscillators exhibiting a chimera state. The second-order phase model reproduces the dependence of the chimera shape on the coupling strength. This feature is not captured by the typically used first-order Kuramoto-like model.
22.07.2024 16:30 Adrien Malacan: From microscopic dynamics to macroscopic patterns: Proof techniques for the TASEP through second class particles2024-07-17T06:46:39ZAdrien Malacantag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240502105919In this talk, we will derive the main ideas to determine the hydrodynamical behaviour of the Totally Asymmetric Simple Exclusion Process (TASEP) on Z, based on a paper by P. Ferrari that leverages the microscopic properties of the process. Specifically, we will emphasize how the nearest neighbour property and total asymmetry play a crucial role in the proof.
Additionally, we will discuss the key role of second-class particles in this context, noting how these objects interestingly capture the macroscopic behaviour of the system.
30.07.2024 18:12 Max Mustermann: Test2024-06-27T16:16:06ZMax Mustermanntag:mathcal.ma.tum.de,2013-04-10:/talk/created/20240627181221Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.
\[ \sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6} \]
Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy text ever since the 1500s, when an unknown printer took a galley of type and scrambled it to make a type specimen book. It has survived not only five centuries, but also the leap into electronic typesetting, remaining essentially unchanged. It was popularised in the 1960s with the release of Letraset sheets containing Lorem Ipsum passages, and more recently with desktop publishing software like Aldus PageMaker including versions of Lorem Ipsum.