Februar 2021

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### 01.02.2021 15:00 Anne Pein (TUM):The parabolic Anderson model with Pareto potential on critical Galton-Watson trees conditioned to surviveVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

We prove that the solution to the parabolic Anderson model with Pareto potential on a critical Galton-Watson tree conditioned to survive with an offspring distribution in the domain of attraction of a stable law localizes with high probability in one single vertex for time going to infinity. The proof relies on the Feynman-Kac representation of the solution and spectral estimates of the Anderson Hamiltonian. This is joint work with Eleanor Archer (Tel Aviv University).

### 01.02.2021 16:00 Lorenzo Taggi (Sapienza Università di Roma):Exponential decay of correlations for O(N) spin systems for arbitrary N(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

The Spin O(N) model is a classical statistical mechanics model whose configurations are collections of unit vectors, called spins, taking values on the surface of a N -1 dimensional unit sphere, with each spin associated to the vertex of a graph. Some special cases of the spin O(N) model are the Ising model (N = 1), the XY model (N = 2), and the classical Heisenberg model (N = 3). Despite the fact that it is a very classical model, there remain important gaps in understanding, particularly in the case N > 2. This talk will present a new recent result about exponential decay of correlations for arbitrary (non-zero) values of the external magnetic field and arbitrary spin dimension N>1, extending previous results which are only valid for N=1,2,3. Our proof is probabilistic and employs a new representation of the model as a system of “coloured" random walks which is of independent interest.

### 03.02.2021 13:00 Martin Brokate TUM Mathematik:Oberseminar : A variational inequality for the derivative of the scalar play operatorPasscode 101816 (https://tum-conf.zoom.us/j/96536097137 , 0 (using zoom))

We show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.

### 03.02.2021 16:00 Holger Dette (Ruhr-Universität Bochum):Testing relevant hypotheses in functional time series via self-normalization(using Zoom, see http://go.tum.de/410163 for more details) (Parkring 11, 85748 Garching)

In this paper we develop methodology for testing relevant hypotheses in a tuning-free way. Our main focus is on functional time series, but extensions to other settings are also discussed. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time series, we propose to test a \textit{relevant} deviation under the null hypothesis. In the two sample problem this means that an $L^2$-distance between the two mean functions is smaller than a pre-specified threshold. For such hypotheses self-normalization, which was introduced by Shao (2010) and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self-normalized procedures for testing relevant hypotheses and demonstrate the particular advantages of this approach in the the comparisons of eigenvalues and eigenfunctions.

### 08.02.2021 15:00 Tania Biswas (UNI PV):Optimal Control Problems for the Cahn-Hilliard-Navier-Stokes SystemVirtuelle Veranstaltung (Boltzmannstr. 3, 85748 Garching)

In this talk I will address various optimal control problems related to the evolution of two dimensional bounded domain. I quote [1], [2], [3], for more details about the model. We prove the existence of an optimal control and establish the Pontryagin maximum principle, which gives the rst order necessary conditions of optimality. We also prove the unique solvability of the corresponding adjoint system and characterize the optimal control in terms of the adjoint variable. Furthermore, we establish the second order necessary and sucient optimality condition for the optimal control problem.

References [1] P. Colli, S. Frigeri, M. Grasselli, Global existence of weak solutions to a nonlocal Cahn-Hilliard-Navier-Stokes system, Journal of Mathematical Analysis and Applications, 386(1) (2012), 428-444. [2] S. Frigeri, M. Grasselli, P. Krejci, Strong solutions for two-dimensional nonlocal Cahn-Hilliard- Navier-Stokes systems, Journal of Differential Equations, 255(9) (2013), 2587-2614. [3] S. Frigeri, C. G. Gal and M. Grasselli, On nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions, Journal of Nonlinear Science, 26(4) (2016), 847-893.

TBA