Dezember 2020

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### 01.12.2020 16:30 Christian Brennecke (Harvard):Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field(using zoom) (Boltzmannstr. 3, 85748 Garching)

In this talk I will present a variational formula for the thermodynamic limit of the free energy of the Sherrington-Kirkpatrick (SK) spin-glass model with transverse field, a quantum generalization of the classical SK model. Through its path integral representation, the quantum SK model can be translated to a classical vector-spin model with the spins taking values in the space of $\{ -1, 1 \}$-valued cadlag paths. I will explain how to approximate the model by a sequence of classical finite-dimensional vector-spin models which enables us to use results of Panchenko to describe the free energy in the thermodynamic limit. The talk is based on joint work with Arka Adhikari.

### 02.12.2020 13:00 Göran Kauermann (LMU):Nowcasting and Forecasting using COVID-19 data(using Zoom, see http://go.tum.de/410163 for more details) (Parkring 11, 85748 Garching)

We analyse the temporal and regional structure in COVID-19 infections, making use of the openly available data on registered cases in Germany published by the Robert Koch Institute (RKI) on a daily basis. We demonstrate the necessity to apply nowcasting to cope with delayed reporting. Delayed reporting occurs because local health authorities report infections with delay due to delayed test results, delayed reporting chains or other issues not controllable by the RKI. A reporting delay also occurs for fatal cases, where the decease occurs after the infection (unless post-mortem tests are applied). The talk gives a general discussion on nowcasting and applies this in two settings. First, we derive an estimate for the number of present-day infections that will, at a later date, prove to be fatal. Our district-level modelling approach allows to disentangle spatial variation into a global pattern for Germany, district-specific long-term effects and short-term dynamics, taking the demographic composition of the local population into account. Joint work with Marc Schneble, Giacomo De Nicola & Ursula Berger The second applications combines nowcasting with forecasting of infection numbers. This leads to a fore-nowcast, which is motivated methodologically. The method is suitable for all data which are reported with delay and we demonstrate the usability on COVID-19 infections.

### 07.12.2020 16:00 Pieter Trapman (Universität Stockholm):Herd immunity, population structure and the second wave of an epidemic(using zoom) (Parkring 11, 85748 Garching-Hochbrück)

The classical herd-immunity level is defined as the fraction of a population that has to be immune to an infectious disease in order for a large outbreak of the disease to be impossible, assuming (often implicitly) that the immunized people are a uniform subset of the population.I will discuss the impact on herd immunity if the immunity is obtained through an outbreak of an infectious disease in a heterogeneous population. The leading example is a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemic outbreaks or waves in the same population structured by a random network. Individuals infected during the first outbreak are (partially) immune for the second one. The first outbreak is analysed through a bond percolation model, while the second wave is approximated by a three-type branching process in which the types of individuals depend on their position in the percolation clusters used for the first outbreak. This branching process approximation enables us to calculate a threshold parameter and the probability the second outbreak is large. This work is based on joined work with Tom Britton and Frank Ball and on ongoing work with Frank Ball, Abid Ali Lashari and David Sirl.

TBA