Münchner Mathematische KalenderKalender mit mathematischen Vorträgen im Raum München2017-10-17T07:48:46Ztag:mathcal.ma.tum.de,2013-04-10:/feed/filter2/year2017/month1017.10.2017 14:15 Prof. Steffen Lauritzen (Humboldt Awardee; University of Copenhagen): Maximum likelihood estimation in Gaussian models under total positivity2017-10-09T05:22:21ZProf. Steffen Lauritzen (Humboldt Awardee; University of Copenhagen)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171005111854The problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2) is investigated. The maximum likelihood estimator (MLE) for such distributions exists based on just two observations, irrespective of the underlying dimension. It is further demonstrated that the MTP2 constraint serves as an implicit regularizer and leads to sparsity in the estimated inverse covariance matrix, determining what we name the ML graph. We show that the maximum weight spanning forest (MWSF) of the empirical correlation matrix is a spanning forest of the ML graph. In addition, we show that we can find an upper bound for the ML graph by adding edges to the MSWF corresponding to correlations in excess of those explained by the forest. We provide globally convergent coordinate descent algorithms for calculating the MLE under the MTP2 constraint which are structurally similar to iterative proportional scaling.
The lecture is based on recent joint work with Caroline Uhler and Piotr Zwiernik.
19.10.2017 16:30 Aiso Heinze: Mathematische Lernvoraussetzungen für MINT-Studiengänge - Eine Delphi-Studie mit Hochschullehrenden2017-10-17T07:47:02ZAiso Heinzetag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171017094447 In MINT-Studiengängen stellen insbesondere die Mathematikveranstaltungen große Hürden für Erstsemesterstudierende dar. Trotz hoher Studienabbruchquoten gibt es von Hochschulseite keine einheitlichen Vorgaben, welche mathematischen Lernvoraussetzungen für den Einstieg in MINT-Studiengänge als notwendig angesehen werden. Auch zeigen die Vorkurse der Hochschulen in Deutschland kein homogenes Bild. Erste Ansätze zur Beschreibung erwarteter mathematischer Lernvoraussetzungen bilden Empfehlungen, die von Arbeitsgruppen für einige Studiengänge entwickelt wurden. Im Vortrag wird eine Delphi-Studie vorgestellt, in der knapp 1000 Hochschullehrenden der Mathematik nach den mathematischen Mindestlernvoraussetzungen für einen erfolgreichen Einstieg in MINT-Studiengänge befragt wurden. Dabei wurden 179 mathematische Lernvoraussetzungen identifiziert; für 144 Lernvoraussetzungen lässt sich ein Konsens der befragten Hochschullehrenden uüber MINT-Studiengänge feststellen. Im Vortrag werden exemplarische Ergebnisse vorgestellt und Implikationen für den Uuml;bergang Schule-Hochschule diskutiert.
23.10.2017 12:00 Volkher Scholz (ETH Zürich): Analytic approaches to tensor networks for critical systems and field theories2017-10-16T07:52:32ZVolkher Scholz (ETH Zürich)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171016094609I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically critical systems and conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that the multiscale renormalization Ansatz (MERA) does approximate conformal field theories. In particular, I will discuss the case of free fermions, both on the lattice and in the continuum, as well as Wess-Zumino-Witten models.
based on joint work with Jutho Haegeman, Glen Evenbly, Jordan Cotler (lattice) and Brian Swingle and Michael Walter (lattice & continuum)
23.10.2017 15:00 Cinzia Soresina (CNR IMATI, Mailand, Italien): About predator-prey reaction cross-diffusion systems derived by time scale arguments2017-10-04T07:52:36ZCinzia Soresina (CNR IMATI, Mailand, Italien)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171004094304We consider predator-prey reaction-diffusion systems, incorporating the dynamics of searching and handling predators, together with active and hidden prey. Reaction cross-diffusion systems involving a Holling-type II or a Beddington-DeAngelis functional response are obtained by suitable scaling and asymptotics. The Turing instabilty is then investigated, by characterizing the instability domains of the systems and comparing them to those obtained when cross-diffusion terms are replaced by a standard diffusion.
23.10.2017 16:30 Katja Miller: TBA2017-09-04T08:08:39ZKatja Millertag:mathcal.ma.tum.de,2013-04-10:/talk/created/20170904100749TBA
25.10.2017 13:15 Dr. Ercan Sönmez (Heinrich-Heine-Universität, Düsseldorf): Hausdorff dimension of multivariate operator-self-similar random fields 2017-10-10T07:23:42ZDr. Ercan Sönmez (Heinrich-Heine-Universität, Düsseldorf)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171010092221The notion of Hausdorff dimension has been introduced in order to characterize sets which do possess a fractional pattern, commonly referred to as fractals. A typical feature of fractals is that they exhibit reappearing patterns, i.e. many fine details of the set resemble the whole set, a phenomenon which is called self-similarity. In case of multivariate self-similar random fields self-similarity means that a time-scaling corresponds statistically to a scaling in the state space, where the scaling relation is with respect to suitable matrices. This talk provides the first results on the sample paths and fractal dimensions of such fields, including quite general scaling matrices. A short introduction to the notion of Hausdorff dimension will also be given.
26.10.2017 15:00 Katrin Wendland (Universität Freiburg): From the heat equation to conformal field theory2017-10-02T15:04:07ZKatrin Wendland (Universität Freiburg)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20170719110059The classical Jacobi theta function may be obtained as fundamental solution of the heat equation with certain periodic initial data. Its main properties can be motivated by this approach, and they enter crucially in the applications of Jacobi theta functions in conformal field theory. We use this as a bridge from the heat equation to conformal field theory, in this talk, assuming no background knowledge in these special quantum field theories.
26.10.2017 16:30 Mario Santilli (Max-Planck-Institut, Golm): TBA2017-10-12T11:47:14ZMario Santilli (Max-Planck-Institut, Golm)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/2017071911022426.10.2017 16:30 Nam Phan: On the Thomas-Fermi approximation and Lieb-Thirring inequality (Antrittsvorlesung)2017-10-17T07:48:46ZNam Phantag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171017094726In the Thomas-Fermi theory, the kinetic energy of a many-electron wave function is conveniently expressed in terms of its one-body density functional. This semiclassical approximation goes back to the early days of quantum mechanics and has been used widely in computational physics and chemistry. However, many questions on the validity of the approximation remain open from a mathematical point of view. I will prove that the Thomas-Fermi approximation is a rigorous lower bound for the many-body kinetic energy, up to a gradient term of lower order. This is an improved version of the Lieb-Thirring inequality.
30.10.2017 15:00 Stefania Ottaviano (Universität Trient, Italien): The influence of the population contact network and stochasticity on the epidemics transmission2017-10-09T09:31:29ZStefania Ottaviano (Universität Trient, Italien)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171009112136Networks represent the backbone of many complex systems and they appear for a large variety of real-world systems in ecology,
epidemiology and neuroscience. In particular, there is a close relationship between epidemiology and network theory, since viral
propagation between interacting agents strongly depends on intrinsic characteristics of the population contact network.
With regard to this, in the first part of the talk, we investigate how a particular network structure, can impact on the long-term behavior
of epidemics. Specifically, we consider networks that are partitioned into local communities. The rationale of this approach is that the
epidemic spreads at a different rate within communities with respect to the rate at which it spreads across the communities. We describe the epidemic process as a continuous-time individual-based susceptible–infected–susceptible (SIS) model using a first-order mean-field
approximation. We give conditions in order to decide whether the overall healthy-state defines a globally asymptotically stable or an
unstable equilibrium. Moreover, we show that above the epidemic threshold another steady-state exists, that can be computed using a
lower-dimensional system, in the case of a certain structural regularity of the graph connectivity.
In the second part of the talk, we consider the inclusion of stochasticity, modeling the infection rates in the form of independent
stochastic processes. This allows us to get stochastic differential equations for the probability of infection in each node. We report on
the existence of the solution for all times. Moreover, we show that there exist two regions, given in terms of the coefficients of the
model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent.