Mathematisches Institutskolloquium

Das Mathematische Institutskolloquium richtet sich an ein breites mathematisches Publikum (mit Bachelor Abschluss in Mathematik). Es soll die Diskussionen über die mathematischen Spezialisierungen der verschiedenen Arbeitsgruppen am Institut fördern. Außerdem sollen auch Studierende (Master-Studierende und fortgeschrittene Bachelor-Studierende) durch das Kolloquium die Gelegenheit erhalten sich über aktuelle Themen der Mathematik zu informieren.

Wintersemester 2021/2022

  • Prof. Constantinos Siettos (University of Naples Federico II, Italy)
    "Numerical Solution of Nonlinear PDEs and Stiff Problems of ODEs with Random Projection Networks and Extreme Learning Machines"
    Abstract: We use a class of machine learning the so-called Random Projections Networks and Extreme Learning Machines to numerically solve nonlinear partial differential equations (PDEs) and stiff problems of ODEs. For our demonstrations, we study several benchmark problems, namely (a) the Rober and Van-der Pol ODEs and, (b) the one-dimensional viscous Burgers and, the one- and two-dimensional Bratu PDEs. We also show how one can expolit the proposed methodology to construct bifurcation diagrams past limit points. The numerical efficiency of the proposed numerical machine learning scheme is compared against well established numerical analysis methods such as the adaptive Runge-Kutta ode45 and the ode15s a variable-step, variable-order solver based on the numerical differentiation formulas for solving the ODEs and central finite differences (FD) and Finite-element (FEM) methods for solving PDEs. We show that the proposed machine learning framework, regarding the solution of ODEs yields good numerical approximation accuracy without being affected by the stiffness, thus outperforming in same cases the ode45 and ode15s integrators, while regarding the solution of PDEs outperforms FD and importantly FEM for medium to large sized grids in terms of computational times and numerical accuracy.
    13.10.2021, 15:15 UhrOnline-Veranstaltung

Sommersemester 2021

  • Dr. Paolo Di Tella (University of Rostock)
    "On Martingale Representation Theorems"
    Abstract:  A central result in Stochastic Analysis is the martingale representation theorem of the Brownian motion. In this talk we are going to present classical result and extensions of the Brownian martingale representation theorem in more general contexts. We shall then present some applications to mathematical finance.
    14.07.2021, 15:15 Uhr, Online-Veranstaltung
  • Prof. Kim Knudsen (Technical University of Denmark)
    "Electromagnetic imaging – mathematical analysis and computations"
    Abstract:
    In this talk we will look at inverse problems related to electromagnetic imaging. One example is Electrical Impedance Tomography (EIT), mathematically known as the Calderón problem, where the goal is to identify a body’s interior electrical conductivity distribution from measurements of voltages and currents on the surface of the body. This problem is severely ill-posed and requires heavy regularization techniques to be implemented before allowing for image reconstruction even with low resolution and contrast.
    Recently, novel hybrid imaging methods such as Acousto-Electric Tomography and Magnetic Resonance EIT have appeared. These approaches exploit different coupled physical phenomena and therefore hold promise for much more accurate and stable methods than EIT.
    From a mathematical analysis and computational perspective we consider the three different examples; we will formulate the relevant models, pose fundamental questions and give (partial) answers.
    16.06.2021, 15:15 Uhr, Online-Veranstaltung

Sommersemester 2020

  • Prof. Dr. Bernd Sturmfels (Direktor am Max-Planck-Institut für Mathematik in den Naturwissenschaften Leipzig; Professor University of California at Berkeley)
    "3264 Conics in a Second"
    Abstract: Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This lecture illustrates how these two fields complement each other, especially in the light of emerging new applications. We start with a gem from19th century geometry, namely the 3264 conics that are tangent to five given conics in the plane. This topic was featured in the January 2020 issue of the Notices of the American Mathematical Society.  We conclude with an application in statistics, namely maximum likelihood estimation for linear Gaussian covariance models.
    17.06.2020, 15:00 Uhr, Online-Veranstaltung
  • Prof. Dr. Bernold Fiedler (FU Berlin)
    "Good to be late, precisely"
    Abstract
    13.05.2020, 15:15 - 16:15 Uhr, Online-Veranstaltung
  • Prof. Dr. Armin Iske (Universität Hamburg)
    "Kernel-based approximation methods for data analysis and machine learning"
    Abstract
    15.04.2020, 15:00 - 16:00 Uhr, Online-Veranstaltung

Wintersemester 2019/2020

  • Prof. Dr. Reinhard Racke (Universität Konstanz)
    "Exponentielle Stabilität für thermoelastische Systeme — die Multiplikatormethode"
    Abstract: Anhand der Wärmeleitungsgleichung bzw. der gedämpften Wellengleichung  wird die Energie- bzw. Multiplikatormethode bei Evolutionsgleichungen vorgestellt, ebenso ein Zusammenhang zur Fourierreihenentwicklung bzw. zur Fouriertransformation, letzteres am Beispiel thermoelastischer Platten. Numerische Resultate unterstreichen die analytisch erhaltenen Abschätzungen.
    13.11.2019, 15:15 Uhr, HS 326/327 (Ulmenstr. 69, Haus 3)
  • Prof. Dr. Markus Reiß (HU Berlin)
    "Statistics for stochastic PDEs"
    Abstract: For a broader audience we shall introduce to basic stochastic ordinary and partial differential equations (SODEs/SPDEs) and consider statistical estimation of the coefficients in these equations. We shall encounter a fundamental difference for drift estimation  for SODEs/SPDEs. Then we consider the specific problem of estimating the space-dependent diffusivity of a stochastic heat equation from time-continuous observations with space resolution h. This will be achieved by a localised Maximum-Likelihood approach. The rather counterintuitive convergence result and its efficiency as h -> 0 will be discussed in detail. (joint work with Randolf Altmeyer, Berlin)
    16.10.2019, 15:15 Uhr, HS 326/327  (Ulmenstraße 69, Haus 3)