The second funding period of the IRTG will start on April 1, 2021.
We are welcoming two new participating researchers in the IRTG in Bielefeld:
We will restructure our research program. In the second funding period, we will have the following research areas.
Participating researchers in Bielefeld: Lars Diening, Sebastian Herr, Moritz Kassmann
Participating researchers in Seoul: Sun-Sig Byun (SNU), Panki Kim (SNU), Soonsik Kwon (KAIST), Ki-Ahm Lee (SNU), Sanghyuk Lee (SNU)
The research on dispersive and integro-differential equations/systems will be continued. One research focus will be the development of the regularity theory of local solutions to nonlinear dispersive equations. For instance, nonlinear Schrödinger and wave equations as well as systems arising in Mathematical Physics will be studied. Harmonic analysis methods are important in this context because solutions are given by oscillatory integrals. Concerning the theory of integro-differential operators, we will also offer research projects on systems such as those from peridynamics. Linear and nonlinear boundary value problems including appropriate function spaces will be studied. Moreover, questions of numerical analysis in this framework will now be considered. The research program develops further the one of the previous research area A.
Participating researchers in Bielefeld: Gernot Akemann, Barbara Gentz, Benjamin Gess
Participating researchers in Seoul: Seung-Yeal Ha (SNU), Nam-Gyu Kang (SNU), Ji Oon Lee (KAIST), Insuk Seo (SNU)
In this research area we consider aspects of dynamical systems such as stability, synchronization and the influence of randomness. Motivated from Physics and machine learning, the following examples of systems shall be analyzed: Open quantum systems and the coupled statistics of eigenvalues and eigenvectors of the Hamiltonian, modeled by non-Hermitian random matrices; Metastability in non-reversible system exhibiting periodic orbits and oscillations as well as noise- induced phenomena in Filippov systems; Methods from stochastic dynamics in machine learning; Stability in infinite dimensional dynamical systems and the influence of randomness, e.g., the effect of stabilization by noise. Common tools in the analysis of such systems are stochastic analysis, spectral theory, potential theory as well as large-deviations theory. However, a finer analysis is intended and will require to go beyond these standard techniques. This research area merges previous areas B and C, where synchronization in the stochastic Kuramoto model (area B) and aspects of many-body and Coulomb systems using random matrices (area C) were studied.
Participating researchers in Bielefeld: Alexander Grigor’yan, Michael Hinz, Michael Röckner
Participating researchers in Seoul: Sun-Sig Byun (SNU), Panki Kim (SNU), Gerald Trutnau (SNU), Ki-Ahm Lee (SNU)
The suggested research program for Research Area III in the second funding period targets problems related to semigroups, Dirichlet forms, partial differential equations, Markov processes and stochastic differential equations. A first compound of projects aims at qualitative features of partial differential equations on Riemannian manifolds and metric spaces and the way these features are governed by the geometry of the respective manifold. A second compound of projects uses Dirichlet forms to study first oder equations and stochastic differential equations on fractal spaces. Continuing former research projects on questions of pointwise regularity within Dirichlet form theory, a third compound of projects is dedicated to stochastic differential equations with singular coefficients and, as a new addition to the portfolio of possible topics, applications of generalized Dirichlet forms to McKean-Vlasov type equations. The research program develops further the one of the previous research area D.
In the second period, the qualification program will be restructured according to the new structure of the research program.