Title: q-bic Hypersurfaces
Friday, 2.12.22, 10:00-11:00, Hörsaal II, Albertstr. 23b
Let’s count: 1, 2, q+1. The eponymous objects are special projective hypersurfaces of degree q+1, where q is a power of the positive ground field characteristic. This talk will sketch an analogy between the geometry of q-bic hypersurfaces and that of quadric and cubic hypersurfaces. For instance, the moduli spaces of linear spaces in q-bics are smooth and themselves have rich geometry. In the case of q-bic threefolds, I will describe an analogue of result of Clemens and Griffiths, which relates the intermediate Jacobian of the q-bic with the Albanese of its surface of lines.
Diracoperatoren mit magnetischer Verschlingung
Monday, 5.12.22, 16:15-17:15, Hörsaal II, Albertstr. 23b
In der Quantenmechanik beschreibt der Aharonov-Bohm-Effekt, welche Auswirkungen ein magnetisches Vektorpotential auf interferierende Elektronenstrahlen hat, die sich außerhalb eines Magnetfeldes befinden. Bei der Verallgemeinerung diese Effekts gehen wir nun von Magnetfeldern in \( \bmathbb{S}^3 \) aus, die auf glatten, geschlossenen Kurven getragen sind. Der Vortrag befasst sich mit Dirac-Operatoren, die das Vektorpotential eines solchen Magnetfeldes beinhalten. Die Selbstadjungiertheit dieser Operatoren ist zu Anfang nur bei der Wahl einer Domain ersichtlich, die sich nicht in der Nähe des Magnetfeldes befindet. Es soll nun darum gehen, selbstadjungierte Erweiterungen zu finden, die das Verhalten nahe des Feldes beschreibt.
TBA
Tuesday, 6.12.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
TBA
Zero Temperature Surface Growth and Some Strange Fully Nonlinear Equations
Tuesday, 6.12.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
I will describe recent work on scaling limits of zero temperature (deterministic) surface growth models, motivated by KPZ universality and related to gradient \bphi interface models. Chatterjee (2021) and Chatterjee and Souganidis (2021) showed that a smooth choice of the dynamics leads to the deterministic KPZ equation. I will describe a class of examples with non-smooth dynamics, which, at large scales, are described by fully nonlinear parabolic equations with discontinuous coefficients. Joint work with P.E. Souganidis.\n
Ramsey Theory and a New Forcing Order
Tuesday, 6.12.22, 14:30-15:30, Raum 318, Ernst-Zermelo-Str. 1
We use parametrized localized Ramsey spaces to\ndefine a new kind of forcing orders. There will be a generalized\ntype of fusion sequence for showing that the forcings preserve\n\(\baleph_1\).\n
Bloch's formula with modulus
Friday, 9.12.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
The general idea of the talk will be to show connections between various invariants of a smooth variety. We shall begin the talk by recalling Bloch's formula for smooth varieties and unramified class field theory over finite fields. After discussing ramified class field theory, we shall explain the meaning of Bloch's formula with modulus. We shall then discuss the main idea of the proof of Bloch's formula with modulus over finite fields. The talk will be based on joint works with Prof. Amalendu Krishna.
What works best? Methods for ranking competing treatments
Friday, 9.12.22, 12:00-13:00, online: Zoom
Systematic reviews often compare multiple interventions simultaneously. Data from such reviews form networks of interventions and are synthesized through network meta-analysis, a technique which is used to combine evidence coming from all possible paths within the network. The main output of network meta-analysis is the set of all relative effects between competing treatments. A treatment hierarchy is also often of interest and several ranking metrics exist. In this talk I will describe available methods for ranking treatments and a method we developed in order to attach ranking to a clinically relevant decision question. Our approach is a stepwise approach to express clinically relevant decision questions as hierarchy questions and quantify the uncertainty of the criteria that constitute them. I will demonstrate the approach using the R package nmarank, available in CRAN.
Hands on the Algebraic Index Theorem
Monday, 12.12.22, 16:15-17:15, Hörsaal II, Albertstr. 23b
In my talk I want to give a summary of results from Fedosov/Tsygan/Nest on the so-called algebraic index theorem, which links symplectic deformation quantizations to topological invariants and reproduces the Atiyah-Singer Index Theorem for the canonical quantization of cotangent bundles. The talk includes a gentle introduction to deformation quantization.
Non-Newtonian fluids with discontinuous-in-time stress tensor.
Tuesday, 13.12.22, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically \((s-1)\)-growth with the parameter \(s\) depending on the spatial and time variable. We do not assume any smoothness of \(s\) with respect to time variable and assume the log-H\b"{o}lder continuity with respect to spatial variable. Such a setting is a natural choice if the material properties are instantaneous, e.g. changed by the switched electric field. We establish the long time and the large data existence of weak solution provided that \(s \bge \bfrac{3d+2}{d+2}\).
Non-local effects and degenerate Cahn-Hilliard equation
Tuesday, 13.12.22, 15:00-16:00, Raum 226, Hermann-Herder-Str. 10
I will discuss several situations when one has to perform\nlimit passage from non-local to local operators in the context of the\ndegenerate Cahn-Hilliard equation. This includes kinetic derivation of\nthe equation (arXiv:2208.01026, with C. Elbar, M. Mason, B. Perthame),\nfairly classical problem of passage to the limit from non-local to\nlocal equation (arXiv:2208.08955, with C. Elbar) and the same problem\nfor aggregation-diffusion system (in progress, together with J. A.\nCarrillo, C. Elbar). Not all of these problems are fully understood and\nto some of them, solutions are available only on the torus.
tba
Monday, 19.12.22, 16:00-17:00, Hörsaal II, Albertstr. 23b
ODD Riemannian metrics
Monday, 19.12.22, 16:15-17:15, Hörsaal II, Albertstr. 23b