Simone Ramello (Università di Torino): Étale methods in the model theory of fields
Thursday, 06.05.2021 10:30 im Raum via Zoom
Introduced by Johnson, Tran, Walsberg and Ye, the so-called étale-open topology effectively acts as a dictionary between the topological and the algebraic worlds; in particular, algebraic properties of a field an be characterized as topological properties of the étale-open topology on the affine line, and moreover the étale-open topology turns out to be the "usual suspects" when considered over certain classes of fields -- the Zariski topology on separably closed fields, the order topology on real closed fields... The étale-open topology also allows to characterize large fields, as introduced by Pop in 1996, precisely as the class of fields over which it is not the discrete topology. This allows to turn a statement like the stable fields conjecture into an almost purely topological question, at least in the large case, and eventually leads to proving the conjecture in this scenario.
Abstract: In a first part, we will discuss large deviation phenomena and existence of large deviation principle for the displacement of random walks on hyperbolic spaces after having introduced related notions from probability theory. In a second part, we will focus on finite time bounds and concentrations for deviations of the displacement off the drift and mention an application to finite-time probabilistic Tits? alternative. Based on joint works with Adrien Boulanger, Pierre Mathieu and Alessandro Sisto (part one above), and with Richard Aoun (part two above).
In this seminar I will review the theory of flat G-chains, as they were introduced by H. W. Fleming in 1966, and currents with coefficients in groups. One of the most recent development of the theory concerns its application to the Steiner tree problem and other minimal network problems which are related with a Eulerian formulation of the branched optimal transport. Starting from a 2016 paper by A. Marchese and myself, I will show how these problems are equivalent to a mass-minimization problem in the framework of currents with coefficients in a (suitably chosen) normed group.
Ringvorlesung 2021: Anna Siffert: Verzerrungen des Weltbildes
Wednesday, 05.05.2021 16:15 im Raum zoom
Unter Verwendung von Methoden aus der Differentialgeometrie*,
werden ein paar unterschiedlichen Kartenprojektionen der Erde diskutiert und aufgezeigt, wie man diese als Manipulationsmittel einsetzen kann.
(*Die Differentialgeometrie ist ein mathematisches Forschungsgebiet,
in dem geometrische Eigenschaften von Kurven, Flächen und deren höherdimensionalen Verallgemeinerungen studiert werden. Es werden keine Kenntnisse der Differentialgeometrie vorausgesetzt. )
Angelegt am Monday, 03.05.2021 10:57 von elke
Geändert am Monday, 03.05.2021 11:44 von elke
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Confusingly for the uninitiated, experts in weak infinite-dimensional
category theory make use of different definitions of an ∞-category, and
theorems in the ∞-categorical literature are often proven "analytically",
in reference to the combinatorial specifications of a particular model. In
this talk, we present a new point of view on the foundations of ∞-category
theory, which allows us to develop the basic theory of ∞-categories ---
adjunctions, limits and colimits, co/cartesian fibrations, and pointwise
Kan extensions --- "synthetically" starting from axioms that describe an ∞-
*cosmos*, the infinite-dimensional category in which ∞-categories live as
objects. We demonstrate that the theorems proven in this manner are
"model-independent", i.e., invariant under change of model. Moreover, there
is a formal language with the feature that any statement about ∞-categories
that is expressible in that language is also invariant under change of
model, regardless of whether it is proven through synthetic or analytic
techniques. This is joint work with Dominic Verity.
We analyze the Gamma-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove compactness with respect to Gamma-convergence and represent the Gamma-limit in an integral form defined on the space of generalized special functions of bounded deformation (GSBD^p). We identify the integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions. In particular, our techniques allow to characterize relaxations of functionals on GSBD^p, and cover the classical case of periodic homogenization. Joint work with Matteo Perugini and Francesco Solombrino.
The Witten deformation on a smooth compact manifold is an analytic proof of the Morse
inequalities, which has been proposed by Witten in the 80s and is inspired from ideas in quantum
field theory. The Witten deformation is one of the main actors in the extension by Bismut and Zhang
of the comparison between analytic and topological torsion of a smooth compact manifold, aka the
The aim of this talk is to explain how to extend the Witten deformation to singular spaces with
conical singularities and radial Morse functions, and how this can be used to achieve a Cheeger-Müller
theorem for these spaces.