Livio Ferretti (UNIGE)
Framed mapping class groups and the monodromy of positive braids abstract
Abstract:
A framing on an orientable surface with boundary is given by a nowhere vanishing vector field (considered up to isotopy). The mapping class group naturally acts on such framings, and the stabilizer of a framing is called a framed mapping class group. Framed mapping class groups arise naturally in a variety of geometric settings, but their algebraic structure is to date very poorly understood. In this talk, we will introduce the basic theory of framed mapping class groups and see how they can be used to study monodromy groups of positive braids (and plane curve singularities). If time permits, we will end discussing applications of similar ideas to the study of more general fibred links.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Dr. Alberto Merici (University of Milan)
Log prismatic cohomology, motivic spectra and comparison theorems abstract
Abstract:
We prove that (logarithmic, Nygaard completed) prismatic and (logarithmic) syntomic cohomologies are representable in the category of logarithmic motives. As an application, we immediately obtain Gysin maps for prismatic and syntomic cohomologies, and we precisely identify their cofibers. In the second part of the talk we develop a descent technique that we call saturated descent, inspired by the work of Niziol on log K-theory. Using this, we prove crystalline comparison theorems for log prismatic cohomology, log Segal conjectures and log analogues of the Breuil-Kisin prismatic cohomology, from which we get Gysin maps for the A_{inf} cohomology.
13:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Gerhard Wanner (UNIGE)
Origin of the Fourier Series
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Prof. Dr. Yi Zhang (Academy of Mathematics and System Science, Beijing)
John domains in variational problems abstract
Abstract:
The notion of a John domain was initially introduced in 1961 by Fritz John, and later named after him by Martio and Sarvas. Typically, its study is motivated by its connections to the properties of quasiconformal and quasisymmetric mappings. Moreover, John domains find extensive applications in the theory of Sobolev functions in metric measure spaces and functional analysis, as they represent essentially the sole class of domains that uphold the Sobolev-Poincaré inequality. In this presentation, I will introduce several recent applications of John domains in the theory of the calculus of variations.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Andrey Krutov (Prague)
Clifford algebra analogue of the Cartan theorem abstract
Abstract:
et $\\mathfrak{g}$ be a complex simple Lie algebra. The Hopf-Koszul-Samelson theorem asserts that the algebra of $\\mathfrak{g}$-invariants in the exterior algebra of $\\mathfrak{g}$ is the exterior algebra over the space of primitive invariants $P$. Kostant proved the analogous result for the Clifford algebra of $\\mathfrak{g}$. Namely, the algebra of $\\mathfrak{g}$-invariants in $Cl(\\mathfrak{g})$ is the Clifford algebra over the space of primitive invariants. Let $\\mathfrak{k}$ be a symmetric subalgebra of $\\mathfrak{g}$ and $\\mathfrak{p}$ be the corresponding isotropy representation. The Cartan theorem states that the algebra of $\\mathfrak{k}$-invariants in theexterior algebra of $\\mathfrak{p}$ is isomorphic to the tensor product of the exterior algebra of the Samelson subspace of $P$, corresponding to the pair $(\\mathfrak{g},\\mathfrak{k})$, and a certain commutative algebra $A$. We prove a Clifford algebra analogue of the Cartan theorem. Namely, we show that the algebra of $\\mathfrak{k}$-invariants in $Cl(\\mathfrak{p})$ is the tensor product of the Clifford algebra over the space of primitive invariant of $\\mathfrak{p}$ with a certain filtered deformation of $A$.
15:30 • Université de Genève, Conseil Général 7-9, Room 1-07
Konstantin Andritsch (ETHZ)
What is... an adelic torus orbit?
16:30 • UZH Zentrum, Building KO2, Room F 150