# Gjesteforelesninger, seminarer og konferanser

## Kommende

Welcome to the SECOND conference on Stochastics of Environmental and Financial Economics. The conference will bring together leading researchers in the fields of stochastic analysis and finance to discuss recent developments and challenges with an edge towards energy, environmental and financial markets.

The conference is also a celebration of professor Bernt Øksendal's 70th anniversary. On Thursday April 23 the program of the conference will mark this big event with a selected list of speakers.

The conference is organized by the Center of Advanced Studies (CAS), Stochastics of Environmental and Financial Economics. Scientific organizers: Fred Espen Benth and Giulia Di Nunno (UiO)

Please note that participation is by invitation only.

## Tidligere

John Christian Ottem, Cambridge University, gives the Seminar in Algebra and Algebraic Geometry:

Abelian varieties XIV: Hodge-formodningen for abelske varieteter.

Arne B. Sletsjøe, UiO, gives the Seminar in Algebra and Algebraic Geometry:

Projektive grenser av spline systemer

Arne B. Sletsjøe, UiO, gives the Seminar in Algebra and Algebraic Geometry:

Abelian varieties XIII

Christian Voigt (Glasgow) will give a talk with title: The structure of quantum permutation groups

Abstract: Quantum permutation groups, introduced by Wang, are a quantum analogue of permutation groups. These quantum groups have a surprisingly rich structure, and they appear naturally in a variety of contexts, including combinatorics, operator algebras, and free probability. In this talk I will give an introduction to these quantum groups, and review some results on their structure. I will then present a computation of the K-groups of the C*-algebras associated with quantum permutation groups, relying on methods from the Baum-Connes conjecture.

Adaptive finite elements: practice and implementation

Alfons van Daele, University of Leuven (Belgium), will give a talk with title: Separability idempotents and quantum groupoids

Andrea Riebler ( Dept. of math., NTNU) gives a seminar in room 107, 1st floor N.H. Abels House at 15:15 December 2nd: Projecting the future burden of cancer: Bayesian APC analysis made simple.

Modular forms are certain complex-analytic functions on the upper-half plane. They can also be interpreted as giving linear-algebraic invariants of elliptic curves, perhaps equipped with some extra structure, and in this way they reveal their algebraic-geometric nature. One of the most fundamental modular forms is the Dedekind eta function. However, it seems that only recently has it been pinned down precisely what extra structure on an elliptic curve is needed to define eta. Namely, Deligne was able to express this extra structure in terms of the 2- and 3-power torsion of the elliptic curve. Deligne's proof, apparently, is computational. In this talk I'll describe a conjectural reinterpretation of Deligne's result, together with some supporting results and a hint at a possible conceptual proof. The reinterpretation is homotopy theoretic, the key being to think of an elliptic curve as giving a class in framed cobordism. This directly connects the number "24" which often appears in the study of eta to the 3rd stable stem in topology.

Johannes Kleppe, Høgskolen i Buskerud og Vestfold, gives the Seminar in Algebra and Algebraic Geometry:

Abelian varieties XII

I will discuss joint work in progress with David Gepner, computing the ring of endomorphisms of the equivariant motivic sphere spectrum, for a finite group. The result is a combination of the endomorphism ring of the equivariant topological sphere spectrum (which equals the Burnside ring by a result of Segal) and that of the motivic sphere spectrum (which equals the Grothendieck-Witt ring of quadratic forms by a result of Morel). This computation is a corollary of a tom Dieck style splitting for certain equivariant motivic homotopy groups.

Martijn Caspers (Münster) will give a talk with title: The Haagerup property for arbitrary von Neumann algebras

Abstract: The Haagerup property is an approximation property for both groups and operator algebras that has important applications in for example the Baum-Connes conjecture or von Neumann algebra theory. In this talk we show that the Haagerup property is an intrinsic invariant of an arbitrary von Neumann algebra. We also discuss stability properties of the Haagerup property under constructions as free products, graph products and crossed products. Finally we discuss alternative characterizations in terms of the existence of suitable quadratic forms.

Jan Fredrik Bjørnstad (Statistics Norway and Dept. of Math.,UiO) gives a seminar in room 107, 1st floor N.H. Abels House at 14:15 November 18th: Survey sampling the way I see it.

This is a work we had done jointly with Garkusha (after Voevodsky) arXiv:1409.4372. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety X in Sm/k, the framed motive M_fr(X) is associated in that category . Also, for any smooth scheme X in Sm/k an explicit quasi-fibrant motivic replacement of its suspension P1-spectrum is given. Moreover, it is shown that the bispectrum (M_fr(X),M_fr(X)(1),M_fr(X)(2), ... ), each term of which is a twisted framed motive of X, has motivic homotopy type of the suspension bispectrum of X. We also construct a compactly generated triangulated category of framed bispectra SH_fr(k) and show that it reconstructs the Morel-Voevodsky category SH(k). As a topological application, it is proved that the framed motive M_fr(pt)(pt) of the point pt = Speck evaluated at pt is a quasi-fibrant model of the classical sphere spectrum whenever the base field k is algebraically closed of characteristic zero.

The goal of this talk is to present some recent computations of the Picard groups of several spectra of topological modular forms. The first part of the talk will introduce the toolbox, which consists of descent theory and a technical lemma allowing us to compare stable and unstable information in spectral sequences. This is joint work with Akhil Mathew.

Finite Element Exterior Calculus and Applications

George Hitching, Høgskolen i Oslo og Akershus, gives the Seminar in Algebra and Algebraic Geometry:

Abelian varieties XI

Weak approximation of stochastic differential equations by a multilevel Monte Carlo method using mean square adaptive numerical integration

Tore Selland Kleppe (University of Stavanger) gives a seminar in room 107, 1st floor N.H. Abels House at 14:15 November 11th: Bandwidth Selection In Pre-Smoothed Particle Filters