## Visiting address

Ullevål StadionSognsveien 77B

0855 OSLO

Norway

Time and place:
Mar. 7, 2018 11:15 AM - 12:00 PM,
Seminar room "End of the Line"

Time and place:
Mar. 7, 2018 10:15 AM - 12:00 PM,
Desolation Row, Sognsveien 77 B

Time and place:
Mar. 6, 2018 10:15 AM - 12:00 PM,
End of the Line, Sognsveien 77B

Recently two different refinements of Voevodsky's theory of presheaves with transfers were introduced: the first one is the theory of framed presheaves based on the unpublished notes by Voevodsky and developed by Garkusha and Panin and the second one is the theory of Milnor-Witt presheaves due to Calmes and Fasel. I will review some relations between these theories and explain that the hearts of the homotopy t-structures on the corresponding categories of motives are naturally equivalent. The talk is based on a joint work with A. Neshitov.

Time and place:
Mar. 6, 2018 8:45 AM - 9:15 AM,
Gates of Eden

Emanuela Rosazza (University of Milano Bicocca) gives a lecture with a title: Time-consistency of risk measures: how strong is such a property?

Time and place:
Mar. 6, 2018 8:30 AM - 5:30 PM,
Gates of Eden

Stochastic Analysis PhD students and Post Docs will be sharing their current projects. Professors and Supervisors are all invited to attend the event.

Time and place:
Mar. 2, 2018 10:00 AM - 11:30 AM,
Ullevål Stadion: Desolation Row

Shiqi Song (University of Evry Val d'Esssone, France) will give a minicourse with the title: Topics on defaultable market and on default valuation

Time and place:
Mar. 1, 2018 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77B

**Abstract:**

The Hodge conjecture is a major unsolved problem in mathematics which forms a subtle bridge between algebraic geometry, differential geometry and topology. Formulated by Hodge in his 1950 ICM address, it asks for a characterisation of the subvarieties of a projective variety in terms of the topology of that variety. Today the conjecture remains widely open, and it is one of the seven `Millenium problems' for which the Clay Institute offers a prize of one million dollars. In this talk I will give an basic introduction to the circle of ideas around the conjecture, focusing on specific examples, pictures and important special cases.

NB! Coffee/Tea/Biscuits from 14.00.

Time and place:
Mar. 1, 2018 10:15 AM - 11:00 AM,
Gates of Eden

Shiqi Song (University Evry Val Essonne) gives the lecture with a title: Multi-dimensional BSDEs whose terminal values are bounded and have bounded Malliavin derivatives

Time and place:
Mar. 1, 2018 9:30 AM - 10:15 AM,
Ullevål Stadion: Gates of Eden

Time and place:
Feb. 28, 2018 2:15 PM - 4:00 PM,
Desolation Row Sognsveien 77B

In this third talk we will define Legendrian contact homology for Legendrian submanifolds in the 1-jet space of a smooth manifold M. Again, this will be the homology of a DGA generated by the double points of the Legendrian under the Lagrangian projection. The differential is defined by a count of punctured pseudo-holomorphic disks in the cotangent bundle of M, with boundary on the projected Legendrian. To prove that this indeed gives a differential we will use the theory of Fredholm operators from functional analysis. I will also say something about Floer theories in general. In particular, one of the main difficulties when defining Floer theories via pseudo-holomorphic curve techniques is to achieve transversality for the dbar-operator. There has been a development of several different machineries to solve these problems, for examle Polyfolds by Hofer et al., and Pardon's work on Virtual fundamental cycles. In our case, however, it is enough to perturb either the Legendrian submanifold or the almost complex structure.

Time and place:
Feb. 28, 2018 10:15 AM - 12:00 PM,
Desolation Row Sognsveien 77B

Time and place:
Feb. 28, 2018 9:30 AM - 11:00 AM,
Ullevål Stadion: End of the Line

Time and place:
Feb. 27, 2018 1:15 PM,
Ullevål Stadion: Gates of Eden

M.Sc. Lisa Smith ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:

**Experiments of Breaking Waves in Pipes and Flumes**

Time and place:
Feb. 27, 2018 10:15 AM,
Ullevål Stadion: Gates of Eden

M.Sc. Lisa Smith ved Matematisk institutt avholder prøveforelesning over oppgitt emne: "Recent advances in medical imaging".

Time and place:
Feb. 27, 2018 9:30 AM - 11:00 AM,
Ullevål Stadion: Hurricane

Time and place:
Feb. 21, 2018 2:15 PM - 4:00 PM,
Desolation Row, Sognsveien 77B

I will review Marcel Bökstedt's calculation of the topological Hochschild homology of prime fields and the integers, taking into account simplifications made in papers by Angeltveit-R. (where BP<m-1> specializes to HFp for m=0 and to HZ(p) for m=1) and Ausoni (proof of Lemma 5.3).

Time and place:
Feb. 21, 2018 11:15 AM - 12:00 PM,
Seminar room "End of the Line"

**Speaker:** Giuseppe Coclite (University of Bari)

**Title:** Nonlinear Peridynamic Models

**Abstract:** Some materials may naturally form discontinuities such as cracks as a result of scale effects and long range interactions. Peridynamic models such behavior introducing a new nonlocal framework for the basic equations of continuum mechanics. In this lecture we consider a nonlinear peridynamic model and discuss its well-posedness in suitable fractional Sobolev spaces. Those results were obtained in collaboration with S. Dipierro (Milano), F. Maddalena (Bari) and E. Valdinoci (Milano).

Time and place:
Feb. 21, 2018 10:15 AM - 12:00 PM,
Desolation Row Sognsveien 77 B

Inspired by the Voevodsky machinery of standard triples a machinery of nice triples was invented in [PSV]. We develop further the latter machiny such that it works also in the finite field case [P]. This machinary is a tool to prove many interesting moving lemmas. It leads to a serios of applications. One of them is a proof of the Grothendieck--Serre conjecture in the finite field case. Another is a proof of Gersten type results for arbitrary cohomology theories on algebraic varieties. The Gersen type results allows to conclude the following: a presheaf of S1-spectra E on the category of k-smooth schemes is A1-local iff all its Nisnevich sheaves of stable A1-homotopy groups are strictly homotopy invariant. If the field k is infinite, then the latter result is due to Morel [M]. An example of moving lemma is this. Let X be a k-smooth quasi-projective irreducible k-variety, Z be its closed subset and x be a finite subset of closed points in X. Then there exists a Zariski open U containing x and a naive A1-homotopy between the motivic space morphism U--> X--> X/U and the morphism U--> X/U sending U to the distinguished point of X/U. Application: suppose E is a cohomology theory on k-smooth varieties and alpha is an E-cohomology class on X which vanishes on the complement of Z, then it vanishes on U from the lemma above.

Time and place:
Feb. 14, 2018 3:15 PM - 4:00 PM,
End of the line, Ullevål Stadion

Soft and Wet is Different

Time and place:
Feb. 14, 2018 2:15 PM - 4:00 PM,
Desolation Row Sognsveien 77B

In this second talk, I will define Chekanov's version of Legendrian contact homology (LCH) for Legendrian knots in R3. I will begin with an example, showing that LCH is more sensitive than the classical invariants. This will use a linearized version of the homology. In the second part of the talk I will focus on the proof that the differential indeed squares to zero, and also say something about invariance under Legendrian Reidemeister moves. This is intended to be a smooth introduction to the next talk, where we will consider Legendrian contact homology defined for Legendrians in arbitrary 1-jet spaces. This case is more delicate, and we have to understand the concept of Gromov compactness for pseudo-holomorphic curves to prove that we get a differential graded algebra associated to each Legendrian, whose homology will give a Legendrian invariant.

Time and place:
Feb. 14, 2018 10:15 AM - 12:00 PM,
Desolation Row Sognsveien 77B

Let G be a finite (abstract) group and let k be a field of characteristic zero. We prove that for a non-singular projective G-variety X over k, and a non-singular G-invariant subvariety Y of dimension >= 3, which is a scheme-theoretic complete intersection in X, the pullback map PicG(X) -> PicG(Y) is an isomorphism. This is an equivariant analog of the Grothendieck-Lefschetz theorem for Picard groups.

Time and place:
Feb. 7, 2018 2:15 PM - 4:00 PM,
Desolation Row Sognsveien 77B

A Cartan-Eilenberg system is an algebraic structure introduced as a model of the diagram obtained by taking the homology of all subquotients in a filtered chain complex. There are two exact couples and a single spectral sequence associated with such a system, and one may thus apply Boardman's theory of convergence to either exact couple. After reviewing parts of this theory, I will clarify the convergence situation in a Cartan-Eilenberg system and in particular present new work on a simpler interpretation of Boardman's whole plane obstruction group.

Time and place:
Feb. 6, 2018 11:00 AM - 12:00 PM,
Gates of Eden

Zahra Afsar (University of Wollongong, Australia) will give a talk with title: Nica-Toeplitz-algebras of *-commuting local homeomorphisms and equilibrium states

Abstract: Given a family of *-commuting local homeomorphisms on a compact space, we can build a compactly aligned product system of Hilbert bimodules. The product system has a Nica-Toeplitz algebra which carries a gauge action of a higher-dimensional torus, and there are many possible dynamics obtained by composing with different embeddings of the real line in this torus. In this work, which is a joint work with Prof. Astrid an Huef and Prof. Iain Raeburn, I will talk about the equilibrium states of these dynamics. If time allows, I will also provide some examples from higher rank graph theory and reconcile our results with those existing ones.

Time and place:
Feb. 1, 2018 2:30 PM - 3:30 PM,
Gates of Eden, Sognsv. 77B

**Abstract:**

If X is a compact metric space, then a measure on X is a linear, bounded and positive operator on the space of continuous functions on X. If f:X->Y is a continuous map between compact metric spaces, then by tautology we can pushforward any measure on X. Can we pullback a measure? No answer had been found in the literature.

In this talk I will explain why we cannot pullback a measure to a measure in general, even in the case where f is an isomorphism over a dense open subset of Y. On the other hand, I will show that if f is a finite covering over a dense open subset of Y, then we can pullback any measure on Y to a more general class of so-called positive strong submeasures. This is then applied to dynamics of meromorphic maps of compact Kahler manifolds. This general class of strong submeasures can also be used in the problem of intersection of hypersurfaces.

NB! Coffee/Tea/Biscuits from 14.00.