## Besøksadresse

Ullevål StadionSognsveien 77B

0855 OSLO

Tid og sted:
27. feb. 2018 09:30 - 11:00,
Ullevål Stadion: Hurricane

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

**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.

Tid og sted:
18. juni 2018 -
22. juni 2018,
Sophus Lie Conference Center, Nordfjordeid, Norway.

Nordfjordeid Summer school 2018

Tid og sted:
21. feb. 2018 14:15 - 16:00,
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).

Tid og sted:
21. feb. 2018 11:15 - 12:00,
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).

Tid og sted:
21. feb. 2018 10:15 - 12:00,
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.

Tid og sted:
14. feb. 2018 15:15 - 16:00,
End of the line, Ullevål Stadion

Soft and Wet is Different

Tid og sted:
14. feb. 2018 14:15 - 16:00,
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.

Tid og sted:
14. feb. 2018 10:15 - 12:00,
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.

Tid og sted:
7. feb. 2018 14:15 - 16:00,
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.

Tid og sted:
6. feb. 2018 11:00 - 12:00,
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.

Tid og sted:
1. feb. 2018 14:30 - 15:30,
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.

Tid og sted:
31. jan. 2018 14:15 - 16:00,
Desolation Row, Sognsveien 77 B

I will give a series of talks about Legendrian contact homology, an invariant of Legendrian submanifolds in 1-jet spaces, defined by a count of pseudo-holomorphic curves. In this first lecture I will give a brief and gentle introduction to symplectic and contact geometry, with focus on Lagrangian and Legendrian submanifolds. No previous knowledge about the subject is needed, except for elementary knowledge about differentiable manifolds.

Tid og sted:
31. jan. 2018 11:15 - 12:00,
Seminar room "End of the Line" (2nd floor), Sognsveien 77B, Ullevål Stadion

Tid og sted:
24. jan. 2018 11:15 - 12:00,
Seminar room "End of the Line" (2nd floor), Matematisk Institutt, Sognsveien 77B, Ullevål Stadion

Norwegian-Ukrainian Winter School 2018 on Stochastic Analysis, Probability Theory and Related Topics

Tid og sted:
22. jan. 2018 10:30 -
26. jan. 2018 16:00,
Seminar room "Gates of Eden" (2nd floor), Matematisk Institutt, Sognsveien 77B, Ullevål Stadion

The winter school, which takes place in Oslo from 22.-26. January 2018 and which is supported by the Norwegian Centre for International Cooperation in Education in connection with a Norwegian-Ukrainian cooperation in mathematical education, brings together students and researchers from Ukraine (National Technical University of Ukraine, "Igor Sikorski Kyiv Polytechnic Institute", Vasyl' Stus Donetsk National University, Vinnitsa and Uzhgorod National University, Uzhgorod) and Norway (University of Oslo).

The talks and mini-courses given at the winter school, which is attended by 40 invited participants, pertain to topics in stochastic analysis, probability theory and related fields.

Further, presentations are also devoted to the issue of training and preparation of students for mathematical olympiads and other international competitions in mathematics.

Tid og sted:
11. jan. 2018 15:00 - 17:00,
PRIO, Hausmannsgate 3, Oslo

This seminar is a part of the UiO-PRIO collaborative effort Oslo Lectures on Peace and Conflict

Tid og sted:
9. jan. 2018 13:15 - 14:00,
Ullevål End of the Line

**Emerging instabilities and bifurcations from deformable fluid interfaces in the inertialess regime **

In this talk, I will present two studies regarding the dynamics of droplets in the creeping flow, focusing on the arising instability and bifurcation phenomena. The first work investigates a buoyancy-driven droplet translating in a quiescent environment and the second a particle-encapsulating droplet in shear flow. There-dimensional simulations based on versatile boundary integral methods were employed to explore the intriguing instability and bifurcation phenomena in the inertialess flow. In the first work, a non-modal stability analysis was performed to predict the critical condition of instability; and in the second, a dynamic system approach was adopted to model and characterize the interacting bifurcations.

Tid og sted:
9. jan. 2018 11:00 - 12:00,
Gates of Eden

Elizabeth Gillaspy from the University of Montana at Missoula, USA, will give a talk with title " Finite decomposition rank and strong quasidiagonality for virtually nilpotent groups "

Abstract: In joint work with Caleb Eckhardt and Paul McKenney, we show that the C*-algebras of discrete, finitely generated, virtually nilpotent groups G are strongly quasidiagonal and have finite decomposition rank. Thus, the only remaining step required to show that primitive quotients of such virtually nilpotent groups G are classified by their Elliott invariant is to check that these C*-algebras satisfy the UCT. Our proof of finite decomposition rank relies on a careful analysis of the relationship between primitive ideals of C*(G) and those of C*(N), where N is a finite-index normal subgroup of G. In the case when N is also nilpotent, we obtain a decomposition of C*(G) as a continuous field of twisted crossed products, which enables us to prove finite decomposition rank of C*(G) by analyzing the decomposition rank of the fibers.

Tid og sted:
19. des. 2017 14:00 - 15:00,
Desolation row, Ullevål

Antoine Julien, Universitetet i Nord, will give a talk with title: Rieffel-type projections in higher-dimensional rotation algebras

Abstract: Rieffel first built a non-trivial projection in the rotation algebra by considering a certain C*-module over this algebra, and exploiting the Morita equivalence which it implements. In this talk, I will present how it is possible to extend these ideas to construct explicitly projections in higher-dimensional noncommutative tori. Precisely, our techniques can be applied to the NC tori which are associated with an R^d-flow on a 2d-torus, or equivalently which are given by the crossed product of C(T^d) by Z^d. I will also hint on how this result can be interpreted as constructing Gabor atoms associated with some lattices in the time-frequency space R^{2d}. This is a joint work with Franz Luef (NTNU).