## Besøksadresse

Ullevål StadionSognsveien 77B

0855 OSLO

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

I will review Witt vectors, KÃ€hler forms and logarithmic rings, and outline how they merge in the logarithmic de Rham-Witt complex. This structure gives an algebraic underpinning for the Hesselholt-Madsen (2003) calculation of logarithmic topological cyclic homology of many discrete valuation rings.

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

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Nordfjordeid Summer school 2018

Tid og sted:
20. mars 2018 10:15 - 12:00,
End of the Line, Sognsveien 77 B

This talk is supposed to be an Introductionary talk to the preprint arXiv:1409.4372v4 (joint work with G.Garkusha). More specifically, using the theory of framed correspondences developed by Voevodsky, the authors introduce and study framed motives of algebraic varieties. This study gives rise to a construction of the big frame motive functor. It is shown that this functor converts the classical Morel--Voevodsky motivic stable homotopy theory into an equivalent local theory of framed bispectra, and thus producing a new approach to stable motivic homotopy theory. As a topological application, it is proved that for the simplicial set Fr(Delta^\bullet_C, S^{^1}) has the homotopy type of the space \Omega^{\infty} Sigma^{\infty} (S^{^1}). Here C is the field complex numbers.

Tid og sted:
8. mars 2018 10:15 - 14:00,
Desolation Row Sognsveien 77 B

I discuss how Bökstedt and Madsen (1994/1995) calculate mod p homotopy for THH(Z) and the fixed-point spectra THH(Z)^{C_{p^n}}, together with the R- and F-operators. This leads to a calculation for TC(Z; p) and K(Z_p), confirming the Lichtenbaum-Quillen conjecture in this case.

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

I will review Bökstedt, Hesselholt and Madsen's calculations of the topological cyclic homology of prime fields and the integers, again taking into account simplifications made in later papers. (If necessary, I will continue on Thursday.)

Tid og sted:
7. mars 2018 11:15 - 12:00,
Seminar room "End of the Line"

Tid og sted:
7. mars 2018 10:15 - 12:00,
Desolation Row, Sognsveien 77 B

Tid og sted:
6. mars 2018 10:15 - 12:00,
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.

Tid og sted:
6. mars 2018 08:45 - 09:15,
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?

Tid og sted:
6. mars 2018 08:30 - 17:30,
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.

Tid og sted:
2. mars 2018 10:00 - 11:30,
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

Tid og sted:
1. mars 2018 10:15 - 11:00,
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

Tid og sted:
1. mars 2018 09:30 - 10:15,
Ullevål Stadion: Gates of Eden

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

Tid og sted:
28. feb. 2018 10:15 - 12:00,
Desolation Row Sognsveien 77B

Tid og sted:
28. feb. 2018 09:30 - 11:00,
Ullevål Stadion: End of the Line

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

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.