## Visiting address

Niels Henrik Abels husMoltke Moes vei 35 (map)

0851 OSLO

Norway

Time and place:
Mar. 22, 2018 12:45 PM - 1:45 PM,
Gates of Eden Sognsveien 77 B

The speedskating 1000-m is a Formula One event, for the Olympics and the annual World Sprint Championships. The skaters are running in pairs, with one starting in inner lane and the other in outer lane, and then exchanging lanes on the backstretch. With speeds up to 60 km/h, there will in particular be technical challenges when negogiating the curves. Once upon a time I managed to change the Olympics, by pinpointing the statistically significant non-zero difference between last inner and last outer lane for the 500-m; the practical solution is to have the skaters running the 500-m twice, with one start in inner and one in outer. I have now properly examined the 1000-m, and found that there is a similar and in fact more dramatic Olympic Unfairness Parameter associated with that event.

Coffee and cakes from 12.00 in the lunch room.

Time and place:
Mar. 21, 2018 2:15 PM - 4:00 PM,
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.

Time and place:
Mar. 20, 2018 10:15 AM - 12:00 PM,
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.

Time and place:
Mar. 8, 2018 10:15 AM - 2:00 PM,
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.

Time and place:
Mar. 7, 2018 2:15 PM - 4:00 PM,
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.)

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