## Visiting address

Ullevål StadionSognsveien 77B

0855 OSLO

Norway

Time and place:
Apr. 11, 2018 2:15 PM - 4:00 PM,
Desolation Row, Sognsveien 77 B

Waldhausen's algebraic K-theory of spaces is an extension of algebraic K-theory from rings to spaces (or ring spectra) which also encodes important geometric information about manifolds. Bivariant A-theory is a bivariant extension of algebraic K-theory from spaces to fibrations of spaces. In this talk, I will first recall the definition and basic properties of bivariant A-theory and the A-theory Euler characteristic of Dwyer-Weiss-Williams. I will then introduce a bivariant version of the cobordism category and explain how this may be regarded as a universal space for the definition of additive characteristic classes of smooth bundles. Lastly, I will introduce a bivariant extension of the Dwyer-Weiss-Williams characteristic and discuss the Dwyer-Weiss-Williams smooth index theorem in this context. Time permitting, I will also discuss some ongoing related work on the cobordism category of h-cobordisms. This is joint work with W. Steimle.

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

Time and place:
Apr. 9, 2018 1:15 PM,
Ullevål Stadion: Gates of Eden

M.Sc. Rune Vegard Skullerud Fjellbo ved Matematisk institutt vil forsvare sin avhandling for graden ph.d.:

**Non-singular simplicial sets**

Time and place:
Apr. 9, 2018 10:15 AM,
Ullevål Stadion: Gates of Eden

M.Sc. Torkel Andreas Haufmann ved Matematisk institutt avholder prøveforelesning over oppgitt emne: "Nonnegative factorization rank of a nonnegative matrix".

Time and place:
Apr. 9, 2018 10:15 AM,
Ullevål Stadion: Gates of Eden

M.Sc. Rune Vegard Skullerud Fjellbo ved Matematisk institutt avholder prøveforelesning over oppgitt emne: "The s-cobordism theorem".

Time and place:
Apr. 3, 2018 10:30 AM - 12:00 PM,
Gates of Eden

On Tuesday the 3rd of April there will be a presentation on the modern problems facing research data and its use. It is highly recommended that all employees at the Department of Mathematics attend.

The presentation will be held in English.

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".