Gjesteforelesninger og seminarer - Side 30

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).

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).

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.   

Soft and Wet is Different

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.

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.   

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.   

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.

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.   

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

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.

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.  

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).

Abstract: Recently, Steve Kaliszewski, Tron Omland, and I have been investigating the following theorem of Pedersen: two actions of a compact abelian group on C*-algebras A and B are outer conjugate if and only if there is an equivariant isomorphism between the crossed products that respects the positions of A and B. We upgraded this to nonabelian groups (using coactions on the crossed products), and then searched for examples showing that the last condition (on the positions of A and B) is necessary. We failed. This lead us to formulate the "Pedersen Rigidity Problem": if the crossed products of A and B are equivariantly isomorphic, are the actions on A and B outer conjugate? We have been finding numerous "no-go theorems", which give various sufficient conditions for Pedersen Rigidity. Quite recently we have done this for ergodic actions of a compact group, assuming that the actions have "full spectrum". In fact, these actions are (not just outer) conjugate if and only if the dual coactions are. I will summarize our progress on the Pedersen Rigidity Problem and outline the proof of the no-go theorem for these compact ergodic full-spectrum actions.

Andreas Carlson og Jean Rabault

Nature has invented ingenious aerodynamic design solutions, some of which are critical for plants as wind dispersal of seeds and fruits is coupled to their flight performance. This formulates into an optimization problem for plants: large seed wings can lead to increased lift and more efficient dispersion, but are costly for the tree to build and can more easily be trapped in the canopy. Double winged seeds/fruits separate from their tree when a specific level of dessication is reached, and autorotate as they descend to the ground. This leads to the question: how is the wing curvature of seeds/fruits linked to their flight performance? To answer this, we develop a theoretical model that suggests the existence of an optimal wing curvature that yields maximal lift. To further understand the interplay between the flow and the wing geometry, we perform a synthetic seed adaptation by deploying 3D printing of double winged fruits that we use in flight experiments, where we span the phase space of aerial dynamics by changing the of wing curvature and seed/fruit weight. Experiments confirm that there is a sweet-spot in curvature to maximise the flight time consisted with geometrical measurements from a wide range of seeds in Nature. Our results highlights the importance of not curving too much or too little for helicopter fruits to have an optimal flight performance.

Elisabeth Seland

In my job as research adviser, I receive a lot of questions about rights, possibilities and problems in connection with scientific publishing and open access. Both EU and the Norwegian Research Council have rules about this, and there is also a UiO policy in place that is relevant for all employees. I will give a short presentation to try to clear up what you have to, must, may, could and should related to Open access. In my experience many of you have the same questions about these issues, so I hope you bring your questions with you and we can address them in the seminar.

I will discuss the differential structure in the mod 2 Adams spectral sequence for tmf, leading to its E_\infty-term.  These calculations were known to Hopkins-Mahowald; in their current guise they are part of joint work with Bruner.

I will report on work in progress on calculations of the motivic homotopy groups of MGL (the algebraic cobordism spectrum) over number fields. It is known that pi_{2n,n}(MGL) is the Lazard ring, and pi_{-n,-n}(MGL) is Milnor K-theory of the base field. We will calculate all of pi_{*,*}(MGL) with the slice spectral sequence (motivic Atiyah-Hirzebruch spectral sequence) over a number field. I will give a brief review of the the tools and sketch the main parts of the calculation: The input from motivic cohomology, the use of C_2-equivariant Betti realization and comparison with Hill-Hopkins-Ravenel to determine the differentials, and settle most of the hidden extensions. 

I will discuss the algebra structure of the E_2-term of the mod 2 Adams spectral sequence for tmf, given by the cohomology Ext_{A(2)}(F_2, F_2) of A(2).  We (Bruner & Rognes) use Groebner bases to verify the presentation given by Iwai and Shimada, with 13 generators and 54 relations. Thereafter I will discuss the relationship between differentials and Steenrod operations in the Adams spectral sequence for E_\infty ring spectra.  

Pawel Kasprzak (Warzaw) will give a talk with title " Quantum actions on discrete quantum spaces"

Abstract:

To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors are finite-dimensional (i.e. when the action is on a discrete quantum space) the relation has finite orbits.  We then apply this

i) to generalize the classical theory of Clifford, concerning the restrictions of representations to normal subgroups, to the framework of quantum subgroups of discrete quantum groups, itself extending the context of closed normal quantum subgroups of compact quantum groups; ii) to the context of idempotent states showing that the  algebra of invariant elements is finite dimensional if and only if the corresponding state is normal. Joint work with K. De Commer, A. Skalski and P. Sołtan.