Wed, 10 May 2023
16:00
L6

Vanishing of group cohomology, Kazhdan’s Property (T), and computer proofs

Piotr Mizerka
(Polish Academy of Sciences)
Abstract

We will look at the vanishing of group cohomology from the perspective of Kazhdan’s property (T). We will investigate an analogue of this property for any degree, introduced by U. Bader and P. W. Nowak in 2020 and describe a method of proving these properties with computers.

Tue, 15 May 2018
17:00
C1

Why do circles in the spectrum matter?

Yuri Tomilov
(Polish Academy of Sciences)
Abstract


I plan to present several results linking the numerical range of a Hilbert space operator to the circle structure of its spectrum. I'll try to explain how the numerical ranges approach helps to unify, extend or supplement several results where the circular structure of the spectrum is crucial, e.g. Arveson's theorem on almost-wandering vectors of unitary actions and Hamdan's recent result on supports of Rajchman measures. Moreover, I'll give several applications of the approach to new operator-theoretical constructions inverse in a sense to classical power dilations. If time permits, I'll also address the same or similar issues in a more general setting of operator tuples. This is joint work with V. M\" uller (Prague).
 

Tue, 07 Jun 2016
17:00
C1

Operator-valued $(L^{p},L^{q})$-Fourier multipliers

Jan Rozendaal (in Warsaw)
(Polish Academy of Sciences)
Abstract
Although much of the theory of Fourier multipliers has focused on the $(L^{p},L^{p})$-boundedness

 of such operators, for many applications it suffices that a Fourier multiplier operator is bounded

 from $L^{p}$ to $L^{q}$ with p and q not necessarily equal. Moreover, one can derive 

(L^{p},L^{q})-boundedness results for $p\neq q$ under different, and often weaker, assumptions

 than in the case $p=q$. In this talk I will explain some recent results on the

 $(L^{p},L^{q})$-boundedness of operator-valued Fourier multipliers. Also, I will sketch some

 applications to the stability theory for $C_{0}$-semigroups and functional calculus theory. 

 

This talk will be transmitted from Warsaw to us and Dresden, provided that Warsaw get things set up.  We will not be using the TCC facility,

so the location will be C1.

Tue, 13 Oct 2015
17:00
Taught Course Centre

Haagerup approximation property for arbitrary von Neumann algebras and Schoenberg correspondence

Adam Skalski
(Polish Academy of Sciences)
Abstract

This talk will be by videolink from Warsaw.  The starting-time will be a little after 17:00 due to a TCC lecture and time needed to establish video connections.

 

Abstract: The Haagerup approximation property for finite von Neumann algebras  (i.e.von Neumann algebras with a tracial faithful normal state) has been studied for more than 30 years. The original motivation to study this property came from the case of group von Neumann algebras of discrete groups, where it corresponds to the geometric Haagerup property of the underlying group. Last few years brought a lot of interest in the Haagerup property for discrete and general locally compact quantum groups. If the discrete quantum group in question is not unimodular, the associated (quantum) group von Neumann algebra cannot be finite, so we need a broader framework for the operator algebraic property. In this talk, I will present recent developments regarding the Haagerup approximation property for arbitrary von Neumann algebras and will also discuss some questions relating it to the issues related to the classical Schoenberg correspondence. (Mainly based on joint work with Martijn Caspers.)

Mon, 08 Mar 2010

17:00 - 18:00
Gibson 1st Floor SR

Global regular solutions to the Navier-Stokes equations in a cylinder with slip boundary conditions

Wojciech ZAJACZKOWSKI
(Polish Academy of Sciences)
Abstract

We consider the motion of a viscous incompressible fluid described by

the Navier-Stokes equations in a bounded cylinder with slip boundary

conditions. Assuming that $L_2$ norms of the derivative of the initial

velocity and the external force with respect to the variable along the

axis of the cylinder are sufficiently small we are able to prove long

time existence of regular solutions. By the regular solutions we mean

that velocity belongs to $W^{2,1}_2 (Dx(0,T))$ and gradient of pressure

to $L_2(Dx(0,T))$. To show global existence we prolong the local solution

with sufficiently large T step by step in time up to infinity. For this purpose

we need that $L_2(D)$ norms of the external force and derivative

of the external force in the direction along the axis of the cylinder

vanish with time exponentially.

Next we consider the inflow-outflow problem. We assume that the normal

component of velocity is nonvanishing on the parts of the boundary which

are perpendicular to the axis of the cylinder. We obtain the energy type

estimate by using the Hopf function. Next the existence of weak solutions is

proved.

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