### Sharp convergence to equilibrium of interacting particle systems

Data e local: 22/04/2021, 16h, Organizado por: Centro de Matemática e Aplicações, NOVA School of Science and Technology

Abstract

In this seminar we will discuss the convergence to equilibrium of Markov chains. We will exhibit the classical examples of card shuffles and use them to introduce our model: the exclusion process with reservoirs. To attend the proposal of the seminar, we will explain how this probabilistic model, as others, can be approached in a very analytical way.

Endereço para transmissão em directo https://videoconf-colibri.zoom.us/j/82268075611

### CFD Analysis in cerebral aneurysms

Data e local: 15/04/2021, 15H00, Organizado por: Departamento de Matemática e CIMA, Universidade de Évora

Orador: Jorge Tiago, Departamento de Matemática e CEMAT, Instituto Superior Técnico, Universidade de Lisboa

Abstract

Blood flow simulations have long been considered as a valuable tool for a deeper understanding of the physiopathology of intracranial aneurysms. Many authors built robust computational settings based on accurate computer-assisted registration, segmentation, and 3D geometry reconstruction from medical images of patient specific cerebral aneurysms, and special techniques to derive appropriate boundary conditions. However, an accurate description of flow mechanics in the near wall region and its connection with the evolution of the wall disease remains linked to several questions not yet fully understood. Recently, a lower order approximation of the Lagrangian dynamics in the near wall region, which allows for a meaningful characterization of both normal and parallel direction to the wall, has been suggested. We verify this computational approach with a cohort of brain aneurysms and try to provide a step further in the understanding of the hemodynamic environment and its possible connection with the risk of rupture. Possible ways to improve such techniques are also discussed.

Para mais detalhes visite a página oficial https://www.dmat.uevora.pt/informacoes/eventos/(item)/32018

### Algebras of convolution type operators with continuous data do not always contain all rank one operators

Data e local: 14/04/2021, 16:10, Organizado por: CIDMA - Universidade de Aveiro

Orador: Alexei Karlovich, Centro de Matemática e Aplicações, Universidade NOVA de Lisboa

Abstract

Let $X(\mathbb{R})$ be a separable Banach function space such that the Hardy-Littlewood maximal operator is bounded $X(\mathbb{R})$ and on its associate space $X'(\mathbb{R})$. The algebra $C_X(\dot{\mathbb{R}})$ of continuous Fourier multipliers on $X(\mathbb{R})$ is defined as the closure of the set of continuous functions of bounded variation on $\dot{\mathbb{R}}=\mathbb{R}\cup\{\infty\}$ with respect to the multiplier norm. It was proved recently by C. Fernandes, Yu. Karlovich and myself that if the space $X(\mathbb{R})$ is reflexive, then the ideal of compact operators is contained in the Banach algebra $\mathcal{A}_{X(\mathbb{R})}$ generated by all multiplication operators $aI$ by continuous functions $a\in C(\dot{\mathbb{R}})$ and by all Fourier convolution operators $W^0(b)$ with symbols $b\in C_X(\dot{\mathbb{R}})$. We show that there are separable and non-reflexive
Banach function spaces $X(\mathbb{R})$ such that the algebra $\mathcal{A}_{X(\mathbb{R})}$ does not contain all rank one operators. In particular, this happens in the case of the Lorentz spaces $L^{p,1}(\mathbb{R})$ with $1 Para consultar o cartaz clique aqui Para mais detalhes visite a página oficial http://seminargafa.web.ua.pt Endereço para transmissão em directo https://videoconf-colibri.zoom.us/j/84676013915?pwd=VTk1Q1dSaGtkc2VEWWVDMlZldjBFQT09 ### Patterns of resemblance - between proof theory and set theory Data e local: 12/04/2021, 16h00-17h00, Organizado por: CMAFcIO - Centro de Matemática, Aplicações Fundamentais e Investigação Operacional Orador: Anton Freund, Technische Universitat Darmstadt Abstract Timothy Carlson's patterns of resemblance offer an astonishingly simple way to describe large computable ordinals, as used in proof theory. In this talk I discuss fundamental definitions and results, without assuming any prerequisites from proof theory. My aim is to explain the following recent theorem: By relativizing patterns of resemblance to dilators, one obtains an equivalence with Pi^1_1-comprehension, a central principle from reverse mathematics (arXiv:2012.10292). Endereço para transmissão em directo https://videoconf-colibri.zoom.us/j/89084793299?pwd=amRYK3pwcFZDTnV5MHhYMDh3Ni9UQT09 ### On the weak convergence of shift operators to zero on Orlicz spaces Data e local: 08/04/2021, 16h, Organizado por: Centro de Matemática e Aplicações, NOVA School of Science and Technology Orador: Oleksiy Karlovych, DM & CMA, NOVA School of Science and Technology Abstract Let$\{h_n\}$be a sequence in$\mathbb{R}^d$tending to infinity and let$\{T_{h_n}\}$be the corresponding sequence of shift operators given by$(T_{h_n}f)(x)=f(x-h_n)$for$x\in\mathbb{R}^d$. We prove that$\{T_{h_n}\}$converges weakly to the zero operator as$n\to\infty$on a separable Orlicz space$L^\phi(\mathbb{R}^d)$if and only if its fundamental function$\varphi_{L^\Phi}$satisfies$\varphi_{L^\Phi}(t)/t\to 0$as$t\to\infty$. On the other hand, we show that$\{T_{h_n}\}$does not converge weakly to the zero operator as$n\to\infty$on all non-separable Orlicz spaces$L^\Phi(\mathbb{R}^d)\$. This is a joint work with Eugene Shargorodksy
(King's College London, UK).

Endereço para transmissão em directo https://videoconf-colibri.zoom.us/j/82268075611