Multigrid solvers for the de Rham complex with optimal complexity in polynomial degree
Brubeck Martinez, P Farrell, P SIAM Journal on Scientific Computing volume 46 issue 3 A1549-A1573 (07 May 2024)
Existence and uniqueness for the non-compact Yamabe problem of negative curvature type
Hogg, J Nguyen, L Analysis in Theory and Applications volume 40 issue 1 57-91 (01 Apr 2024)
Thu, 01 Feb 2024

12:00 - 13:00
L3

Stop-and-go, hovercrafts and helicopters: the complex motility of droplet microswimmers driven by interfacial instabilities

Dr. Corinna Maaß
(University of Twente & Max Planck Institute for Dynamics and Self-Organization, Dynamics of Complex Fluids, Göttingen)
Abstract
In both experiment and numerics, active droplets are a simple but versatile toy model to study active processes from single agents to collective scales.
One hallmark of active or living matter lies in the conversion of microscopic free fuel energy to mesoscopic directed motion. Bio-microswimmers have evolved complex and sophisticated motility, like helical swimming or run-and-tumble dynamics, with similarly complex  mechanical or biochemical actuation.
However, similar periodic or chaotic motion may also arise simply from the nonlinear dynamics of fuel conversion that set autophoretic droplet swimmers in motion, leading to a wealth of biomimetic phenomena. In this talk, I will demonstrate how the interaction of a self-propelling droplet with its self-generated chemical and hydrodynamic environment generates swimming and pumping states, unsteady reorientation, helical dynamics and complex collective states.
Wed, 21 Feb 2024
16:00
L6

Groups Acting Acylindrically on Trees

William Cohen
(University of Cambridge)
Abstract

It was shown by Balasubramanya that any acylindrically hyperbolic group (a natural generalisation of a hyperbolic group) must act acylindrically and non-elementarily on some quasi-tree. It is therefore sensible to ask to what extent this is true for trees, i.e. given an acylindrically hyperbolic group, does it admit a non-elementary acylindrical action on some simplicial tree? In this talk I will introduce the concepts of acylindrically hyperbolic and acylindrically arboreal groups and discuss some particularly interesting examples of acylindrically hyperbolic groups which do and do not act acylindrically on trees.

Mon, 05 Feb 2024

16:30 - 17:30
L5

Characterising rectifiable metric spaces using tangent spaces

David Bate
(Warwick)
Abstract

This talk will present a new characterisation of rectifiable subsets of a complete metric space in terms of local approximation, with respect to the Gromov-Hausdorff distance, by finite dimensional Banach spaces. Time permitting, we will discuss recent joint work with Hyde and Schul that provides quantitative analogues of this statement.
 

Mon, 03 Jun 2024

16:30 - 17:30
L4

On the well-possedness of time-dependent three-dimensional Euler fluid flows

Josef Malek
(Mathematics Faculty at the Charles University in Prague)
Abstract

We study the mathematical properties of time-dependent flows of incompressible fluids that respond as an Euler fluid until the modulus of the symmetric part of the velocity gradient exceeds a certain, a-priori given but arbitrarily large, critical value. Once the velocity gradient exceeds this threshold, a dissipation mechanism is activated. Assuming that the fluid, after such an activation, dissipates the energy in a specific manner, we prove that the corresponding initial-boundary-value problem is well-posed in the sense of Hadamard. In particular, we show that for an arbitrary, sufficiently regular, initial velocity there is a global-in-time unique weak solution to the spatially-periodic problem. This is a joint result with Miroslav Bulíček. 

Mon, 27 May 2024

16:30 - 17:30
L4 tbc

Stability of equilibria in PDE systems arising in continuum thermodynamics

Miroslav Bulicek
(Mathematics Faculty at the Charles University in Prague)
Abstract

We present a general concept that is suitable for studying the stability of equilibria for open systems in continuum thermodynamics. We apply such concept to a generalized Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity in three dimensional domain. For large class of constitutive relation for the Cauchy stress, we identify a class of proper solutions converging to the equilibria exponentially in a suitable metric and independently of the distance to equilibria at the initial time. Consequently, the equilibrium is nonlinearly stable and attracts all weak solutions from that class. The proper solutions exist and satisfy entropy (in)equality.

Mon, 15 Jan 2024

16:30 - 17:30
L5

Functions of bounded variation and nonlocal functionals

Panu Lathi
(Academy of Mathematics and Systems Science of the Chinese Academy of Sciences)
Abstract

In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by means of non-local functionals. In my recent work I have studied two such functionals: a BMO-type (bounded mean oscillation) functional, and a functional related to the fractional Sobolev seminorms. I will discuss some of my results concerning the limits of these functionals, the concept of Gamma-convergence, and also open problems. 

Wright Meets Markowitz: How Standard Portfolio Theory Changes When Assets Are Technologies Following Experience Curves
Way, R Lafond, F Lillo, F Panchenko, V Farmer, J (01 Jan 2017)
Wright meets Markowitz: How standard portfolio theory changes when assets are technologies following experience curves
Way, R Lafond, F Lillo, F Panchenko, V Farmer, J (09 May 2017)
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