Thu, 15 Feb 2024
16:00
L3

A New Solution to Time Inconsistent Stopping Problem

Yanzhao Yang
(Mathematical Insittute)
Further Information

Please join us for refreshments from 15:30 outside L3.

Abstract
Time inconsistency is a situation that a plan of actions to be taken in the future that is optimal for an agent according to today's preference may not be optimal for the same agent in the future according to corresponding preference.
In this talk, we study a continuous dynamic time inconsistent stopping problem with a flow of preferences which can be in general form. We will define a solution to the problem by the rationality of the agent, and compare it with other solutions appeared in literature. Some examples with respect to specific preferences will be shown as a part of our analysis.
 
This is a joint work with Hanqing Jin.
Tue, 14 May 2024 10:00 -
Tue, 28 May 2024 12:00
C5

Current topics in Lorentzian geometric analysis: Non-regular spacetimes

Dr Clemens Sämann
(Mathematical Insittute)
Further Information

Sessions led by Dr Clemens Sämann will take place on:

Tuesday, 14 May 10am-12pm C5 (Lecture)
Thursday, 16 May 10am-12pm C5 (Lecture)
Tuesday, 28 May 10am-12pm C5 (Reading group)

Participants should have a good knowledge of differential geometry and metric spaces (basics of Lorentzian geometry will be reviewed). Some knowledge of measure theory, functional analysis (in particular Sobolev spaces) and optimal transport is recommended but we will try to be as self-contained as possible.

Abstract

Course Overview
The course gives an introduction to a topic of current interest in Lorentzian geometic analysis and mathematical General Relativity: an approach to nonregular spacetimes based on a “metric” point of view.
 

Learning Outcomes
Becoming acquainted with Lorentzian length spaces, sectional and Ricci curvature bounds for non-regular Lorentzian spaces and the appropriate techniques.
 

Course Synopsis
Lecture 1a: Review of Lorentzian geometry, spaces of constant curvature, causality theory, singularity theorems.
Lecture 1b: Introduction to Lorentzian length spaces, timelike sectional curvature bounds.


Lecture 2a: Optimal transport, timelike Ricci curvature bounds
Lecture 2b: Sobolev calculus for time functions. Literature: [O’N83, KS18, CM20].
 

Reading group: Depending on student’s interest one could discuss the papers [GKS19, AGKS21, ABS22].

 

References
[ABS22] L. Aké Hau, S. Burgos, and D. A. Solis. Causal completions as Lorentzian pre-length spaces. General Relativity and Gravitation, 54(9), 2022. doi:10.1007/s10714-022-02980-x.
[AGKS21] S. B. Alexander, M. Graf, M. Kunzinger, and C. Sämann. Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theorems. Comm. Anal. Geom., to appear, 2021. doi:10.48550/arXiv.1909.09575. arXiv:1909.09575 [math.MG].
[CM20] F. Cavalletti and A. Mondino. Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications. Cambridge Journal of Mathematics, to appear, arXiv:2004.08934 [math.MG], 2020. doi:10.48550/arXiv.2004.08934.
[GKS19] J. D. E. Grant, M. Kunzinger, and C. Sämann. Inextendibility of spacetimes and Lorentzian length spaces. Ann. Global Anal. Geom., 55(1):133–147, 2019. doi:10.1007/s10455-018-9637-x.
[KS18] M. Kunzinger and C. Sämann. Lorentzian length spaces. Ann. Glob. Anal. Geom., 54(3):399–447, 2018. doi:10.1007/s10455-018-9633-1.
[O’N83] B. O’Neill. Semi-Riemannian geometry with applications to relativity, volume 103 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983.

 

Should you be interested in taking part in the course, please send an email to @email  by 10 May 2024. 

Tue, 18 May 2021
14:30
Virtual

Numerical analysis of a topology optimization problem for Stokes flow

John Papadopoulos
(Mathematical Insittute)
Abstract

A topology optimization problem for Stokes flow finds the optimal material distribution of a Stokes fluid that minimizes the fluid’s power dissipation under a volume constraint. In 2003, T. Borrvall and J. Petersson [1] formulated a nonconvex optimization problem for this objective. They proved the existence of minimizers in the infinite-dimensional setting and showed that a suitably chosen finite element method will converge in a weak(-*) sense to an unspecified solution. In this talk, we will extend and refine their numerical analysis. We will show that there exist finite element functions, satisfying the necessary first-order conditions of optimality, that converge strongly to each isolated local minimizer of the problem.

[1] T. Borrvall, J. Petersson, Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77–107. doi:10.1002/fld.426.

 

A link for this talk will be sent to our mailing list a day or two in advance.  If you are not on the list and wish to be sent a link, please contact @email.

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