[Facets-of-complexity] Invitation to Monday's Lecture & Colloquium Feb.7 - online via Zoom.

["I.Brunke" <i.brunke@fu-berlin.de>]

Dear all,

next Monday's Lecture and Colloquium will take place online via Zoom on February 7.

Please find link to Zoom Meeting here:

https://tu-berlin.zoom.us/j/69716124232?pwd=dzFlcTFHMmFXRTE5QmZLaEV5N0FRUT09

A password is not required!

You all are cordially invited!

Location:

Online via Zoom.

Monday's Lecture: Neil Olver (London School of Economics and Political Science)

Time: Monday, February 7 - 14:15 h

Title: Continuity, Uniqueness and Long-Term Behaviour of Nash Flows Over Time

Abstract:

We consider a dynamic model of traffic that has received a lot of attention in the past few years. Users control infinitesimal flow particles aiming to travel from a source to destination as quickly as possible. Flow patterns vary over time, and congestion effects are modelled via queues, which form whenever the inflow into a link exceeds its capacity. We answer some rather basic questions about equilibria in this model: in particular uniqueness (in an appropriate sense), and continuity: small perturbations to the instance or to the traffic situation at some moment cannot lead to wildly different equilibrium evolutions.

To prove these results, we make a surprising connection to another question: whether, assuming constant inflow into the network at the source, do equilibria always eventually settle into a "steady state" where all queue delays change linearly forever more? Cominetti et al. proved this under an assumption that the inflow rate is not larger than the capacity of the network - eventually, queues remain constant forever. We resolve the more general question positively.

(Joint work with Leon Sering and Laura Vargas Koch).


Break

Monday's Colloquium: Manuel Radons (Technische Universität Berlin)

Time: Monday, February 7 - 16:00 h s.t.

Title: Nearly flat polytopes in the context of Dürer's problem

Abstract:

Dürer's problem asks whether every 3-polytope P has a net. Is there always a spanning tree T of its edge graph, so that if we cut P along T the resulting surface can be unfolded into the plane without self-overlaps? A common technique in recent works is to fix a spanning tree and then study the deformations of the corresponding unfolding induced by an affine stretching or flattening of P. In the first part of my talk I will highlight landmark results by Ghomi, O'Rourke and Tarasov that emanated from this approach. In the second part I will present my own work on the unfoldability of nested prismatoids, which follows a similar ansatz.

You all are cordially invited!

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