School of Mathematics/Computer Science

Institute for Mathematics

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Oberseminar Angewandte Analysis

Oberseminar Stochastik

11.12.2018 um 12:00 Uhr in Raum 69/E15

Alexander Hinse (WIAS Berlin)

Vulnerability & security in ad-hoc networks

The use of D2D technology in future telecommunication systems presents a great opportunity to increase connectivity as well as capacity in networks under the pressure of accelerating demand for faster and larger volume services. On the other hand, D2D systems present their own set of vulnerabilities, essentially coming from the lack of operated infrastructure.

We consider a spatial system of devices on a random street system in R 2 forming an ad-hoc communication system. We study the propagation of malware and efficiency of countermeasures in form of an interacting particle system.

Depending on the speed of the malware, the competing processes undergoes a phase transition. Above thecritical value, the malware, started from an initial infection, percolates with positive probability (and is able to survive as t → ∞). Below the critical speed it dies out almost surely.

We are able to proof this phase transition for random rebooting (contact process) and the ’White Knight’model: an active countermeasure where a so called Goodware actively spreads through the system competing against the malware. The model was also labelled ’chase-escape’ by Durrett (’18).

The project is a joint work with Benedikt Jahnel and Wolfgang König (WIAS/TU).

18.12.2018 um 12:00 Uhr in Raum 69/E15

Grace Itunuoluwa Akinwande

Poisson Approximations for Random Simplicial Complexes

Oberseminar Algebra

Kollegseminar „Kombinatorische Strukturen in der Geometrie“

11.12.2018 um 16:15 Uhr in 69/125 :

Gaku Liu (Max Planck Institut Leipzig)

Cubical Pachner moves and cobordisms of immersions

We study various analogues of theorems from PL topology for cubical complexes. In particular, we characterize when two PL homeomorphic cubulations are equivalent by Pachner moves by showing the question to be equivalent to the existence of cobordisms between immersions of hypersurfaces. This solves a question and conjecture of Habegger and Funar. The main tool is a theorem to show that any cubical PL decomposition of a disk is regular after some cubical stellar subdivision; this extends a result of Morelli. Joint work with Karim Adiprasito.

18.12.2018 um 16:15 Uhr in 69/125:

Binh Hong Ngoc (Universität Osnabrück)


Oberseminar Topologie

11.12.2019 um 14:15 Uhr in 69/117:

Viktor Tabakov (Freie Universität Berlin)

Milnor-Witt K-theory of finite fields

The main goal of the talk will be the computation of Milnor-Witt K-theory of a finite field when the characteristic is not equal to 2. This can be done by generalizing the proof for Milnor K-theory, which also will be given in the talk. If time permits, we will discuss necessary parts of the theory of quadratic forms over a field.