(Speaker: TBA)
PhD Seminar
Date and Time: Every second week Thursday 16:00 in Seminarraum 1 (starting on 23 October)
The purpose of this seminar is to provide a space for PhD students in mathematics and computer science to meet, connect, and exchange ideas about their research. Each session features a 50–60 minute talk on any topic in mathematics or computer science that the speaker wishes to share. The presentations should be accessible to PhD students in both mathematics and computer science. If you would like to give a talk, please contact either Jorn van Voorthuizen (jvoorthu at uni-koeln.de) or Marvin Plogmann (plogmann at math.uni-koeln.de).
Schedule
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Stochastic Control in Insurance (Speaker: Kira Dudziak)
The surplus process of an insurance company depends on various factors. Premium income, claims payments, dividend distributions, investments, etc. determine the capital. To ensure that the insurer can meet its financial obligations at all times, it is essential to control the surplus process. But what does an optimal strategy look like? In this talk, I will briefly introduce how we can use stochastic methods to model the surplus process and find an optimal strategy depending on the set goal. By using a simple example, I will explain the so-called Hamilton-Jacobi-Bellman approach, in which we derive and solve a differential equation.
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Singularities of currents (Speaker: Shuang Su)
In algebraic geometry, counting the singular point of algebraic curves is a crucial problem. Currents can be viewed as a natural generalization of algebraic varieties. In this talk, I will explain how to measure the singularities of currents and give an estimate for the volume of the singular locus.
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Galois connections (Speaker: Jonathan Lindell)
Galois connections allow us to formalise the situation where we have two kinds of collections of objects, with some inherent order, and some correspondence which allows us to move between the two different collections. This kind of setup is common both in math and outside, and in this talk we'll define Galois collections and give examples from different areas of mathematics (and maybe outside of mathematics if time allows).
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Data analysis, Topology and Representation Theory (Speaker: Maximilian Kaipel)
There are many possible ways of analysing a given data set. One recent approach is to describe the topological features of the data. I will describe this approach and explain the role that representations of quivers play in this context.
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Everything is relative: the structure of space and time (Speaker: Jorn van Voorthuizen)
General relativity unites space and time into a single geometric object: spacetime. In this talk, we will journey from Newton's absolute notions of space and time to Einstein's relativistic picture, where geometry and causality are intertwined. We will introduce the basic geometric ingredients of a spacetime and examine how these encode its causal structure. Finally, we will turn the question around: to what extent does the causal structure determine the spacetime itself? Malament's theorem gives a striking answer: the causal structure determines the spacetime up to a conformal factor.