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Winter Term 2018/19, Doctoral School Events
2018-11-16 Doctoral School Seminar (Inst. Mathematik, Heinrichstr. 36, 14:00—16:30, KFU)
Jordan McMahon (KFU, advisor K. Baur): Higher cluster-tilting for algebras of type A2d⊗A2d via abstract barycentric algebras [show abstract]
Arnur Nigmetov (TU, advisor M. Kerber): Distributed merge tree computation on AMR data with local exchanges [show abstract]
Nicola del Giudice (TU, advisor M. Kang): Subcritical random hypergraphs [show abstract]
Lukas Andritsch (KFU, advisor K. Baur): A note on friezes of type Λ4 and Λ6 [show abstract]
2018-12-7 Doctoral School Seminar (Seminarraum 2 des Instituts für Geometrie, Kopernikusgasse 24, 10:30—13:00, TU)
Gundelinde Wiegel (TU, advisor W. Woess): The Frog Model: A Model for information spreading [show abstract]
Rene Corbet (TU, advisor M. Kerber): A Kernel for Multi-Parameter Persistent Homology [show abstract]
Martin Schwinzerl (KFU, advisor G. Haase): SixTrackLib: Towards Modular, Scalable and Numerically Efficient Symplectic Particle-Tracking [show abstract]
Stefan Lendl (TU, advisor B. Klinz): Dispersing obnoxious facilities on a graph [show abstract]
2019-01-18 Doctoral School Seminar (Inst. Mathematik, Heinrichstr. 36, 14:00—16:30, KFU)
Michael Preischl (TU, advisor R. Tichy): Optimal reinsurance for Gerber-Shiu Functions in the Cramer-Lundberg Model

Abstract: We want to minimize expected discounted utility functions (or Gerber-Shiu functions) in a Cramer-Lundberg model by choosing optimal reinsurance. Reinsurance strategies are modelled as time dependant control functions, which leads to a setting from the theory of optimal stochastic control and ultimately to the problems Hamilton-Jacobi-Bellman equation.Though several authors have already contributed literature on stochastic optimal control, the focus has not been on Gerber Shiu functions so far.

Hannah Schreiber (TU, advisor M. Kerber): Discrete Morse Theory for Computing Zigzag Persistence

Abstract: We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. A zigzag filtration is defined by a sequence of complexes connected by forward and backward inclusions. From a zigzag filtration, we introduce a zigzag Morse filtration whose complexes are Morse reductions of the original complexes such that they both have same persistent homology. This zigzag Morse filtration generalizes the filtered Morse complex of Mischaikow and Nanda, defined for standard persistence.

Amr Ali Al-Maktry (TU, advisor S. Frisch): On Null Polynomials of Higher Order

Abstract: Let R be a finite commutative ring with unity. For a natural number k, f∈R[x] is said to be a null polynomial of order k if f,f',...,f(k) induce the zero function on R. The polynomial f then induces the zero function on some homomorphic images of the polynomial ring R[x1,...,xk]. For a prime p and a natural number 1≤n≤p, we characterize and count null polynomials of order k over the ring Zpn. Moreover, when n≤p we count the polynomial functions and the polynomial permutations over a homomorphic image of Zpn[x1,...,xk] that is isomorphic to Zpn[x1,...,xk] / (x12,..., xk2).

Mahadi Ddamulira (TU, advisor R. Tichy): On the x-coordinates of Pell equations which are k-generalized Fibonacci numbers

Abstract: For an integer k≥2, let {F(k)n}n≥0 be the k-generalized Fibonacci sequence which starts with 0,..,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this seminar, for an integer d≥2 which is square-free, we show that there is at most one value of the positive integer x participating in the Pell equation x2-dy2= ±1 which is a k-generalized Fibonacci number, with a few exceptions that we completely characterize. This paper extends previous work from Luca et. al 2017 for the case k=2 and Luca et. al 2018 for the case k=3. This is joint work with Florian Luca.

2019-02-01 Doctoral School Seminar (Seminarraum 2 des Instituts für Geometrie, Kopernikusgasse 24, 10:30—13:00, TU)
Laura Marx (KFU, advisor G. Plank):
Irene Parada (TU, advisor O. Aichholzer):
Karli Gilette (KFU, advisor G. Plank):
Gernot Holler (KFU, advisor K. Kunisch): A bilevel approach for parameter learning in inverse problems