Sprecher:
Stefan Hollands
Koordinator:
Jörg Lehnert
Addresse:
Inselstraße 22
04103 Leipzig
Deutschland
Kontakt:
+49(0)341-9959-641
+49(0)341-9959-658
IMPRS
Stochastics and Discrete Structures
Scientific Members working in this area
- Alexey Bufetov (Mathematical Institute of Leipzig University)
- Benjamin Gess (MPI for Mathematics in the Sciences)
- Guido Montúfar (MPI for Mathematics in the Sciences)
- Artem Sapozhnikov (Mathematical Institute of Leipzig University)
- Peter F. Stadler (Institute for Computer Science of Leipzig University)
- Max von Renesse (Mathematical Institute of Leipzig University)
Description of Research
An active research area of this group is information theory. On one hand, the approach of information geometry brings powerful tools from geometry to bear on questions in statistics and data analysis. On the other hand, information theoretical concepts like graphic models are useful for understanding information processing in neural and cognitive systems. In the life sciences, we model and analyze gene regulation, protein-protein interaction and metabolic networks and develop new tools from discrete mathematics like graph relations to investigate them. We also explore the links between stochastic analysis and statistical physics. Furthermore, concentration inequalities and Wasserstein geometries provide deep links between stochastic analysis, partial differential equations and geometry.
Gegenwärtige Doktoranden
| Nachname, Vorname | Telefon | Raum | Homepage | |
| Müller, Fenna | Fenna.Muller | 964 | F2 10 | |
| Müller, Johannes | Johannes.Mueller | 725 | E2 04 | external |
| Tseran, Hanna | Hanna.Tseran | 727 | E2 04 | external |
Alumni
| Name | Advisor | Graduation | Topic |
| Sarah Berkemer | Peter F. Stadler | 2020 | Towards dynamic programming on generalized data structures and applications of dynamic programming in bioinformatics (see more) |
| Holger Bernigau | Nihat Ay | 2015 | Causal models over infinite graphs and their application to the sensorimotor loop : general stochastic aspects and gradient methods for optimal control (see more) |
| Florian Kunick | Benjamin Gess, Felix Otto | 2022 | Analysis and numerics of stochastic gradient flows (see more) |
| Guido Montúfar | Nihat Ay | 2012 | On the expressive power of discrete mixture models, restricted Boltzmann machines, and deep belief networks - a unified mathematical treatment (see PDF) |
| Marius Neuß | Benjamin Gess | 2021 | Stochastic partial differential equations arising in self-organized criticality (see more) |
| Wolfgang Otto | Peter Stadler | 2011 | Transcriptional regulatory elements : detection and evolutionary analysis (see more) |
| Johannes Rauh | Nihat Ay | 2011 | Finding the maximizers of the information divergence from an exponential family (see more) |
| Angel Eduardo Rodríguez Fernández | Peter F. Stadler | 2021 | On the study of fitness landscapes and the Max-Cut problem (see more) |
| Lorenzo Taggi | Artem Sapozhnikov | 2015 | Absorbing-state phase transition in activated random walk and probabilistic cellular automata (see more) |