Universität Wien
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250147 VO Topics Course Biomathematics (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 03.10. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 06.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.10. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 13.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.10. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 20.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.10. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 27.10. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.10. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 03.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.11. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 10.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.11. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 17.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.11. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 24.11. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.11. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 01.12. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.12. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Monday 12.12. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 15.12. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.01. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 12.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.01. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 19.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.01. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock
  • Thursday 26.01. 08:00 - 09:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.01. 16:45 - 18:15 Seminarraum 4 Oskar-Morgenstern-Platz 1 1.Stock

Information

Aims, contents and method of the course

This class will cover several probabilistic models arising in biomathematics, with a particular focus on population genetics. One of the major challenge of population genetics is the inference of the evolutionary history of a population (or a species) from the observation of its extant genetic diversity. From a mathematical point of view, the approach consists in starting from tractable models in order to make theoretical predictions on the genetic signature of various evolutionary scenarii: natural selection, mutation, demography (i.e. migration, population expansion etc.), pure genetic drift or recombination.
In this course, I will introduce several of the aforementioned probabilistic models and introduce various technics to analyse them. I will start from the Wright-Fisher diffusion(s) describing the evolution of the genetic composition in large populations. I will show that an efficient way to analyse such models relies on the description of their underlying genealogical structure. More precisely, if several individuals are sampled from an extent population, one can trace backward in time the genealogical lines of those individuals. I will show how coalescent theory (Kingman coalescent, $\Lamda$-coalescents) provides an elegant description of this genealogy, and how it allows to draw predictions on the genetic structure of large populations.
If time permits, I will also show how the previous approaches can be carried through in epidemiogy in order to describe a viral expansion (Feller diffusion) and its underlying genealogical structure of such a population (coalescent point processes).
Along the way, I hope to introduce general probabilistic concepts which will be of independent interest : martingales, duality, exchangeability etc.

Assessment and permitted materials

Will be distributed by email

Minimum requirements and assessment criteria

Strong undergraduate probability. Some knowledge on the following topics: Stochastic processes, Markov processes (discrete and continuous time), Brownian motion, diffusions. No knowledge of measure theory will be required.
Art der Leistungskontrolle und erlaubte Hilfsmittel
Two graded home-works will be assigned during the semester. The final exam will be an oral exam (duration to be determined).

Examination topics

Reading list

Will be distributed by email.

Association in the course directory

Last modified: Fr 03.03.2023 12:29