Universität Wien

250147 VO Topics Course Biomathematics (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
VOR-ORT
Moodle

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Details

Sprache: Deutsch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

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

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Will be distributed by email.

Mindestanforderungen und Beurteilungsmaßstab

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).

Prüfungsstoff

Literatur

Will be distributed by email.

Zuordnung im Vorlesungsverzeichnis

Letzte Änderung: Fr 03.03.2023 12:29