Universität Wien

250160 VU Kinetic theory applied to biology (2018W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 31.10. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.11. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.12. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.12. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.01. 16:45 - 18:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Emergent phenomena are ubiquitous in nature: it corresponds to the appearance of large-scale structure from underlying microscopic dynamics. At the microscopic level particles or agents interact following some rules, but the macroscopic structures are not encoded directly in these rules and, therefore, it is a challenge to explain how the macroscopic or observable dynamics emerge from the microscopic ones. Examples of emergence are collective dynamics (flocks of birds, school of fish, pedestrians…), network formation (capillary formation, leaf venation, formation of gullies…), opinion dynamics, tumor growth, tissue development… Understanding emergence in science is key to explaining why observable phenomena take place. The mathematical tools to studying emergence come from kinetic theory, which originally was developed to study problems in Mathematical Physics in the field of gas dynamics. The application of these tools to explore questions coming from biology poses many new interesting challenges at the level of the modeling and mathematical analysis. In this course we will explore the following four main topics:
1. What is emergence and how does kinetic theory contributes to its study?
a. Challenges in applications to biology.
2. Modeling of microscopic or agent-based dynamics (interacting particle systems).
a. What makes a good model?
b. Jump models (continuous-time Markov Chains).
c. Newtonian models.
d. Other types of models.
3. Mean-field limits: from microscopic models to kinetic equations.
4. Hydrodynamic limits: from kinetic equations to macroscopic models.
a. Hilbert expansion method.
b. Generalised Collision Invariant.
c. Bifurcations.

Assessment and permitted materials

Attendance to class is compulsory. The assimilation of the lectures will be based on 'learning by doing'. This is why there is no exam but instead many activities and exercises thorough the duration of the course. Particularly, evaluation will be based on the completion of exercises; reading and presenting research papers; writing and presenting a dissertation on a research topic.

Minimum requirements and assessment criteria

Previous knowledge required: knowledge in Mathematical Analysis (particularly functional analysis), a course in Partial Differential and some basics in Probability.

Examination topics

Reading list

Lecture notes will be provided with a comprehensive bibliography.

Association in the course directory

MAMV, MBIV

Last modified: Mo 07.09.2020 15:40