Universität Wien

250155 VU Cosmic Structures: Theory, Numerics, and Statistics (2024S)

6.00 ECTS (3.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 05.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.03. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.04. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.04. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.05. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.05. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 11.06. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.06. 09:45 - 11:15 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

How did structure in the Universe form? And how do we describe it mathematically? The formation of complex structure in our Universe from quantum fluctuations through non-linear processes is one of the key topics of modern cosmology. The goal of this course is to study the wide range of mathematical concepts (analytical, numerical, statistical) relevant for this rich problem.

This course is aimed at a broad audience of students in applied mathematics, physics, astrophysics, or computational science. We will touch on a wide range of topics in applied mathematics such as (not in chronological order)
- random fields and properties of excursion and level sets
- analytical methods for PDEs and ODEs: perturbation theory and asymptotic methods
- numerical solutions of PDEs: N-body and finite volume methods
- data analysis and spatial statistics
- and inverse problems (time permitting)

We will motivate the key equations and then approach their solutions and the associated phenomenology. The relevant (astro-)physical concepts (the expanding universe, the cosmic microwave background, cosmic inflation, the Vlasov-Poisson and Euler-Poisson system, the distribution of galaxies, and more…) will be briefly introduced and discussed to motivate the physical background and context.

An important aspect of the course will be hands-on exercises based on (1) numerical experiments with Python, as well as (2) analytical/perturbative calculations.

Some familiarity with Python is necessary to carry out the numerical exercises. Please note that familiarity with Differential Geometry/General Relativity, or Astrophysics is *not* a pre-requisite for this course.

Assessment and permitted materials

The final mark will come from a series homework problem sets, as well as a short focus project paper (i.e., a more in-depth follow-up study of one of the topics of the course, topics will be suggested and mutually agreed upon).

Minimum requirements and assessment criteria

Final mark will be 67% from homework problems points, 33% from 4-5 page write-up of focus project at the end of term. Homework can be done in groups, focus project must be carried out and submitted individually.

Examination topics

n/a

Reading list

Lecture notes will be provided ahead of each session through moodle.

Association in the course directory

MAMV

Last modified: We 31.07.2024 12:06