**First Meeting: **

**Class Timings: **

**Course Description: **

- how populations grow: logistic models and frequency dependent growth
- how multiple species coexist: biodiversity, predator-prey and Lotka-Volterra models
- how populations interact: resource competition and cooperation, consumer-resource models
- how ecosystems remain stable: the May bound and the ecological instability transition
- random matrix, network science and geometric approaches to ecology
- multistability, stochasticity, and catastrophes in ecosystems
- statistical inference and data-driven approaches to ecology
- spatiotemporal structure and metacommunity ecology
- evolutionary processes: selection, mutation, and drift
- dynamics on fitness landscapes, epistasis and ruggedness
- recombination and linkage disequilibrium

**Course Evaluation: **Homework assignments, mid-semester & end-semester exams

**Perquisites: **Mathematical physics at 1st year graduate student level

**Textbooks:**

- Mark Kot, Elements of Mathematical Ecology (Cambridge University Press, 2012
- Robert May and Angela McLean, Theoretical Ecology: Principles and Applications (Oxford University Press, 2007)
- Kevin S. McCann and Gabriel Gellner, Theoretical Ecology: Concepts and Applications (Oxford University Press, 2020)
- Martin Nowak, Evolutionary Dynamics: Exploring the Equations of Life (Harvard University Press, 2006)

**References**

Statistical physics and dynamics of evolution

- “Evolution in rapidly evolving populations”, BH Good, Harvard University (2016)
- "Evolutionary dynamics", DS Fisher, Les Houches Course (2006)
- "Statistical Genetics and Evolution of Quantitative Traits", RA Neher and BI Shraiman, Reviews of Modern Physics (2011)
- "Genetic demixing and the evolution in linear stepping stone models", K. S. Korolev, Mikkel Avlund, Oskar Hallatschek, and David R. Nelson,Reviews of Modern Physics (2010)

**Venue: **Feynman Lecture Hall

**First Meeting: **9 January 2024

**Class Timings: **Tuesdays from 10:00 - 11:30 AM

**Course Description:** This course will provide a concise introduction to astronomical objects e.g. stars, galaxies, the different kinds of observations that are being made today, and a basic model for each . This will include the relevant physics when not already covered in the prerequisites. It is aimed at new entrants to the graduate programme, (second semester) or others who may want some basic astrophysical background for their own research, or out of general interest.

**References:**

- Astrophysics for Physicists by Arnab Rai Choudhuri, Cambridge university press, 2010
- An Introduction to modern astrophysics Carroll and Ostlie Addison Wesley 2007

**Course Evaluation:** Will be based on assignments which fill in details and applications outlined in the lectures, and one presentation of a topic (different for each student) going into more depth than in the course, based on independent study of available materials.

**Course Outcome: **For new entrants to the graduate programme, it will prepare them to do second year projects in the more advanced areas of astrophysics being pursued at ICTS, help them decide whether to pursue a PhD in those areas. For those who go into research in other areas e.g. condensed matter, particle physics etc. it would act as a basic introduction to the subject.

**Perquisites:** Basic knowledge of condensed matter physics at the level of Ashcroft
and Mermin, second quantization, relativistic quantum mechanics

- Teacher: Rajaram Nityananda