ICTS

In the 1960’s Barry Mazur called attention to an ‘analogy between knots and primes’, in terms of which he conceptualised the Main Conjecture of Iwasawa Theory relating p-adic L-functions and ideal class groups. This analogy led his research away from topology and into number theory, after which he...more

In these lectures I will outline a proof of the Atiyah-Singer Index theorem. I will begin with the definition of the symbol $\sigma_l$ of a linear differential operator $L$ and the notion of ellipticity of $L$. I go on to define the analytic index $i_a(L)$ of a linear elliptic differential operator...more

Lecture -01: Introduction to modular forms and modular curves Speaker: Anna-Maria Pippich (University of Konstanz, Germany) Date & Time: 13th March 2024 from 10:30 AM to 11:30 AM (IST) Abstract: In the first lecture, we will give an introduction to the classical theory of modular forms for the...more

Course Description: This is a semester course on compact groups with special emphasis on compact connected Lie groups, their structure theory and the theory of representations of such groups. We first prove general results like complete reducibility , Schur's lemma , and orthogonality relations. We...more

On the occasion of A.N. Kolmogorov’s 120th Birthday the symposium will feature talks by leading researchers in the fields where Kolmogorov had an impact on in its early stages. Zoom link: https://icts-res-in.zoom.us/j/84556101498?pwd=ZU9HU0YzcnhZR1ZqcU9EWC81Vm9rUT09 Meeting ID: 845 5610 1498...more

ICTS is pleased to announce a special lecture series by Prof. Sunil Mukhi as a centennial tribute to Prof. Amal Kumar Raychaudhuri. Amal Kumar Raychaudhuri (14 Sep 1923 – 18 June 2005) was an Indian physicist, known for his pioneering work in general relativity and cosmology. His most significant...more

In these informal lectures, I shall try to describe the procedure for computing perturbative amplitudes in superstring theory. This can be regarded as a crash course on the subject, primarily for advanced graduate students and post-docs, where I shall skip many derivations but will try to explain...more