Skip to main content

Talks

Here is a (still small) list of talks and presentations that I have delivered.
  1. Completeness in Propositional Logic (May 2022); a student presentation in the 9th Indian School on Logic and Applications (ISLA).
  2. Basic Mathematics (September 2023); a talk on basic set theory and the language of mathematics, aimed at first-year undergraduate students.
  3. An Introduction to Fraïssé Constructions (November 2023); seminar presentation on Fraïssé constructions in first order logic, which allow us to construct special models of a theory in some situations.
  4. The Poincaré Recurrence Theorem (April 2024); seminar presentation on the Poincaré recurrence theorem, a simple yet foundational result in ergodic theory.
  5. The Bonnet-Myers Theorem (November 2024); presentation for a course in Riemannian Geometry. I closely stuck with the presentation in Lee's "Introduction to Riemannian Manifolds" but had to blackbox a crucial Laplacian comparison theorem due to time constraints.
  6. Wittgenstein's Language Games: A Defence Using Large Language Models (November 2024); presentation for a course in Philosophy of Language. Inspired by this article, I decided to pursue a defence of language games paradigm using LLMs. While largely unconvinced if my argument stands up to scrutiny, I believe LLMs provide an interesting playground for several philosophical problems.

Popular posts from this blog

Maths Teachers Orientation Camp: Some Reflections on Maths Education in India

Last week, IISER-Mohali hosted the Mathematics Teachers Orientation Camp (MTOC) sponsored by Homi Bhabha Centre for Science Education (HBCSE), TIFR. The objective of this camp (and similar camps conducted by HBCSE elsewhere in the country) is to introduce and expose high school mathematics teachers and educators to fresh perspectives on their subject through interactive talks and problem-solving sessions. This is not strictly bound to the school curriculum, but the topics centre around things that can be assumed to be reasonably accessible for someone out of touch with (under)graduate level mathematics for years. As a volunteer for this camp (primarily engaged in hospitality for the educators arriving on the campus), I got to interact with many of these educators who hailed from Uttarakhand and Punjab (teachers from other regions, especially J&K, Himachal, and Haryana, had to back out due to the approaching final exams). While I missed out on the opportunity to hear about the exper...
Post a Comment
Read more

The Poincaré Recurrence Theorem

Recurrence in phenomena, physical or otherwise, has piqued the curiosity of humans for a long time. Without going into a historical detour on the study of periodic phenomena (of which the author is painfully ignorant), we cut to the chase and introduce one of the foundational results of ergodic theory: the Poincaré Recurrence Theorem. The theorem essentially states that under certain transformations of a space (to be made precise shortly), the system will almost return to its initial state under repeated iterations of the transformation. Preliminaries In order to state the theorem, we recall the definition of a probability space and a measure-preserving transformation here. Definition. [Probability Space] A probability space $(X,\mathcal{B},\mu)$ is a nonempty set $X$, a $\sigma$-algebra $\mathcal{B}$ on $X$, and a measure $\mu$ on $(X,\mathcal{B})$ with $\mu(X)=1$. Assume further that the space $(X,\mathcal{B},\mu)$ is complete, in the sense that all subsets of measurable subs...
Post a Comment
Read more