Skip to main content

Maths and Physics Seminars

I will be maintaining a public calendar for our ongoing maths and theoretical physics seminars here.

The seminars so far have been about abstract harmonic analysis (following Deitmar-Echterhoff), differential geometry (loosely following several different books and notes), and some basic physics from a mathematical standpoint (a bit of Hall's Quantum Theory for Mathematicians, and possibly some general relativity in the future). Currently, we are also reading Cohen-Gelander's "An Invitation to Analytic Group Theory" and have planned a series of lectures that build up to the spectral theorem for normal operators. For any questions, comments, or suggestions, feel free to reach out!

Popular posts from this blog

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...
Read more

गणित क्यूं?

यह लेख एम. ए. सोफी के "ग्रेटर कश्मीर" में प्रकाशित "Public Perception of Mathematics" से प्रेरित है। सोफी उस अपेक्षित प्रश्न का उत्तर देने का प्रयास करते हैं जिससे हर (भारतीय) गणितज्ञ अपने जीवनकाल में निरंतर जूझते हैं - "आख़िर गणित में शोध होता क्या है"? अक़्सर अगली टिपण्णी गणित के "समाप्त" हो जाने की दिशा में होती है (इस सवाल से मेरी पहली मुलाक़ात बारहवीं कक्षा में ही हो गई थी)। इस लेख के माध्यम से मैं गणित के इतिहास और विकास के चुनिंदा पहलुओं से परिचय करवाना चाहूंगा। साथ ही, मैं गणित में शोध की प्राकृतिक पृष्ठभूमि पर प्रकाश डालने का प्रयत्न करूंगा।  यह कहना पूर्णतः गलत नहीं होगा कि गणित का प्राचीन काल में निर्माण काफ़ी हद तक मानव सभ्यता की आवश्यकताओं के कारण हुआ था। लगभग अलग-अलग सभ्यताओं (भारत, चीन, मिस्र, मेसोपोटामिया, ग्रीस, इत्यादि) में अंकगणित और ज्यामिति का विकास हिसाब-किताब, संसाधनों के उचित बंटवारे, और विभिन्न निर्माण कार्यों में उपजने वाली समस्याओं के साथ तालमेल में हुआ। जमा, गुना, घटा, भाग, अनुपात, अथवा ज़मीन और निर्माण से संबंधित परिम...
Read more

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...
Read more