The Department of Mathematics, in collaboration with the National Centre for Mathematics, organised an AIS school on p-adic methods in Arithmetic from June 26 to July 15, 2023 at the campus. Over 58 students, research scholars, post-doc fellows and faculty from reputed universities such as IIT Hyderabad, IIT Guwahati, IISER, University of Hyderabad, Pondicherry University, Banaras Hindu University etc. participated in the three-week-long AIS school, which was conducted with the prime objective to study the p-adic numbers and the p-adic methods in arithmetic.
Prof. C S Rajan, Ashoka University; Dr Manish Kumar Pandey and Dr Sazzad Ali Biswas, SRM University-AP; Dr Amiya Kumar Mondal, IISER Berhampur; Dr Santosh Nadimpalli, IIT Kanpur; Dr Shaunak Deo, IISc, Bangalore; and Dr Mihir Sheth, Post-Doc, IISc, Bangalore were the speakers at the school. The sessions were delivered in collaboration with course associates /tutors. Dr Arindam Jana, Postdoc, TIFR Mumbai; Dr Ravitheja Vangola, Postdoc, IISC Bangalore; Mr Sagar Shrivastava, Mr Manodeep Raha, and Mr Niladri Sekhar Patra, PhD scholar, TIFR Mumbai were the tutors mentoring the participants.
Prof. C S Rajan delivered 9 lectures – four lectures in the first week of the programme and five lectures at the end of the programme. The first part of his session covered topics such as Hensel’s Lemma and Local-Global Principle while the latter part focused on the Main Conjecture of Iwasawa Theory and Introduction to the work of Ribet (Converse to Herbrand) and subsequent work.
Dr Sazzad Ali Biswas offered his insights on topics like Construction of p-adic numbers, Various Properties (algebraic and Analytic) of p-adic numbers, Arithmetic operations of p-adic numbers and Local-Global Principle in five sessions. Dr Manish Kumar Pandey gave two lectures on the Special values of the Riemann zeta functions.
Local Fields, Global Fields and p-adic algebraic numbers were the focal points of the four lectures delivered by Dr Mihir Sheth. Dr Amiya Kumar Mondal took five lectures on Modular Forms and Dr Santosh Nadimpally gave five lectures on the Construction of p-adic zeta functions and the Various properties of p-adic Zeta function. Dr Shaunak Deo dealt with topics including Cyclotomic Fields, Iwasawa’s Construction of p-adic L-fucntions and p-adic Family of Modular Forms through six lectures.
The AIS School was organised by Prof. C S Rajan of Ashoka University and Assistant Professors Dr Manish Kumar Pandey and Dr Sazzad Ali Biswas of the Department of Mathematics at SRM University-AP. The programme successfully concluded with the active participation of students, scholars and faculty who assembled to exchange constructive discourse on p-adic methods in Arithmartics.