Sometime in the summer of 2019, I was back in India from my postdoc at Vienna, looking for jobs within India, and met my friend Amitabha Tripathi in his office in IIT, Delhi. At this time, Amitabha told me that he has a couple of students, and would I like to co-advise them?

Now Amitabha has played an important role in my career from time to time. In particular, he introduced me to egurucool.com, where I became head of Academics (essentially the “owner” of the product). At this time, it was not clear what he was thinking. Perhaps he had many PhD students at the time, and was too busy.

My own motive to accept the proposal was clear — I could now say to everyone: I have no job, but I have PhD students. Even though Amitabha told me that I would be an unofficial advisor, getting no credit whatsover in the IIT system.

Anyhow, over the next few months I gave a weekly lecture on techniques in Special Functions in Amitabha’s office, to Archna, Surbhi and perhaps a couple more students in Amitabha’s group. Around January 2020, they formally told me they would like to be my students, that is, work with me in q-series or related areas. Very soon thereafter, the covid lockdowns began. Our work continued for long after their PhD scholarships expired, and continued while they were Teaching Fellows in Ashoka University.

Here are the lecture notes: Special Functions by Example. The objective of the lectures was to quickly explain the techniques needed for work in this area. After these lectures, they both began working on finding new theorems.

The highlighted picture is from Cafe Central in Vienna, taken during their visit to Vienna in June 2023.

Update (July 9, 2025): Archana defended her thesis. Here is a picture with both her official and unofficial advisors.

This work generalises some formulas of Liu.

Archna’s work is in elliptic combinatorics, with an even more unofficial advisor, Michael Schlosser. The three of us wrote 2 joint papers.

The third paper with Archna is on elliptic hypergeometric series. It has appeared in the Proceedings of the American Math Society. The reference is:

1. Expansion formulas for elliptic hypergeometric series (with Archna Kumari), Proc. Amer. Math. Soc. 153 (2025), 3099-3112.

The images are from Archna and Surbhi’s visit to Vienna after a conference in Poland where they presented their work. They were invited by Michael Schlosser to give a talk in the University of Vienna to his students.

Here is a picture of Michael and me, going to the summer party of the math department (at Markus Fulmek’s house) in the same year.