Prof. Dr. P. Stevenhagen’s Report on his visit to LUMS, Lahore (Oct-Nov ’24)

“My second visit to the Syed Babar Ali School of Science and Engineering (SBASSE)
at LUMS took place from October 21 to November 15, 2024. […] I started my Algebra teaching on the Tuesday my plane landed in Lahore, and gave a final lecture on constructible numbers in the final afternoon before my departure, bringing 23 very full days to a close. Having taken some more time than the two standard weeks typically allotted to an international IMM lecturer enabled me to have a truly gratifying program. This time, I could advertise IMM a bit in other parts of Pakistan, and discover some parts of Pakistan that were very different from Lahore, and the home of some of our students.

The Advanced Algebra course that formed my teaching assignment had been organized a bit differently from last year. Frank Neumann (Pavia) had taken care of the initial part of the course dealing with group theory in September, and local teacher Imran Anwar had made a beginning with the ring theory part of the course. My task was to treat Galois theory, which makes up the final part of the standard Leiden Algebra course that we are mostly following in IMM. I used the two lectures I had in my first week to treat some additional group theory needed to explain the RSA cryptosystem and used the occasion to talk on applied algebra and, more in particular, cryptography. Weeks 2 and 3 were devoted to intensive teaching leading up to the understanding of the main theorem of Galois theory, which fits on a postcard
but comes to life only by a wealth of examples and applications. […] The final lecture on constructible numbers in week 4 showed the long history of the subject and its famous applications to problems that had remained unsolved for many centuries.

Apart from my ‘first year teaching’ for a dozen IMM students, I also spent time with the three second-year students who had chosen to do their master thesis topic with me: Amna, Usama, and Zoha. We selected topics matching their interest, and they made a beginning with their study of these topics. The supervision by international faculty is an intrinsic part of the IMM program, and I am in regular contact
now with my students, who have also started their application process for graduate programs in the US, and who appreciate receiving help and guidance and, of course, letters of recommendation. My interaction with all IMM students was just as pleasant and friendly as last year. This year’s group is maybe even more (inter)active than last year’s.

The main difference between this year’s and last year’s visit was my commitment to travel a bit inside Pakistan. Already on the night of my second day in Lahore, LUMS had organized transportation for me and 2 students (Masood and Zoha) to Peshawar, where I gave talks at 3 very different universities in the 2 following days: University of Peshawar, City University (private) and Government Degree College Hayatabad. The talks had a correspondingly different focus, dealing with mathematics in different ways, how to have a career in mathematics, and what the role of IMM might be in this.

Walking around in KPK and the bazaar of Peshawar is an experience that is currently not shared by many international visitors, but a very pleasant experience when organized with Pashtun hosts. The same applied to the weekend afterward, when Masood’s former undergraduate advisor Adil Khan invited us for lunch at his family house in Swat Valley and showed us around. On our final day in KPK, we visited Malam Jabba, a mountainous part that has skiing in winter, before catching a bus back to Islamabad. Even more mountainous was the Gilgit region that I could visit in my final week, and that does attract tourists in summer fleeing the heat. The natural beauty there is stunning, and flying there is an adventure in itself.

My hosts there were from Karakoram University, and I could meet up with LUMS Math Department faculty who were active there in a teacher training program. Here I gave a talk on Mathematics and Art focused on the mathematical phenomenon that underlies Dutch graphic artist Maurits Escher’s 1956 lithograph Print Gallery followed by a presentation on studying abroad in general, and of course on IMM. The Escher talk featured video clips using the software developed by the Leiden number theory group and went into the occurrences of the so-called Droste effect in images taken from all over the world. It can be adapted to almost any audience and is invariably appreciated – in Gilgit just as much as at the COMSATS campus in Lahore, where I was also invited to give it, shortly before leaving for Gilgit.

In general, I think that it is a good thing that the international teachers at IMM-LUMS contribute to its broader exposure in Pakistan. As for the future of IMM Pakistan, I am convinced that the formula chosen by IMM holds great promise for the future. Stability has to come from the Associazione
IMM on one side, on from structural support by LUMS on the other side. Following a longer conversation with the Dean of SBASSE that I had during my stay, I am confident that LUMS is aware of the value of its IMM program, which is well on its way to finding a stable and sustainable form. Just as last year, I conclude with a word of thanks and appreciation for the support staff of the LUMS math department, which made every aspect of my visit a totally smooth and problem free experience.”

Peter Stevenhagen