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Daniele Angella

Professore Ordinario

Universita Degli Studi Firenze ·

The aim of my visit to LUMS has been to teach part of the course on Advanced Topology for the LUMS-ITCP International Mathematics Master. More precisely, I taught the first part of the course. My lectures covered the introduction of topological spaces and continuous functions, topologies on metric spaces, some fundamental topological invariants, constructions of products and quotients of topological spaces, including function spaces, and the concept of connectedness. I delivered four lectures of 75 minutes each and seven tutorials of 90 minutes each. The rest of the course is taught by prof. Haniya Azam of LUMS and prof. Christian Blanchet of Institut de Mathématiques de Jussieu, Université de Paris.

I had 9 students, seven of them from Pakistan and two from Algeria. The overall background was quite good, albeit with differences among them. While some had previously completed a Topology course with a solid foundation, others exhibited lacks in specific topics, and one student had never attended a Topology course. The course organization, including lectures and tutorials, has, I hope, allowed me to both address the students with a weaker exposition to topology and engage the more motivated students with new topics and examples.

They all shared a keen interest for the subject. They were highly engaged, participating actively both during the lectures and in post-class discussions. Their level was generally better than the level of second-year bachelor students in Italy, which is the level requested by the course.

During my stay I gave two assignments. A midterm exam is planned for mid-February. I corrected the first assignment while I still was in Lahore and the results were excellent: all students passed it, with marks between 95 % and 98 %. The second assignment is due in a couple of days : some students already submitted or discussed their solutions with me, therefore I expect similar positive results, although the difficulty level is higher than for the previous assignment.

The logistics and the facilities in the Department of Mathematics in LUMS were very good. Both classrooms I used had good blackboards and the wi-fi was working well in the whole building. I had access to a highly functional office in the Department 24 hours a day, and also the students could enter the Department and use the common room and a dedicated office for study and discussions at any time. The library at LUMS is not only accessible and comfortable but also furnished with an excellent catalog of books in mathematics, among other disciplines.

During my stay, I also gave a general interest talk on « Classification of surfaces : a path from topology to differential geometry to complex analysis » for the John Conway Spirited Mathematics Seminar Series. The conference room was technologically well-equipped. The talk was widely promoted, not only within the Department of Mathematics but throughout the entire School of Science and Engineering. The audience comprised faculty members and students, as well as online participants tuning in via streaming. I also delivered a similar talk at the University of Education, Bank Road Campus. It was an excellent opportunity for discussions, exchanging experiences and ideas, and establishing connections with the faculty members and students of the University of Education.

The administrative staff is excellent; they are very competent and were able to solve any problem I might have had. The lodging arrangements on the LUMS campus, as well as other services such as dining facilities, were very satisfactory too. In summary, I believe that the Department of Mathematics at LUMS can offer an excellent environment for the students of the International Mathematics Master and can facilitate valuable connections between the local faculty, other faculties in Lahore and Pakistan, and the worldwide mathematical community.


Applicants are divided into two groups: "International Applicants" who have foreign citizenship and "Pakistani Applicants" who either hold Pakistani citizenship, have dual citizenship, or are Pakistanis residing outside the country.

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