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Marco Abate

Dipartimento di Matematica

Universit `a degli Studi di Pisa · Italy

The aim of my visit to LUMS has been to teach part of the course on Differential geometry for the LUMS-ITCP International Mathematics Master. More precisely, I taught the part of the course concerning the definitions of regular surfaces in space, of smooth functions on regular surfaces, of tangent spaces of regular surfaces and of differential of a smooth function on regular surfaces. The rest of the course is taught by prof. Waqas Ali Azhar of LUMS and Prof. Abdelghani Zeghib of ENS-Lyon.

I had 14 students, most from Pakistan but some also from foreign countries. Their background was quite diverse, but they all shared a keen interest for the subject; in particular, they were quite active in class as well as after class, asking many intelligent questions and sometimes even suggesting alternative approaches. Their level was, on the average, comparable to third-year bachelor students in Italy, which is the level requested by the course. They all had a reasonably solid background in real analysis of several variables; on the other hand, some of them were less familiar with the basics of topology.

During my stay I gave a midterm exam and two assignments. I corrected the exam while I still was in Lahore and the results were quite good: all students passed it, four of them with full marks.

The assignments were more difficult, but they had more time to return them. The first assignment has been failed by three students only (and two received full marks); the results of the second assignment were slightly worse, but still more than half of the students passed it reasonably well (and one received full marks).

The logistics and the facilities in the Department of Mathematics in LUMS were very good. Both classrooms I used had good blackboards and comfortable seats for the students. The wi-fi was working well in the whole building. I had an once with all what I needed. I also noticed that the students could enter the common room of the Department and use it for study and discussions at any time, which is quite a good thing.

I also gave a general interest talk to the Faculty of LUMS, in a well-furnished conference room; in that occasion I also had the possibility to visit laboratories and other facilities available to students and professors. I found particularly interesting the start-up incubator with the possibility of building prototypes.

The administrative staff is excellent; they are very competent and were able to solve any problem I might have had. The lodgings arrangements in the LUMS campus were quite satisfactory too. Summing up, the Department of Mathematics at LUMS in my opinion can provide a good environment for the students of the International Mathematics Master and can foster useful relations between the local Faculty 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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