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Professor Dr. Frank Neumann

Dipartimento di Matematica ‘Felice Casorati’

Università di Pavia via Ferrata, 5 · 27100 Pavia Italia

The main objective of my visit to LUMS in Lahore has been to teach parts of the course on Complex Analysis as part of the LUMS-ICTP International Mathematics Master (IMM) programme.

The rest of the course is taught by Prof. Sultan Sial (LUMS) and Prof. Alberto Abbondandolo (Bochum). I prepared detailed lecture notes and in addition slides for the course as well as assignments with sample solutions. All material is shared on the LUMS online learning platform (LMS). The course is attended by 11 IMM master students, nine from Pakistan and two foreign students from Algeria. The background of the students was very mixed, but most of them had already seen some basic concepts from complex analysis. The students were always very engaging during class and tutorials. The level is comparable with good 3rd year undergraduate students in Italy. I gave two assignments on the material which were marked individually by me. The results were in general pretty good. The students were asked to discuss and work on the problems in one of the tutorials and then were voluntarily asked to present their solutions at the board to the others. This worked very well, and I was very impressed about their enthusiasm and engagement. The results of the assignments and the presentations of solutions were of a very good standard. Several students also obtained full marks on one or even both assignments. The first exam was given on February 19.

I taught the part of the course concerning basic material on complex numbers and complex-valued functions, complex differentiation, holomorphic and meromorphic functions, classification of singularities, power series and basics of complex integration.

The environment, facilities, and logistics at the Department of Mathematics at LUMS were excellent. The classrooms and the lecture room were very good with large blackboards and a data projector for slide presentations. The internet was working well everywhere in the department and on campus in general. I was given excellent office space in the department and students came frequently to see me and discuss the material from the course and beyond.

The administrators of the Department of Mathematics at LUMS are excellent and very supportive. They helped me with anything I needed and acted very competently and promptly. It was a great pleasure to work with them and I am very grateful for their support. I was also very impressed by the professionalism, support and enthusiasm concerning the IMM programme from anyone in the Department of Mathematics.

Besides the IMM lecture course on complex analysis, I also gave a research talk in the research seminar as well as a general interest talk as part of the John Conway spirited seminar series. This series is an excellent idea, and it is becoming already a well-received worldwide institution as the list of the many high-level local and international speakers and topics of talks clearly shows. I was also invited through LUMS contacts to give a general audience talk at Kinnaird College for Women in Lahore. This was a great success and an additional wonderful outreach experience. It is clear for me that other universities in Lahore will also profit from the enthusiasm and engagement with the international mathematics community by the LUMS mathematics faculty. I like to mention, in particular the Chair of the Department of Mathematics Prof. Imran Anwar who does an incredible job and his enthusiasm is amazing. The Department of Mathematics at LUMS can play a leading role as a center of excellence for international collaboration with Pakistan.

In conclusion, I believe that the Department of Mathematics at LUMS provides an excellent environment for the IMM programme and beyond and that lasting sustainable relations including future research collaborations between the local LUMS faculty and the international mathematical community will arise as a result of the IMM programme.


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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