The Makerere-CIMPA School on “Effective Algebra and the LMFDB” is a mathematical research and training event organized in collaboration with the Centre International de Mathématiques Pures et Appliquées (CIMPA) and Makerere University.
This 2025 Makerere-CIMPA School hosted by the Department of Mathematics, College of Natural Sciences at Makerere University took place on 13th-24 January.
The school is designed to provide advanced training in Algebra, Number Theory, Geometry and Cryptography and to facilitate the exchange of knowledge and ideas among researchers and students from various countries. The main focus of this year was the number theory around the L-functions and modular forms database (LMFDB), aimed at introducing the students to the main ideas and philosophies around modularity theorems. These relate to the mathematics behind the famous Fermat’s Last Theorem which connect algebraic curves and abelian varieties on one side with modular forms and L-functions on the other. Theoretically, such ideas are part of the Langlands program; the LMFDB can be seen as a way to make this program accessible and concrete by means of a huge treasure trove of examples. Participants learnt the concepts behind modularity conjectures, and how these relate with the huge treasure trove of examples furnished by the LMFDB. They also obtained deeper knowledge on one of the themes of a number of research groups that was devoted to supervised research on a more specialized mathematical topic in the area.
A series of plenary lectures by Prof. Aurel Page introduced the students to L-functions, Galois representations modular forms, elliptic curves, and their mutual relations. Besides this, the School featured five research groups on the following topics:
1. Isogeny graphs and the resulting cryptography.
2. Abelian varieties over finite fields and their isogeny classes.
3. The Sato–Tate and Galois representations.
4. L-functions and Galois representations associated to elliptic curves.
5. Artin-Schreier curves.
The School was co-organised by Prof. Jeroen Sijsling (Ulm University, Germany, and Dr. Alex Samuel Bamunoba (Makerere University).
Members of the scientific committee included Prof. Elisa Lorenzo Garcia (Switzerland, and the CIMPA representative at the school), Prof. David Ssevviiri, Dr. Innocent Ndikubwayo, Dr. Mahadi Ddamulira, all from Makerere University, Dr. Olivia Nabawanda (MUST), Dr. Sarah Nakato (Kabale University), and Dr. Annet Kyomuhangi (Busitema University).
The speakers were from USA, UK, Italy, Germany, Denmark, France, Egypt, and included the following; Prof. Sorina Ionica, Prof. Sabrina Kunzweiler, Prof. Stefano Marseglia, Prof. Leonardo Colo, Prof. David Kohel, Prof Barinder Banwait, Prof. Aurel Page, Prof. Ahmad ElGuindy, Prof. Fabien Pazuki, Prof. Elisa Lorenzo Garcia and Prof. Beth Malmskog. There were about 45 participants (masters, PhD students and postdocs) from countries like, Cameroon, Ghana, Chad, Tanzania, Kenya, Uganda, India, Egypt and South Africa.
These research schools are typically held as part of CIMPA’s mission to promote mathematical education, collaboration and research, especially in developing regions. The Makerere-CIMPA School, in particular, provides an opportunity for students and researchers from across Africa to deepen their mathematical understanding, engage in collaborative research, and learn from world-reknowned mathematicians, which is in line with University’s current mission of graduate training, research and innovation.
The School generally features lectures, practical sessions on a specific mathematical topic or research area, often focusing on a blend of both pure and applied mathematics. This encourages networking and foster collaborations between mathematicians, especially those from countries with emerging or developing mathematical research communities.
By hosting such schools, Makerere University and CIMPA contribute to strengthening the mathematical community in Uganda and Africa, providing a platform for further mathematical advancements and fostering the growth of young researchers in the region.
The Makerere-CIMPA School plays a significant role in building bridges between academic institutions, researchers, and students from different parts of the world.
The School was mainly funded by CIMPA, Makerere University, Elsevier Inc., Journal of Number Theory (an Elsevier journal), International Mathematical Union – Center for Developing Countries (IMU-CDC in short), and the Uganda Mathematical Society (UMS).
