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The main focus of this CIMPA school will be the modern number theory around the L-functions and modular forms database (LMFDB). It will introduce the students to the main ideas and philosophies around modularity theorems, 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.
The goal of the school is to introduce its participants to areas of current research in number theory. It is suitable for students from the master level onward, also including PhD and postdoctoral students. Its participants will not only learn the concepts behind modularity conjectures, but they will also see how these relate with the huge treasure trove of examples furnished by the LMFDB. Finally, they will obtain deeper knowledge on one of the themes of a number of research groups that will be devoted to supervised research on a more specialized mathematical topic in the area.
A main series of plenary lectures by Aurel Page will introduce the students to L-functions, Galois representations modular forms, elliptic curves, and their mutual relations. Besides this, the school will feature five research groups on the following topics:The main focus of this CIMPA school will be the mathematics around the L-functions and modular forms database (LMFDB). It is intended to introduce its participants to new active areas of research, and is suitable for students from the master level onward, also including PhD and postdoctoral students. The school will introduce the students to the main ideas and philosophies around modularity theorems, 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.
[A1] Isogeny graphs and the resulting cryptography. Sorina Ionica and Sabrina Kunzweiler.
[A2] Abelian varieties over finite fields and their isogeny classes. Stefano Marseglia.
[B1] The Sato--Tate and Galois representations. Leonardo Colò and David Kohel.
[B2] L-functions and Galois representations associated to elliptic curves. Barinder Banwait and Ahmad El-Guindy.
[C1] Artin-Schreier curves. Fabien Pazuki, Elisa Lorenzo García and Beth Malmskog.
Organizing Committee
- Prof. Elisa Lorenzo Garcia, CIMPA supervisor (Universite de Neuchatel, Switzerland)
- Prof. Jeroen Sijsling, international coordinator (Ulm University, Germany)
- Dr. Alex Samuel Bamunoba, local coordinator (Makerere University)
- Dr. Innocent Ndikubwayo (Makerere University)
- Dr. Geoffrey Ismail Mirumbe (Makerere University)
- Dr. Annet Kyomuhangi (Busitema University)
- Dr. Mahadi Ddamulira (Makerere University)
- Prof. David Ssevviiri (Makerere University)
- Dr. Sarah Nakato (Kabale University)
- Dr. Olivia Nabawanda (Mbarara University of Science and Technology)
For any more information regarding the school, please contact the local organisers at cimpa2025makerere@gmail.com: click here to send an e-mail
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