A CIMPA school on
Effective Algebra and the LMFDB
at Makerere University, Uganda
January 13 - 24, 2025













CIMPA poster here!
  • CIMPA poster
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    The main focus of the school will be the mathematics 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. A main series of plenary lectures will introduce the students to L-functions, modular forms, elliptic curves, and their relations. It will also show how these interconnections generalize to broader contexts, such as those of curves of small genus and abelian varieties. Besides this lecture series and an initial recapitulation of some topics in elementary arithmetic geometry, the school will feature eight research groups on the following topics:
    1. Geometry of algebraic curves of small genus.
    2. Arithmetic of algebraic curves of small genus.
    3. Modular curves, modular forms, and the associated geometric constructions.
    4. L-functions and Galois representations associated to elliptic curves.
    5. Isogeny graphs and the resulting cryptography.
    6. Abelian varieties over finite fields and their isogeny classes.
    7. Arithmetic statistics, including the Sato--Tate conjecture.
    8. Cyclic Galois covers of the projective line (Superelliptic curves and Artin-Scheier curves).

    Organizing Committee
    1. Prof. Elisa Lorenzo Garcia, CIMPA supervisor (Universite de Neuchatel, Switzerland)
    2. Prof. Jeroen Sijsling, international coordinator (Ulm University, Germany)
    3. Dr. Alex Samuel Bamunoba, local coordinator (Makerere University, Uganda)
    4. Dr. Innocent Ndikubwayo (Makerere University, Uganda)
    5. Dr. Geoffrey Ismail Mirumbe (Makerere University, Uganda)
    6. Dr. Annet Kyomuhangi (Busitema University, Uganda)
    7. Dr. Mahadi Ddamulira (Makerere University, Uganda)
    8. Prof. David Ssevviiri (Makerere University, Uganda)
    9. Dr. Sarah Nakato (Kabale University, Uganda)
    10. Dr. Olivia Nabawanda (Mbarara University of Science and Technology, Uganda)

    For any more information regarding the school, please contact the local organisers at cimpa2005makerere@gmail.com: click here to send an e-mail
    We gratefully acknowledge the support of: