Thesis topic: Explicit description of isogeny and isomorphism classes of Drinfeld modules of higher rank over finite fields.
Dr. Sedric Nkotto Nkung Assong, AIMS-Cameroon alumnus of the 2014-2015 batch and tutor from September 2015 to September 2017, has successfully earned a doctorate in Mathematics, precisely in the field of Algebraic Number Theory at the University of Kassel, Germany.
This breakthrough was realized under the supervision of Prof. Dr. Hans Georg Rück, with the main aim being threefold: (1) to explicitly determine the complete list of Weil polynomials describing the isogeny classes of Drinfeld modules; (2) to explicitly characterize the isomorphism classes of Drinfeld modules, and (3) to describe the orders occurring as endomorphism rings of Drinfeld module in a given isogeny class.
During his defense on July 1st 2020, Sedric came up with three major results. The first describes, explicitly, the Weil polynomials defining the isogeny classes of rank r Drinfeld modules for any r > 2 and provides an algorithm that helps to compute the complete list of these polynomials. The second provides a necessary and sufficient condition for an order in the endomorphism algebra associated to some isogeny classes to occur as endomorphism ring of a Drinfeld module. For the last major result, Sedric provided a new isomorphy invariant he termed “fine isomorphy invariant” proving that this invariant, together with the J-Invariants, completely determines the L-isomorphism classes of Drinfeld modules defined over a finite field L.
“I would first of all like to thank the AIMS network especially AIMS-Cameroon where everything started. From my Structured Master degree (2014/15) to the 2 years of job opportunity as tutor at AIMS-Cameroon, I have learned a lot during those years and met wonderful people. I will never ever forget it”, he said, while acknowledging the efforts of all parties that contributed to the successful completion of his PhD studies.
“I owe many thanks to the University Kassel for the opportunity I got to pursue my PhD studies at its Institute of Mathematics and also for the Teaching Assistant job opportunity I got that allowed me to fund my PhD study” he added.
Dr. Nkotto has been working as Teaching Assistant at the Institute of Mathematics of the University of Kassel since September 2017. With this achievement, he joins the ever growing list of AIMS-Cameroon alumni to have defended a PhD like Dr. Merlin Mouafo, Dr. Woldegebriel Assefa, Dr. Nkongho Ayuketang, Dr. Jean-Daniel Djida, Dr. Bertrand Teguia and Dr. Noé Carème Fouotsa. His research interests include the arithmetic of function fields and the drinfeld modules.