În data de 10 martie 2015, ora 12.30, în amfiteatrul Tiberiu Popoviciu din clădirea centrală a Universităţii Babeş-Bolyai va avea loc conferinţa invitată a dlui prof. dr. Gavril FARKAS, Humboldt Universität zu Berlin, Institut für Mathematik, cu titlul What is an abelian variety of dimension six?

Prof. dr. Gavril Farkas este absolvent al facultăţii noastre în anul 1995, fiind un matematician din prima linie a cercetării ştiinţifice de Geometrie algebrică, cu publicaţii în reviste de top, precum Annals of Mathematics, Inventiones Mathematicae, Mathemaische Annalen, sau Journal of the European Mathematical Society. De asemenea, prof. Gavril Farkas se numără printre câştigătorii premiilor Ad Astra privind excelenţa în cercetare pe anul 2014.

Abstract: Abelian varieties are group varieties, that is, loci of points given by polynomial equations which simultaneously admit a group structure. Abelian varieties are fundamental mathematical objects playing a central role in algebraic geometry, complex analysis (via the theta functions), dynamical systems or theoretical physics. It has been known for a century that all abelian varieties of dimension at most five are either Jacobians corresponding to algebraic curves, or Prym varieties. This allows one to reduce the study of abelian varieties of small dimension to the rich and concrete theory of curves.

In the first half of this talk, I will present a mathematical and historical introduction to the classification problem of abelian varieties. In the second half, I will discuss recent decisive progress on finding a structure theorem for abelian varieties of dimension six, as Prym-Tyurin varieties associated to coverings of curves with fibres having the structure of the set of 27 lines on a cubic surface.