Seminario del grupo de teoría de Lie

Julia Pevtsova – Lunes 30 de noviembre 14:00hs

Resumen:

This talk will be dedicated to the memory of Len Evens who sadly passed away earlier this month.

In 2004 Etingof and Ostrik stated in print a conjecture which had existed in a folkloric form for at least two decades before that: “{\it the cohomology ring of a finite tensor category is finitely generated}”. The first evidence of the conjecture appears in the work of Golod, Venkov and Evens in 1959-1961 who showed that the cohomology of a finite group with mod p coefficients is finitely generated. Evens was the one who realized what the correct finite generation condition should mean and also left us with a wonderful tool now known as the «Evens lemma” which keeps making appearances in the proofs of finite generation again and again.  

Since then finite generation of cohomology has been established for many different representation categories, such as the ones for modular Lie algebras, small quantum groups, Lie superalgebras, finite group schemes, and Nichols algebras of diagonal type. The general case of the conjecture remains wide open though.

In the talk I’ll (partially) describe what is known and will try to touch upon some geometric applications which are the major driving forces for the recent interest in the finite generation conjecture. 

Based on joint work with N. Andruskiewitsch, I Angiono, S. Witherspoon; and also with C. Negron.