Department of Mathematics


  •  Romyar Sharifi, UCLA
  •  Modular symbols and the arithmetic of cyclotomic fields
  •  10/10/2019
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

The arithmetic of cyclotomic fields, and the structure of their class groups, has been studied since the time of Kummer in connection with Fermat’s Last Theorem. The work of Ribet in 1976 uncovered a subtle influence of the geometry of modular curves on this structure. I’ll discuss how this connection goes even deeper and define a surprisingly explicit map from the homology group of a modular curve to a K-group related to the class group of a cyclotomic field. I’ll then indicate how this is turning out to be just one instance of a more general phenomenon, touching briefly on joint work with Takako Fukaya and Kazuya Kato and separate joint work with Akshay Venkatesh.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science