Princeton University/IAS Number Theory Seminar

This seminar meets each Tuesday at 4:45 and Thursday at 4:30, with the venue alternating between Fine Hall at PU and Simonyi Hall at the IAS. The one-hour-long talks present current research progress in number theory and related fields.  

For more information about this seminar, contact Rafael von Kanel, William Chen (IAS), Aaron Pollack (IAS).

Please click on seminar title for complete abstract.

October 24, 2017
4:45pm - 5:45pm
Elliptic curves of rank two and generalised Kato classes

The generalised Kato classes of Darmon-Rotger arise as p-adic limits of diagonal cycles on triple products of modular curves, and in some cases, they are predicted to have a bearing on the arithmetic of elliptic curves over Q of rank two. In this talk, we will report on a joint work in progress with Ming-Lun Hsieh concerning a special case of the conjectures of Darmon-Rotger.

IAS Room S-101
Speaker: Francesc Castella ,
Princeton University
October 26, 2017
4:30pm - 5:30pm
A converse theorem of Gross-Zagier and Kolyvagin: CM case.

Let E be a CM elliptic curves over rationals and p an odd prime ordinary for E. If the Z_p corank of p^\infty Selmer group for E equals one, then we show that the analytic rank of E also equals one.

This is joint work with Ashay Burungale.

IAS Room S-101
Speaker: Ye Tian,
Chinese Academy of Sciences
November 2, 2017
4:30pm - 5:30pm
On the notion of genus for division algebras and algebraic groups.

Let D be a central division algebra of degree n over a field K. One defines the genus gen(D) of D as the set of classes [D'] in the Brauer group Br(K) where D' is a central division K-algebra of degree n having the same isomorphism classes of maximal subfields as D. I will review the results on gen(D) obtained in the last several years, in particular the finiteness theorem for gen(D) when K is finitely generated of characteristic not dividing n. I will then discuss how the notion of genus can be extended to arbitrary absolutely almost simple algebraic K-groups using maximal K-tori in place...

IAS Room S-101
Speaker: Andrei Rapinchuk ,
University of Virginia
November 30, 2017
4:30pm - 5:30pm
TBA-Laurent Fargues
IAS Room S-101
Speaker: Laurent Fargues,