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.  
Organizer(s): 

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.

Location
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.

Location
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...

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