Schedule of Talks: Autumn

Time/Location : Seminar will be on Tuesdays 4:15-5:15pm in Cockins 228


 

TIME SPEAKER TITLE HOST
September 3 
T 4:15pm 
CH228 
Roy Joshua Brauer groups of schemes associated to symmetric powers of smooth projective curves in arbitrary characteristics Joshua
September 17 
T 4:15pm 
CH228 
Kapil Paranjape, IISER, Mohali and Washington University Hodge and Generalised Hodge Conjecture for K3 surfaces and some 3-Folds Joshua
October 1 
T 4:15pm 
CH228 
Open
October 15 
T 4:15pm 
CH228 
Open
October 29 
T 4:15pm 
CH228 
Sasha Shlapentokh (East Carolina University) The World of Definability Park
November 12 
T 4:15pm 
CH228 
John Voight, Dartmouth A Prym variety with everywhere good reduction over the quadratic field of discriminant 61 Park
November 26 
T 4:15pm 
CH228 
Open


Schedule of Talks: Spring

Time/Location : Seminar will be on Tuesdays at 4.15


 

TIME  SPEAKER TITLE HOST
January 14 
T 4:15pm 
CH228 
Netan Dogra Katz
January 28 
T 4:15pm 
CH228 
Open
February 11 
T 4:15pm 
CH228 
Daniel Litt, University of Georgia Katz
February 25 
T 4:15pm 
CH228 
Open
March 17 
T 4:15pm 
CH228 
Open
March 31 
T 4:15pm 
CH228 
Open
April 14 
T 4:15pm 
CH228 
Open

Abstracts

( Joshua talk): The theory of Brauer groups has a long and rich history. In recent years there seems to be a renewed interest in this area, and there have been several important developments in the last 10-15 years using sophisticated techniques. It is also one of the few topics that can be studied both from a complex algebraic geometry point of view as well as using algebraic tools, notably ́etale cohomology. In this talk we show that the \ell^n -torsion part of the cohomological Brauer groups of certain schemes associated to symmetric powers of a projective smooth curve over a separably closed field k are isomorphic, when \ell is invertible in k. The schemes considered are the symmetric powers themselves, then the corresponding Picard schemes and also certain Quot-schemes. We also obtain similar results for Prym varieties associated to certain finite covers of such curves. This is joint work with Jaya Iyer.

(Paranjape Talk): This talk is based on joint work with Madhav Nori which arose in the study of the Hodge conjecture for some K3 surfaces with complex multiplication. This leads to the study of the Generalised Hodge Conjecture on certain 3-folds. The conjecture can be resolved in some (restricted) cases.

(Sasha Talk): We will discuss some old and recent results concerning definability and decidability over subrings and algebraic extensions of Q. In particular, we will address the results concerning the big subrings of number fields and so-called p-bounded extensions of Q.

(Voight Talk): We compute an equation for an abelian surface that has everywhere good reduction over the quadratic field of discriminant 61. This surface does not admit a principal polarization, so we realize it as a factor of a Jacobian of an explicit curve of genus 3. This is joint work with Nicolas Mascot and Jeroen Sijsling.



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