TIME  SPEAKER  TITLE  HOST 
October 18
T  N Ramachandran, University of Maryland, College Park  Brauer groups and elliptic curves  Joshua 
October 25
T  Jay Swar, Mathematical Institute, Oxford University (UK)  Symplectic geometry and Selmer schemes  Joshua 
November 15
T  Amalendu Krishna, Indian Institute of Science, Bangalore  Brauer group and 0cycles on smooth varieties.  Joshua 
November 22
T  
November 27
T  Open  
TIME  SPEAKER  TITLE  HOST 
January 31
T  Connor Cassady (University of Pennsylvania)  Quadratic forms, localglobal principles, and field invariants  Joshua 
February 7
T  James Hotchkiss (University of Michigan)  The periodindex problem over the complex numbers  Joshua 
February 14
T  Open  
February 21
T  Open  
February 28
T  Open  
March 7
T  Soumya Sankar (OSU)  
March 21
T  Rahul Singh (Louisiana State University)  Joshua  
March 28
T  Open  
March 28
T  Open  
April 4
T  unavailable  
April 11
T  Open 
(Ramachandran Talk) I will report on some recent joint work with Lichtenbaum, Suzuki and with Rosenberg about Brauer groups, elliptic curves and derived categories. This will be an inperson talk, held in Scott Lab E241, 45pm.(Swar talk) The rational points of a hyperbolic curve over a number field inject into nonabelian Galois cohomology with coeffients given by the curve's geometric etale fundamental group. This suggests that studying such Galois cohomology sets should yield Diophantine consequences; an instance of this is realized in the ChabautyKim method. The central objects in this method are Selmer schemes which are obtained by considering "Selmer intersections" of group cohomological functors. In this talk, we'll introduce these group cohomological functors and Selmer schemes. We'll show that a wide class of group cohomological functors can be shown to possess symplectic structures and that the related Selmer schemes can be naturally realized as intersections of multiple Lagrangians. Lastly, we'll explain some of the utility of this description, especially towards effective Diophantine questions. (Krishna talk) In this talk, I shall recall a well known relation between the Brauer group and the group 0cycles on a smooth projective variety over a field. I shall then consider the special case of this relation over a local field and present some new results I recently obtained in a joint work with Jitendra Rathore and Samiron Sadhukhan. (Cassady talk) Abstract: Given a quadratic form (homogeneous degree two polynomial) q over a field k, some basic questions one could ask are: *Does q have a nontrivial zero (is q isotropic)? *Which nonzero elements of k are represented by q? *Does q represent all nonzero elements of k (is q universal)? Over global fields F, the HasseMinkowski theorem, which is one of the first examples of a localglobal principle, allows us to use answers to these questions over the completions of F to form answers to these questions over F itself. In this talk, we'll explore when the localglobal principle for isotropy holds over more general fields k, as well as connections between this localglobal principle and universal quadratic forms over k. (Hotchkiss talk) Abstract: The periodindex problem for the Brauer group of a field asks, briefly, how the size of a division algebra is constrained by its order in the Brauer group. I will describe a Hodgetheoretic interpretation of the problem for complex function fields, and explain some consequences for the integral Hodge conjecture and for Brauer groups. 


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