Schedule of Talks: Autumn 2022

Time/Location : Seminar will be on Tuesdays either at 3:00-4:00pm (in Mw 154) or 4-5pm (in Scott Lab E241)and either via Zoom or in person


 

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 

 
Amalendu Krishna, Indian Institute of Science, Bangalore Brauer group and 0-cycles on smooth varieties. Joshua
November 22 

 
November 27 
T  
 
Open


Schedule of Talks: Spring

Time/Location : Seminar will be on Tuesdays 4-5pm via Zoom or in person. (In person talks in Smith lab 1138)


 

TIME  SPEAKER TITLE HOST
January 31 
T  
 
Connor Cassady (University of Pennsylvania) Quadratic forms, local-global principles, and field invariants Joshua
February 7 
T  
 
James Hotchkiss (University of Michigan) The period-index 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

Abstracts

(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 in-person talk, held in Scott Lab E241, 4-5pm.

(Swar talk) The rational points of a hyperbolic curve over a number field inject into non-abelian 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 Chabauty-Kim 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 0-cycles 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 non-trivial zero (is q isotropic)? *Which non-zero elements of k are represented by q? *Does q represent all non-zero elements of k (is q universal)? Over global fields F, the Hasse-Minkowski theorem, which is one of the first examples of a local-global 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 local-global principle for isotropy holds over more general fields k, as well as connections between this local-global principle and universal quadratic forms over k.

(Hotchkiss talk) Abstract: The period-index 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 Hodge-theoretic interpretation of the problem for complex function fields, and explain some consequences for the integral Hodge conjecture and for Brauer groups.

(Singh talk)

(Fourth talk)

  • Arithmetic Geometry Seminar calendar from 2020-2021
  • Arithmetic Geometry Seminar calendar from 2019-2020


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