Computational Algebra Seminar: Bright -- Computing Brauer-Manin obstructions

Some families of Diophantine equations, such as quadratic forms, have a very    
useful property: if an equation has solutions in the real numbers and in        
each p-adic field, then it has a rational solution. Such families of            
equations are said to satisfy the Hasse principle. In general the Hasse         
principle does not hold, but many violations are described by the so-called     
Brauer-Manin obstruction. This obstruction was first defined by Manin and is    
based on the Brauer group of the variety.  I will talk about how to compute     
the Brauer-Manin obstruction for certain classes of varieties, using many       
ingredients from algebraic geometry and number theory.