Homotopy Theory

Speaker: Dan Christensen (Western)

"Models of (homotopy) type theory"

Time: 14:00

Room: MC 107

I will describe what it means to give a model of type theory, and give some examples of models, including some that arise from Quillen model categories.

Comprehensive Exam Presentation

Speaker: Somnath Chakraborty (Western)

"Etale cohomology of Classifying Simplicial Scheme of Affine Group Schemes, with torsion coefficients"

Time: 14:00

Room: MC 107

We consider the category of etale sheaves on a simplicial scheme, define etale cohomology in terms of derived functors, and then mention some spectral sequences connecting Cech and etale cohomology. We consider the model structure on the category of simplicial sheaves on an arbitrary Grothendieck site C , and for a fibrant simplicial sheaf X, and a sheaf of abelian groups F, we consider morphisms to the Eilenberg-MacLane constructions K(F; n), in Ho(C ). For a linear algebraic group scheme G, we show that this is the sheaf cohomology arising out of the model structure coincides with etale cohomology. Finally, we mention about the etale cohomology of BGLn(k), and carry out the calculation when n = 1 for any finite extension of Q.