Geometry and Topology

Speaker: Thomas Fiore (University of Michigan-Dearborn)

"Waldhausen Additivity: Classical and Quasicategorical"

Time: 15:30

Room: MC 107

We given an elementary proof of Waldhausen Additivity using key ideas from earlier proofs. Then we discuss how to prove the quasicategorical version. Model category arguments do not play a role, nor do any technical results about quasicategories. This is joint work with David Gepner and Wolfgang Lueck.

Graduate Seminar

Speaker: Ali Al-Khairy (Western)

"More Properties in Category Theory"

Time: 16:30

Room: MC 107

This talk will discuss further properties of categories, such as opposite functors and changing variance, products and bifunctors, adjoint functors, and exactness.

Geometry and Combinatorics

Speaker: Mehdi Garrousian (Western)

"Tropical Geometry III"

Time: 14:00

Room: MC 104

Last time, we gave a precise definition for a tropical variety as the closure of the image of a classical variety under an evaluation map. We'll continue the analysis by giving an equivalent description in terms of initial ideals and show that a tropical variety is a subcomplex of the Groebner complex. Next interesting topics in the line are the zero tension condition and Bezout's theorem as an intro to tropical intersection theory.

Algebra Seminar

Speaker: Claudio Quadrelli (University of Milano-Bicocca)

"Bloch-Kato groups and Galois groups? "

Time: 14:40

Room: MC 107

Every profinite group is a Galois group, but which one is also an ${\textit{absolute}}$ Galois group? The cohomological implications of the Bloch-Kato conjecture -- positively solved by M.~Rost and V.~Voevodsky -- allows us to define ${\bf{Bloch-Kato}}$ ${\bf{pro-}}$$p$ ${\bf{groups}}$, which play a crucial role, since they arise naturally as maximal pro-$p$ quotients and Sylow pro-$p$ subgroups of absolute Galois groups. In this seminar I will present the state of the art of the research on Bloch-Kato groups, with a particular mention of the 'Elementary Type Conjecture' of maximal pro-$p$ Galois groups. Yet, there's still a lot of work to do: indeed every maximal pro-$p$ Galois group is equipped with an ${\textit{orientation}}$ $G_F(p)\rightarrow\mathbb{Z}_p^\times$, arising from the action on the group of the roots of unity of $p$-power order. The study of such orientation for Bloch-Kato groups will provide hopefully new results.