03.29.11:
Luis Pereira (
MIT).
Koszul duality for algebraic operads.
In this talk we will present the Koszul duality for dg-operads discovered by
Ginzburg and Kapranov as reinterpreted by Getzler and Jones, who noticed
that it could be restated in terms of dual bar/cobar constructions between the
categories of operads and cooperads that induce equivalences on homotopy
categories. We will present a sketch of the proof of this equivalence and, time
permiting, some relevant examples.
03.08.11:
Inna Zakharevich (
MIT).
The Dehn-Sydler Theorem.
In 1901 Dehn proved that there exist polyhedra that are not
scissors congruent. His proof consisted of a scissors congruence
invariant on polyhedra which was different for an equilateral
tetrahedron and a cube of the same volume. The fact that this
invariant is sufficient (that if two polyhedra have the same volume
and the same Dehn invariant) was proved in 1965 by Sydler. In this
talk we will demonstrate a proof of the Dehn-Sydler theorem.
NOTE: This talk will exceptionally take place in room 4-159 at 3:30pm
03.01.11:
Geoffroy Horel (
MIT).
Deligne Conjecture.
The Deligne conjecture can be expressed in the following way :
the topological Hochschild cohomology of an associative algebra in the
category of spectra is acted on by an E_2 operad. McClure and Smith
developed a general method to show that the totalization of a cosimplicial
spectrum has an action of an E_k operad. As a corollary they were able to
prove the Deligne conjecture. The purpose of this talk is to give an idea
of their proof.
02.15.11:
Rune Haugseng (
MIT).
Homotopy Limits and Wojtkowiak's Obstructions.
If we have a functor F to spaces and a map from each F(x) into
some space Y, when do these maps fit together into a map from the homotopy
colimit of F to Y? More generally, when does a choice of a component in
each of the spaces G(x) for some functor G to spaces lift to a component of
the homotopy limit of G? Zdzisław Wojtkowiak developed an obstruction
theory for the existence and uniqueness of such lifts. I'll talk a bit
about homotopy limits and colimits and define these obstructions, which lie
in certain cohomology groups constructed from the functors pi_n F.
