Babytop Seminar

Upcoming talks

The seminar will meet Tuesdays at 4:00pm in 2-139 unless otherwise noted.

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.

Past seminars

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.

Please send mailing list requests and questions to Luis Alexandre Pereira.

Other useful links: