We meet (online) every other Thursday at 1pm (Mexico City/Central time). If you'd like to participate, please contact Bernardo Villarreal (villarreal at matem dot unam dot mx) so we can add you to our email list. A link to the meeting will be sent the day of the talk.
Aug 19. Mauricio Bustamante, Universidad Católica de Chile
Title: (Talk in spanish) Propiedades de finitud de espacios móduli de variedades suaves.
Abstract: El espacio móduli BDiff(M) de una variedad suave M es el espacio que clasifica haces fibrados con fibra M. Entender su tipo de homotopía es entonces la tarea que tiene todo topólogo interesado en clasificar haces fibrados. Para bien o para mal, estos espacios tienden a ser bastante complicados, por lo cual nos toca conformarnos con tratar de calcular algunos de sus invariantes topológicos. Esto tampoco es tarea fácil, incluso en los casos más simples (eg. M una esfera) son pocas las cuentas que hay disponibles. Sin embargo, hay algo un poco más "cualitativo" que sí se puede afirmar en mucha generalidad: si M es una variedad suave compacta conexa de dimensión par mayor que 5 y con grupo fundamental finito, entonces todos los grupos de homotopía y homología del espacio móduli BDiff(M) son finitamente generados. En esta charla voy a discutir algunas de las ideas que M. Krannich, A. Kupers y yo usamos en la demostración de ésta afirmación.
Sep 2. Martina Rovelli, UMass Amherst
Title: An (∞, 2)-categorical pasting theorem
Abstract: Power's 2-categorical pasting theorem, asserting that any pasting diagram in a 2-category has a unique composite, is at the basis of the 2-categorical graphical calculus, which is used extensively to develop the theory of 2-categories. In this talk we discuss an (∞, 2)-categorical analog of the pasting theorem, asserting that the space of composites of any pasting diagram in an (∞, 2)-category is contractible. This result, which is joint with Hackney—Ozornova—Riehl, rediscovers independent work by Columbus.
Sep 30. Dan Ramras, IUPUI
Title: Dynamical Induction and Cohomology of Crystallographic Groups
Abstract: Adem, Lueck, and their collaborators have shown that in various situations, the Lyndon-Hochschild-Serre spectral sequence associate to a crystallographic group collapses at the second page. Crystallographic groups are built from integral representations finite groups. We describe a generalized notion of induction, which we call dynamical induction, originating in the theory of C*-algebras, and we show that these collapse results are preserved under induction in an appropriate sense. In particular, we show that the spectral sequence associated to a semidirect product of the form Z^n \rtimes Q collapses whenever the action of Q on Z^n is induced up from an action of a group of square-free order. This is joint work with my recent Ph.D. student, Chris Neuffer.
Oct 21 (note the change of date). Tobias Barthel, MPI Bonn
Title: TBA
Oct 28. Elizabeth Viduarre, Molloy College
Title: TBA
Nov 11. Andrea Bianchi, Copenhagen
Title: TBA
Nov 25. Benjamin Brück, ETH Zürich
Title: TBA
Dec 9. Manuel Krannich, Cambridge
Title: TBA