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Friday's Topology Seminar 2017-2018

Speaker: Sune Precht Reeh (UAB)
Title: Constructing a transporter infinity category for fusion systems
Place: CRM, Aula petita
21th February at 12:10

Abstract: In this research talk, I will give a tour of the progress I have made in the last two weeks on constructing an infinity category that is supposed to model the transporter category for a fusion system (when given a choice of locality/linking system).

I will explain the construction itself as a category enriched in Kan complexes. I will talk about the results obtained so far, with details as time permits, and I will explain the open problems that I am still working on, including how to adapt this transporter category into a working orbit category.


Speaker: Bob Oliver (Université Paris 13)
Title: Recent constructions and theorems on fusion systems due to Michael Aschbacher
Place: Seminari C3b/158
23th February at 12:00

Abstract: Fix a prime p. The fusion system of a finite group G with respect to a Sylow subgroup S ∈ Sylp(G) is the category FS(G) whose objects are the subgroups of S, and whose morphisms are the homomorphisms induced by conjugation in G. More generally, an abstract fusion system over a p-group S is a category whose objects are the subgroups of S and whose morphisms are injective homomorphisms between the subgroups that satisfy certain axioms formulated by Lluis Puig and motivated by the Sylow theorems for finite groups.

Starting 10–15 years ago, Michael Aschbacher and some other finite group theorists became interested in fusion systems, hoping that they can be used to help shorten some parts of the proof of the classification of finite simple groups. This has led to many new structures and results such as generalized Fitting subsystems of fusion systems, as well as intersections, central products, and centralizers of normal fusion subsystems. In many cases, these are analogs of basic, elementary structures or operations in finite groups, but are surprisingly difficult to define in the context of fusion systems.

See the calendar for upcoming events.

Friday's Topology Seminar 2016-2017

Speaker: Ramón Flores (Universidad de Sevilla)
Title: Espacios clasificadores de grupos de trenzas.
Place: Seminari C1/366
28th July at 10:00.
En esta charla mostraremos cómo se puede calcular la dimensión del espacio clasificador de los grupos de trenzas respecto de la familia de grupos virtualmente cíclicos. Las herramientas utilizadas incluyen el modelo de Lück-Weiermann de estos espacios, la clasificación de trenzas de Nielsen-Thurston, y resultados homológicos sobre los conmensuradores de los subgrupos cíclicos.

See the calendar for upcoming events.

Friday's Topology Seminar 2015-2016

This semester we will read Benson-Greenlees paper "Stratifying the derived category of cochains on BG for G a compact Lie group".

Our aim will be study the results and see if we can generalize them to the p-compact case. The tentative schedule is the following:

1) February 19th. W. Pitsch. Overview
2) March 4th. L. Carlier. Tensor triangualted categories
3) April 1st. T. Lozano. p-compact groups
4) April 15th. W. Pitsch. Stratification I
5) April 29th. W. Pitsch Stratification II
6) May 6th. J. Kock Pointfree Topology on Spec R and support I
7) May 13rd. J. Kock Pointfree Topology on Spec R and support II
8) May 20th W. Pitsch Some results on D(R) for R a ring spectrum
9) June 3rd N. Castellana Noetherianity in cohomology
10) July 1st N. Castellana Chouinard's theorem for finite p-local groups and p-compact groups

Date and place: Fridays 12h00-13h00, CRM Room A1.

Friday's Topology Seminar 2014-2015

Date and place: July 10,  2015. 12:00. CRM Aula A1.
Speaker :
Ramsés Fernandez Valencià (Swansea University)
Sobre teorías topologicas conformes de campos no orientadas.
En la charla se aboradará el concepto de TCFT no orientada (KTCFT). Concretamente, se dará una nueva demostración para la clasificación de KTCFTs abiertas, se introducirá la extensión universal de KTCFTs abiertas a teorías abierto-cerradas y se aboradará la relación de la parte cerrada de una KTCFT abierto-cerrada con el complejo de Hochschild involutivo.

Date and place: June 19,  2015. 12:00. CRM Aula A1.
Speaker : Leandro Lombardi (Universidad de Buenos Aires, Argentina)

Álgebras de cactus compatiblemente bigraduadas
Se mostrará una correspondencia entre la estructura de álgebra sobre el operad (de cadenas celulares del operad topológico) de cactus y el álgebra asociativa libre subyacente, en presencia de una bigraduación compatible.
En toda álgebra de cactus puede considerarse un producto pre-Lie.
En el caso de que este álgebra sea de la forma T V para V un espacio vectorial, este producto, restringido a V, resulta asociativo. Se muestra que una estructura de álgebra de cactus en TV induce una estructura de biálgebra asociativa y coasociativa en  H = V + 1 donde 1 es la unidad formal de dicho producto.  Esto muestra, junto con trabajos previos de Kadeishvili y Menichi que estas estructuras están en correspondencia biunívoca con las estructuras álgebra de cactus en TV (que extienden la de álgebra asociativa) con cierta condición de compatibilidad con la graduación, propiedad motivada por el ejemplo del complejo de Hochschild.

Friday's Topology Seminar 2013-2014


Date and place: July 18, 2014. 12am. CRM, small lecture room.
Speaker : Shizuo Kaji (Yamaguchi U)
A product in equivariant homology for compact Lie group actions
The Tate cohomology for a finite group integrates group homology and cohomology into one theory. It is equipped with a cup product, which coincides with the usual one on cohomology and gives a ring structure on homology. A few attempts have been made to generalise this product structure on homology. We follow the line of Kreck and Tene. Kreck defined a product on H_*(BG;Z) for a compact Lie group G based on his geometric homology theory and Tene showed it coincides with the cup product on the Tate cohomology when G is finite. We will generalise this product to one on the equivariant homology of a manifold with a nice action of a Lie group. Our construction is simple and purely homotopy theoretical. This is a joint work with Haggai Tene.

Date and place: June 20, 2014. 12am. CRM, small lecture room.
Speaker : Conchita Martínez (U Zaragoza)
Title: On dimension invariants for groups admitting a cocompact model for proper actions.

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