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Barcelona Algebraic Topology Group

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Friday's Topology Seminar 2016-2017

Speaker: David White (Denison University)
Model Categories and the Grothendieck Construction
Place: Seminari C3b
23rd June at 12:00.
I will report on joint work with Michael Batanin studying the homotopy theory of the Grothendieck construction, given a category B and a functor F from B to CAT. From the Grothendieck construction we produce a “horizontal" model structure on the base B and “vertical” model structures on the fibers F(b). I will focus on examples, including pairs (R,A) where R is a (commutative) monoid and A is an R-module, pairs (P,A) where P is a (symmetric or non-symmetric) colored operad and A is a P-algebra, and pairs (T,A) where T is a 2-monad on Cat with rank and A is a T-algebra. I will also discuss how to get a semi-model structure under extremely general conditions. Additionally, we study when these model structures are left proper, and when a weak equivalence in B gives rise to a Quillen equivalence of fibers. Applications include change of rings, rectification of operad-algebras, strictification for categorical structures, and preservation of algebraic structure under left Bousfield localization. I will also explain the relationship of this work to that of Harpaz and Prasma.

Speaker: Rune Haugseng (Københavns Universitet)
Title: Enriched infinity-operads
Place: Seminari C3b
23rd June at 14:30.
I will discuss joint work with Hongyi Chu setting up foundations for a theory of enriched infinity-operads. In cases of interest such as spectral operads and dg-operads this recovers the usual homotopy theory of enriched operads, but is far better behaved - for example, there are natural infinity-categories of algebras over enriched infinity-operads. Time permitting, I will also discuss work in progress describing enriched infinity-operads as monoids in symmetric sequences; this will hopefully be a good setting for understanding Koszul duality beyond characteristic zero.

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.

Friday's Topology Seminar 2012-2013

Friday June 7th, 2013, CRM (Aula petita):

12:00 Dietrich Notbohm : Depth and homology decompositions

Abstract:  Homology decomposition techniques are
a powerful tool used in the analysis of the homotopy theory of (classifying)
spaces. The associated Bousfield-Kan spectral sequences involve higher
derived limits of the inverse limit functor. We study the impact of
depth conditions on the vanishing of these higher limits and apply our theory
in several cases,. In particular we will dicuss our theory in the context of group cohomology and  of polynomial invariants.

Check the calendar for upcoming events

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