This semester we will read BensonGreenlees 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 pcompact 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. pcompact 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 plocal groups and pcompact groups
Date and place: Fridays 12h0013h00, CRM Room A1.
Date and Place: July 15th 12h00, CRM room A1 Speaker: Nicolas Ricka (Wayne State University) Title: The stable Picard group of motivic A(1)
Abstract: Let A be the modulo 2 Steenrod algebra, and A(1) be the subalgebra of A generated by the two first Steenrod squares. As the cohomology of the real Ktheory spectrum is A//A(1), the structure of the category of A(1)modules is of particular importance for ko(co)homology computations. In this talk, I will talk about a determination of the Picard group of the stable category of modules over a motivic version of A(1). I will then discuss some possible applications in the A^1stable motivic category, and its version of the connective real Ktheory spectrum.
Date and Place: July 11th 14h30, CRM room A1 Speaker: Darwin Gutiérrez (Cinvestav, México) Title: Complejidad topológica superior de variedades de banderas
Abstract: En esta charla analizaremos el concepto de complejidad topológica superior (TC_s) que es una generalización de la complejidad topológica de Farber, y veremos como las cotas que brindan el zero cup length y la dimensión del espacio sobre TC_s nos dan valores de este invariante homotópico para familias infinitas de variedades de banderas.
Además veremos un estudio que generaliza el resultado clásico TC(RP^n)=Inm(RP^n) para cada n distinto de 3,5,7 para TC_s en condiciones particulares.
Regular seminar:
Date and Place: July 8th 12h00, CRM room A1 Speaker: Marcelo FIORE (Cambridge Univ.) Title: The Calculus of Generalised Species of Structures
Abstract: Generalised species of structures are a categorical analog of exponential generating functions in which operations on exponential generating functions (eg substitution, addition, multiplication, differentiation) translate into a combinatorial calculus. Drawing analogies from analysis, linear algebra, (linear) logic, and (stable) domain theory, I will give an introduction to the categorical calculus of generalised species presenting its differential and cartesian closed structures.
Extraordinary session:
Date and Place: June 9th 12h00, CRM room A1 Speaker: Michael Batanin (Macquarie Univeristy) Title: A less known Deligne's conjecture
Abstract: A now famous Deligne's conjecture on Hochschild cochains (proved by many authors) asserts that this complex is naturally a E_2algebra i.e. an algebra of an operad weakly equivalent to the little 2disk operad. In 1992 Alexey Davydov introduced a construction of a deformation complex of a monoidal functor which reminds the classical Hochschild complex but in many respect is a very different creature. For example, you can apply this construction to the identity functor. The corresponding cohomology classify obstructions for infinitesimal deformations of the associator of a tensor category (like classical Hochschild cohomology classify obstructions for infinitesimal deformations of the multiplication of an associative algebra). So, in some sense, this is a second order or categorification of the Hochschild cohomology. Deligne (in a letter to Davydov in 1993) suggested a simple algebraic condition called ncommutativity for a cosimplicial complex of associative algebras and conjectured that an ncommutative complex has a natural E_{n+1}algebra structure. It can be easily proved that in general Davydov's complex is a 1commutative complex in Deligne's sense but the deformation complex of an identity functor is 2commutative.
Regular seminar:
Date and Place: June 3rd 12h00, CRM room A1 Speaker: Natàlia Castellana (UAB) Title: Noetherianity in cohomology
Abstract: We will show why various cohomologies of interest (pcompact group, plocal groups) have noetherian cohomology. The proofs rest on nice properties of various transfers in these different settings.
Date and Place: May, 27th 12h00, CRM room A1 Speaker: Jean Barge (Prof. Honoraire à Univ. Grenoble) Title: Cancellation of projective modules old and new
Date and Place: May, 20th 12h00, CRM room A1 Speaker: Wolfgang Pitsch (UAB) Title: Some results on D(R) for R a ring spectrum
Date and Place: May, 6th 12h00, CRM room A1 Speaker: Joachim Kock (UAB) Title: Pointfree Topology on Spec R and support
Abstract: We will present the basics of pointfree approach to support the basics
Date and Place: April, 26th 2016, 12h00, CRM room A2 (first floor) Speaker: Antonio Díaz (Universidad de Málaga) Title: On Quillen's conjecture for psolvable groups
Abstract: Quillen's conjecture on the psubgroups complex was figured out for solvable and psolvable groups in the 80's and 90's thanks to the work of Quillen, Aschbacher, Smith and Alperin. Here we present a fresh new geometric approach to the subject. This includes an asymptotic version for the psolvable case that does not use the Classification of the Finite Simple Groups. The methods are potentially applicable to the general case of the conjecture.
Date and Place: April, 29th 2016, 12h00, CRM room A1 Speaker: Wolfgang Pitsch (UAB) Title: Stratification of triangulated categories II
Abstract: Presentaré un esbozo de la teoría de estratificación de categorías trianguladas Rlineales, R un anillo noeteriano, segun BensonIyengarKrause.
Date and Place: April, 15th29th 2016, 12h00, CRM room A1 Speaker: Wolfgang Pitsch (UAB) Title: Stratification of triangulated categories
Abstract: Presentaré un esbozo de la teoría de estratificación de categorías trianguladas Rlineales, R un anillo noeteriano, segun BensonIyengarKrause.
Date and Place: April, 8th 2016, 12h00, CRM room A1 Speaker: Tom Leinster (Universiry of Edinburgh) Title: The categorical origins of entropy
Abstract: Entropy is fundamental to many parts of mathematics (including dynamical systems, information theory and probability theory) as well as many branches of applied science, but it is less often considered in topology and algebra. However, I will show that the concept of Shannon entropy is present in the heartlands of pure mathematics, whether we like it or not. Specifically, I will describe a categorical machine which, when given as input the concepts of topological simplex and real number, produces as output the concept of Shannon entropy. The most important component of this machine is the notion of "internal algebra" in an algebra for an operad (generalizing the notion of monoid in a monoidal category). The resulting characterization of Shannon entropy can be stated with no categorical language, giving a simple and entirely elementary characterization. This last theorem is joint work with John Baez and Tobias Fritz (arXiv:1106.1791).
Date and Place: April, 1st, 2016, 11h00, CRM Room A1 Speaker: Toni Lozano (UAB) Title: pcompact groups Abstract: This will be a review of the theroy of pcompact groups.
Date and Place: March, 11th, 2016, 11h00, CRM Room A1
Speaker: Mark Weber (Macquarie University)
Title: Vines and internal algebras
Abstract: A vine is a generalisation of a braid in which strings are allowed to merge. The category of natural numbers and vines between them is a canonical object  it is the universal braided monoidal category containing a commutative monoid. In this talk we describe a conceptual approach to verifying this universal property, and describe the general theory of internal algebras of which this is an instance. Other examples relating to the study of transferred model structures on categories of operads, and the study of E_n operads will also be discussed.
Date and Palce: March, 11th, 2016, 12h00, CRM Room A1
Speaker: Norio Iwase (Kyushu University)
Title: Diffeological Spaces
Abstract: The idea of a space with smooth structure is a generalization of an idea of a manifold. K.T. Chen introduced such a space as a differentiable space in his study of a loop space to employ the idea of iterated path integrals. Following the pattern established by Chen, J.M. Souriau introduced his version of a space with smooth structure, which is called a diffeological space. These notions are strong enough to include all the topological spaces. However, if one tries to show de Rham theorem, he must encounter a difficulty to obtain a partition of unity and thus the MayerVietoris exact sequence in general. I will introduce a new version of differential forms to obtain a partition of unity, the MayerVietoris exact sequence and a version of de Rham theorem in general. In addition, if we restrict ourselves to consider only CW complexes, we obtain de Rham theorem for a genuine de Rham complex, and hence the genuine de Rham cohomology coincides with the ordinary cohomology for a CW complex.
Date and place: March, 4th, 2016. CRM Room A1 12h00 Speaker : Louis Carlier Title: Tensor triangulated Categories Abstract: This will be a reminder of some basic properties of tensor triangulated categories.
Date and place: February 26th, 2016. CRM Room A1 Speaker : Celeste Damiani (Univ. Caen) Title: Alexander invariants of ribbon tangles and circuit algebras. Abstract: Ribbon 2knotted objects are locally flat 2dimensional submanifolds of $\mathbb{R}^4$ that bound immersed 3manifolds with only ribbon singularities. They appear as topo logical realizations of welded knotted objects, where welded knot theory is a quo tient of virtual knot theory. We consider colored ribbon tangles and cobordisms, and observe that the action of cobordisms on tangles endows the set of colored ribbon tangles with a structure of circuit algebra $Tan_\mu$over the cobordisms operad. We construct a morphism of $Tan_\mu$ to the algebra of modules over a Laurent poly nomial ring. Moreover, we use the diagrammatic representation of ribbon tangles through welded diagrams to describe a purely combinatorial model for our invari ant, that extends a construction by Archibald and BarNatan. When restricted to tangles without virtual crossings, the invariant coincides with a functor intro duced by Bigelow, Cattabriga and Florens. In particular, when restricted to colored oriented braids, it coincides with exterior powers of BurauMagnus representation.
Date and place: February 19th, 2016. CRM Room A1 Speaker : Wolfgang Pitsch Title: Overview of BensonGreenlees paper. Abstract: We will give an overview of BensonGreenlees paper.
Date and place: January 29, 2016. CRM
Speaker : Jesper Møller (University of Copenhagen)
Title: Equivariant Euler characteristics of partition posets
Abstract: We discusss the equivariant Euler charachteristics of the $\Sigma_n$poset of partitions of the $n$set.
Date and place: January 22, 2016. CRM Speaker : Bob Oliver (Université Paris 13) Title: The role of tameness in Aschbacher's program Abstract: I plan to start with some general remarks on Aschbacher's program for classifying certain simple 2fusion systems, with focus on how he analyzes centralizers of involutions. In particular, I'll describe the role played by tameness when carrying out this reduction process.
Date and place: January 15, 2016. CRM Speaker : Ran Levi (University of Aberdeen) Title: Groups of unstable Adams operations on plocal compact groups Abstract: A plocal compact group is an algebraic object modelled on the homotopy theory associated with pcompleted classifying spaces of compact Lie groups and pcompact groups. In particular plocal compact groups give a unified framework in which one may study pcompleted classifying spaces from an algebraic and homotopy theoretic point of view. Like connected compact Lie groups and pcompact groups, plocal compact groups admit unstable Adams operations  self equivalences that are characterised by their cohomological effect. Unstable Adams operations on plocal compact groups were constructed in a previous paper joint with F. Junod and A. Libman. In this talk we consider groups of unstable operations from a geometric and algebraic point of view. We give a precise description of the relationship between algebraic and geometric operations, and show that under some conditions unstable Adams operations are determined by their degree. We also examine a particularly well behaved subgroup of operations.
Date and place: January 8, 2016. CRM Speaker : Ismar Volic (Wellesley College) Title: Embedding spaces and calculus of functors Abstract: Manifold calculus of functors and related homotopytheoretic techniques have in recent years been applied with great success to spaces of embeddings, most notably knot and link spaces. During this time, some interesting problems arose as a consequence. After describing the general setup of manifold calculus of functors and how it specializes to knots and links, I will describe some of these problems relating to certain spaces of diagrams and trees, homology of link spaces, and subspace arrangements. Time permitting, I will make some general comments about how functor calculus might provide a different point of view on some recent results surrounding the Tverberg Conjecture.
Date and place: December 18, 2015. CRM Speaker : Carlos Giraldo Title: Minimal Fibrations that are not Fibre Bundles Abstract: By using the structure of simplicial cofibrantly generated model category over the category S^C of Cdiagrams of simplicial sets (where C is a small category), we formulate one definition of minimality for Cdiagrams that are free. When C is an EIcategory with a finite number of objects, it is possible to show that any free Cdiagram X has a minimal model with good properties. Using this tool, we are able to classify fibrations in S^C whose base space is a constant diagram. Moreover, when the category C is a rooted tree, it is possible to classify fibrations in S^C whose base space is an arbitrary Cdiagram. This is a joint work with Carles Broto and Ramón Flores.
Date and place: October 30, 2015. 12:00. CRM Aula petita. Speaker : Alejandro González (Kansas State University) Title: Aproximacions finites de grups plocals compactes. Abstract: Els grups plocals compactes són estructures algebraiques que modelen espais classificadors (pcompletats) de grups finits, grups de Lie compacts i grups pcompactes, entre altres exemples. En aquesta xerrada presentaré una versió plocal d'un resultat de Friedlander i Mislin que relaciona espais classificadors de grups de Lie compactes amb telescopis d'espais classificadors de grups finits. Aquest resultat permet deduir una versió plocal del teorema d'elements estables per calcular la cohomologia mòdul p d'un espai classificador, entre altres resultats que comentaré si hi ha temps.
Date and place: October 16, 2015. 12:00. CRM Aula A1. Speaker : Sejong Park (National University of Ireland Galway)Title: Sharpness conjecture for plocal finite groups and Mackey functors Abstract: Sharpness of various homology decompositions of classifying spaces of finite groups has been studied extensively, especially by Dwyer. In particular, subgroup decomposition with respect to centric subgroups is sharp for finite groups, but an analogous statement for plocal finite groups is still open. I will present some confirmed cases and explain ingredients of proof. In particular, it will be noted that sharpness can be seen in terms of general Mackey functors, not just the cohomology functor. This is a joint work with Antonio Díaz and Radu Stancu.
