### Invited Speakers

**Michael Joachim** (Universität Münster, Alemania)

Title: **Twisted spin bordism and its relations to geometry****Abstract:** In our talk we will explain the concept of twisted spin bordism and present an explicit model for it. In the sequel we discuss some fundamental structural results on the homotopy type of twisted spin bordism and demonstrate how this shall lead to several explicit applications in geometry.

**José Manuel Gómez** (Universidad Nacional de Colombia, sede Medellín, Colombia)

Title: **Twisted and untwisted equivariant K-theory of actions with maximal rank isotropy****Abstract:** Suppose that G is a compact Lie group. We say that G acts on a space with maximal rank isotropy if the isotropy subgroup of every point of X is connected and contains a maximal torus in G. The goal of this talk is to compute the twisted and untwisted equivariant K-theory for such actions. Some examples with explicit computations will be provided. This is a joint work with Alejandro Adem and José Cantarero.

**Ping Xu** (Pennsylvania State University, USA)

Title: **Localized equivariant twisted cohomology****Abstract:** We will discuss our proposal for establishing a de Rham model of equivariant twisted K-theory using machinery from noncommutative geometry. More precisely, for a given class in the third G-equivariant cohomology group of M, where G is a compact Lie group acting on a compact manifold M, we introduce a notion of localized equivariant twisted cohomology and discuss its relation with twisted equivariant K-theory. This is a joint work with Jean-Louis Tu.

**Bernardo Uribe** (Universidad del Norte, Colombia)

Title: **On the Atiyah Hirzebruch Spectral Sequence on Equivariant K-theory****Abstract: **Consider G a finite group and H a subgroup of G. In this talk I will show the results of a joint project with José Manuel Gómez on which we stablish explicitly the third differential of the Atiyah Hirzebruch Spectral Sequence associated to the G equivariant K-theory of EH.

**Paulo Carrillo **(Institut de Mathématiques de Toulouse, France)

Title: **A groupoid approach to twisted index theory****Abstract:** In this talk I will survey the approach to index theory for twisted groupoids that I have been working in collaboration with Bai-Lin Wang (ANU). In particular I will explain the construction of the Geometric Baum-Connes assembly for twisted di erentible stacks based on the wrong way functoriality in twisted K-theory that we proved using deformation groupoids. I will explain with basic examples the fundamental role of the deformation groupoids in our approach.

**Mario Velásquez** (Pontificia Universidad Javeriana, Colombia)

Title: **The Baum-Connes Assembly map and configuration spaces****Abstract:** In this talk we describe a definition of K-homology using configuration spaces. Let G be discrete group. Let X be a proper G-CW-complex, we define a configuration space C(X,G) such that we have a natural isomorphism between the nth homotopy group of C(X,G) and the G-equivariant connective nth K-homology group of X. We describe the assembly map of the Baum-Connes conjecture for the above description.

**Alejandro Adem** (University of British Columbia, Canada)

Title: **An infinite loop space associated to commuting matrices****Abstract: **Let G denote a Lie group. We show that a construction introduced by Adem-Cohen-Torres built out of the commuting elements in G plays the role of a classifying space for commutativity. We will discuss how this is reflected in properties of these spaces and show that for the unitary group U we obtain a new infinite loop space. This leads to the notion of commutative K-theory, with characteristic classes computed using multisymmetric polynomials. This is joint work with José Manuel Gómez, John Lind and Ulrike Tillmann.

**Ernesto Lupercio** (CINVESTAV, Mexico)

Title: **Non-commutative geometry and sandpiles****Abstract: **Sandpile models were discovered by physicists as discrete models of 1/f-noise. In this talk I will review my joint results with Kalinin and Shkolnikov on the relation to noncommutative geometry.

**Daniel Juan Pineda** (CCM-UNAM Morelia, México)

Title: **Topological rigidity of higher graph manifolds ****Abstract:**In this talk I will describe the construction of higher graph manifolds and an outline of the validity of the Borel conjecture for these manifolds.

**Elmar Wagner** (Universidad Michoacana de San Nicolás de Hidalgo, México)

Title: **Compact quantum surfaces of any genus****Abstract:** I will construct a noncommutative version of all closed compact 2-surfaces as subalgebras of the Toeplitz algebra which is also known as the quantum disc algebra. Furthermore, I will show that the corresponding C*-algebras have the same K-groups as their classical counterparts and that the computation of the K-groups of the noncommutative version is quite similar to the classical case with the disc replaced by the quantum disc.