The **Seminar on diffeology and related topics **will be held monthly, on the first Thursday of each month in a regular basis. Each talk in the seminar will last approximately 1-1.5 hours, together with 0.5 hour discussion afterwards**.** A reminder will be sent to everybody who asks to be on the mailing list (send us an email), one or two day before the seminar. The time is announced in Greenwich Mean Time, use the GMT tool to convert it to your time zone.

### Next Talks

๐ **Serap Gรผrer** (Galatasaray University)**When**: Thursday February 10th, 2022 โ 12:30 GMT.**Where**: Zoom link**Title**: Orbifolds as Stratified Diffeologies**Abstract**: Every diffeological space is naturally stratified by the action of its diffeomorphisms: the Klein Stratification. I will describe this stratification for (diffeological) orbifolds in the general context of formal and geometric stratifications in diffeology.

### Previous Talks

โ **Hong Van Le** (Czech Academy of Sciences)**When**: Thursday January 13th, 2022 โ 12:30 GMT.**Where**: Zoom link**Title**: Diffeological statistical models and Machine Learning**Abstract**: In Machine Learning we develop mathematical methods for modeling data structures, which express the dependency between observables, and design efficient learning algorithms for estimation of such dependency. The most advanced part of Machine Learning is statistical learning theory that takes into account our incomplete information of observables, using probability theory, or preferably, using measure theory and functional analysis. In this way we not only unveil hidden structure of data but also make a prediction for the future. In my lecture I shall consider some important problems in statistical learning theory and demonstrate the efficiency of categorical language, manifested, in particular, in terms of probabilistic morphisms, and the use of natural geometric constructions, e..g. diffeological Fisher metric, in solving these problems.

โ **Ralph Twun** (University of Legon, Ghana)**When**: Thursday December 2nd, 2021 โ 12:00 GMT.**Where**: Zoom link**Title**: Diffeologial categories and induced representations**Abstract**: In this talk I will discuss the properties of the category of Diffeological Spaces which make it suitable as an enriching category. Using the concepts of indexed colimits and their relation to Kan extensions, I will discuss induced representations for diffeological groups and related ideas.

โ **Jordan Watts** (Central Michigan University)**When**: Thursday November 4th, 2021 โ 12:00 GMT.**Where**: Zoom link**Title**: Sheaves for Diffeological Spaces.**Abstract**: We will define sheaves for diffeological spaces and give a construction of their ฤech cohomology. As an application, given an abelian diffeological group \(G\), we will show that the first degree ฤech cohomology classes for the sheaf of smooth \(G\)-valued functioned classify diffeological principal \(G\)-bundles..

โ **Patrick Iglesias-Zemmour** (The Hebrew University of Jerusalem, Israel)**When**: Thursday October 7th, 2021.**Where**: Zoom link / paper / Slides**Title**: *Why irrational tori are important…***Abstract**: I will comment two constructions / theorems in symplectic diffeology that exist only because diffeology gives us a non trivial access to quotients of the type \({\bf R}/\Gamma\), where \(\Gamma\) is any subgroup. In particular, I will show how “Every symplectic manifold is a (linear) coadjoint orbit”. In other words: *coadjoint orbits are the universal model of symplectic manifolds*.

โ **David Miyamoto** (Toronto University, Canada)**When**: Thursday September 2nd, 2021 โ 12:00 GMT.**Where**: Zoom link**Title**: The basic forms of a singular foliation.**Abstract**: A singular foliation F gives a partition of a manifold M into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space M/F, and that of the basic differential forms on M. We prove the pullback by the quotient map provides an isomorphism of these complexes in the following cases:

– when F is a regular foliation,

– when points in the leaves of the same dimension assemble into an embedded (more generally, diffeological) submanifold of,

– and, as a special case of the latter, when F is induced by a linearizable Lie groupoid.

โ **Enxin Wu** (Shantou University, China)**When**: Thursday July 8th, 2021 โ 12:00 GMT.**Where**: Zoom link**Title**: *Diffeological vector spaces*.**Abstract**: Diffeological vector spaces appear in various places in diffeology. In this talk, I will give a detailed discussion of many important classes of them. Many open questions will be posted.

โ **Katsuhiko Kuribayashi** (Shinshu University, Japan),**When**: Thursday June 3rd, 2021 โ 12:00 GMT.**Where**: Zoom link, Slides**Title**: *A singular de Rham algebra and spectral sequences in diffeology*.**Abstract**: In this talk, I will introduce a singular de Rham algebra under which

the de Rham theorem holds for every diffeological space.

The Leray-Serre spectral sequence and the Eilenberg-Moore spectral sequence

are also discussed in diffeology.

โ **Norio Iwase** (Kyushu University, Japan)**When**: Thursday May 6th, 2021 โ 12:00 GMT.**Where**: Zoom link**Title**: *Whitney Approximation sor Smooth CW Complexes*.**Abstract**: In this talk, we introduce a notion of smooth CW complex using disks, while we know there are different definitions using cubes or simplexes instead of disks. It is a kind of future work for us to clarify the relationship among them. With our definition of a smooth CW complex, we show Whitney Approximation for smooth CW complex, which enables us to obtain that any continuous CW complex is continuously homotopy equivalent to a smooth CW complex.

We observe also that a smooth CW complex has enough many functions, *i.e. *it has an open base of the form \(\phi^{-1}(]0,1[)\). Furthermore, it follows that, for any D-open covering of a smooth CW complex, there exists a partition of unity subordinate to the covering.

โ **Patrick Iglesias-Zemmour** (The Hebrew University of Jerusalem, Israel)**When**: Thursday April 1st, 2021 โ 1PM GMT.**Where**: Zoom link / Lecture Notes**Title**: *Orbifolds, Quasifolds as Diffeologies and C*-algebras*.**Abstract**: I will show how to associate to these special diffeological spaces that are orbifolds, and more generally quasifolds, a C*-algebra in a functorial way, in which diffeomorphisms translate into Morita equivalences.