# Seminar

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

🔊 Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem, Israel)
When: Thursday October 7th, 2021.
Where: Zoom link / paper
Title: Why irrational tori are so 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.

🔊 Jordan Watts (Central Michigan University)
When: Thursday November 4th, 2021 — 12:00 GMT.
Where: Zoom link
Title: To be announced.
Abstract: To be announced.

🔊 Serap Gürer (Galatasaray University, Turkey)
When: Thursday December 2nd, 2021 — 12:00 GMT.
Where: Zoom link
Title: To be announced.
Abstract: To be announced.

### Previous Talks

David Miyamoto (Toronto University, Canada)
When: Thursday September 2nd, 2021 — 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.

Enxin Wu (Shantou University, China)
When: Thursday July 8th, 2021 — 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.

Katsuhiko Kuribayashi (Shinshu University, Japan),
When: Thursday June 3rd, 2021 — 12:00 GMT.
Where: Zoom link
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.

Norio Iwase (Kyushu University, Japan)
When: Thursday May 6th, 2021 — 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.

Patrick Iglesias-Zemmour (The Hebrew University of Jerusalem, Israel)
When: Thursday April 1st, 2021 — 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.