We will continue online on Thursday, February 11th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Paolo Perrone

Kan extensions are partial colimits

Abstract:
One way of interpreting a left Kan extension is as taking a kind of "partial colimit", where one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called bar construction of monads. The (pseudo)monads of interest for forming colimits are the monad of diagrams and the monad of small presheaves, both on the category CAT of locally small categories. 

We also define a morphism of monads between them, which we call "image", and which takes the "free colimit" of a diagram. This morphism allows us in particular to generalize the idea of "confinal functors", i.e. of functors which leave colimits invariant in an absolute way. This generalization includes the concept of absolute colimit as a special case.
The main result of this work says that a pointwise left Kan extension of a diagram corresponds precisely to a partial evaluation of its colimit. This categorical result is analogous to what happens in the case of probability monads, where a conditional expectation of a random variable corresponds to a partial evaluation of its center of mass.

Joint work with Walter Tholen. arXiv:2101.04531.

We will continue online on Thursday, February 4th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Jiří Rosický

Metric monads

Abstract:
We develop universal algebra over an enriched category and relate it to finitary enriched monads. Using it, we deduce recent results about ordered universal algebra where inequations are used instead of equations. Then we apply it to metric universal algebra where quantitative equations are used instead of equations. This contributes to understanding of finitary monads on the category of metric spaces.

Dear friends,
in view of the continuing pandemic the standard arrangement of our winter school is impossible. Finally, we gave up the assumed hybrid form and the 41st event in the row will be run as a ZOOM online meeting in two days only, January 19 and 20, 2021.

The ZOOM meeting will be at same link for both days and I will open it around 1:30pm for checking the screen sharing and possible chat (see more details below): https://cesnet.zoom.us/j/8496363962

Programme

• Anton Alekseev (Geneva) - Tuesday 2pm
  The Knizhnik-Zamolodchikov equation and its amazing properties
• Ugo Boscain (Paris) - Tuesday 3pm
  Quantum confinement for the curvature Laplacian −Delta + c K on 2D-almost-Riemannian manifolds
• Georgios Dimitroglou Rizell (Uppsala) - Tuesday 4:30pm
  Lagrangian classification and recurrence via pseudoholomorphic foliations.
• Jean Petitot (Paris) - Wednesday 2pm
  Sub-Riemannian Neurogeometry of the primary visual cortex
• Frederic Bourgeois ( Paris) - Wednesday 3pm
  An overview of contact homology
• Dmitri Alekseevsky (Moscow) - Wednesday 4:30pm
  Geometry of rank r= 2 and 3 special Vinberg cones

Short abstracts are available here .

Meeting ID: 849 636 3962
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Meeting ID: 849 636 3962

Find your local number: https://cesnet.zoom.us/u/acaswD6HRD

Jan Slovak
on the behalf of the Organizing Committee

Dovolujeme si Vás pozvat na habilitační přednášku RNDr. Martiny Pavlačkové, Ph.D. (Moravská vysoká škola Olomouc), která se bude konat v pondělí 11. ledna 2021 ve 12 hod prostřednictvím aplikace Zoom

https://cesnet.zoom.us/j/96398280717 .

Název přednášky:

Bound sets approach to multivalued boundary value problems.