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Online algebra seminar - February 11th, 1pm PDF Print

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

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.

Last Updated on Tuesday, 09 February 2021 16:27
Online algebra seminar - February 4th, 1pm PDF Print

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

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.

Last Updated on Wednesday, 03 February 2021 09:05
41st WINTER SCHOOL GEOMETRY AND PHYSICS Czech Republic (Srni), January 2021 PDF Print

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):


  • 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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Jan Slovak
on the behalf of the Organizing Committee

Last Updated on Monday, 18 January 2021 09:09
Pozvánka na habilitační přednášku RNDr. Martiny Pavlačkové, Ph.D. PDF Print

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 .

Název přednášky:

Bound sets approach to multivalued boundary value problems.

Last Updated on Monday, 18 January 2021 09:01
Ivan Kolář, professor emeritus, has died PDF Print

With deep sorrow we announce that prof. RNDr. Ivan Kolář, DrSc., passed away on December 15, 2020.

Ivan Kolář was born on May 22, 1936 in Brno and most of his academic career was linked to Brno, too. Already during his study at Masaryk University, he joined the research group following the geometric footsteps of Eduard Čech. Influenced by the abstract and coordinate free approach to infinitesimals which had been recently introduced by Charles Ehresmann, Ivan Kolář worked out an abstract general version of the Cartan moving frame method and employed the newly emerged theory of jets and iterated differentials in numerous areas of differential geometry, variational calculus, and mathematical physics. Soon, these interests naturally moved his focus towards the abstract theory of natural objects and operations in differential geometry.

After a decade spent at the Brno military academy, in 1969 Ivan Kolář accepted Borůvka’s invitation to join the Brno branch of the Mathematical Institute of the Academy of Sciences of the Czech Republic. He later led this institution with grace through the difficult period of normalization until 1989. During this time, he also pushed forward the research culminating in the celebrated Springer monograph Natural Operations in Differential Geometry (published 1993, co-authored by Peter Michor and Jan Slovák, the most highly cited item ever in the 58A MathSci category, and perhaps also the initial impulse towards the 58A32 subcategory Natural Bundles in MSC2000).

In 1980, Ivan Kolář organized the very first meeting of the (still running) series of international conferences Differential Geometry and its Applications, and from 1985 he cochaired the (also still running) Central European Seminar with Peter Michor, perhaps the only regular seminar happening across the “iron curtain” before 1990. From 1991 onwards, Ivan Kolář was working at the Faculty of Science of Masaryk University, where he contributed in an essential way to several further research directions, including the covariant approach to the so-called Weil bundles, the abstract axiomatic geometric approach to infinitesimals.

Ivan Kolář was the main driving force in the differential geometry group in Brno for at least forty years, and there is a large group of grateful students and collaborators pushing his views and hopes further.

Announcement in PDF

Last Updated on Monday, 21 December 2020 12:32

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