We will continue online on Thursday, June 17th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Leonardo Larizza

Lax factorisation systems and categories of partial maps

Abstract:
Lax factorisation systems and categories of partial maps
Factorisation systems describe morphisms in a category by factorising them into pairs of composable morphisms. Their definition depends on a kind of orthogonality relation between morphisms, which entails the existence of some diagonal morphisms for certain squares. In this seminar we present the new notion of lax weak orthogonality between morphisms, which involves lax squares and the factorisation systems it generates. Then we will introduce lax versions of functorial and algebraic weak factorisation systems and some of their properties. These lax factorisation systems are discussed, keeping the theory of ordinary factorisation systems as a blueprint and providing useful properties.
An overview of the examples of such lax factorisation systems is presented in the context of partial maps. We conclude with a discussion of general constructions of these examples and their description in the particular case of sets with partial maps.

The Department of Mathematics and Statistics together with Faculty of Mathematics and Physics of Charles University and the Union of Czech Mathematicians and Physicist organize the 5th International Workshop on Functional and Operatorial Statistics.

IWFOS 2021 will be held from 23rd to 25th June 2021 online, and during 3 days, the workshop will offer about 7 invited talks, 42 contributed talks and a poster session on theory, methods and applications in the vibrant field of functional data analysis from all over the world. The web page of the conference is https://iwfos2021.sci.muni.cz/

The purpose of the series of IWFOS is to highlight the major trends in different areas of functional statistics through the exchange of ideas and the promotion of collaboration between researchers from different countries. It aims at contributing to future developments of such areas. The workshop will be a platform for communication, exchange of ideas and interaction for researchers in statistics for infinite-dimensional and high-dimensional problems.

We will continue online on Thursday, June 10th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Noam Zeilberger

Skew monoidal categories and the proof-theoretic anatomy of associativity (and unitality)

Abstract:
Based on joint work with Tarmo Uustalu and Niccolò Veltri.

The talk will survey a recent line of work, which takes a proof-theoretic approach to solving the coherence problem(s) for skew monoidal categories and related structures. I will begin by discussing the so-called Tamari order on fully-bracketed words induced by a semi-associative law (AB)C <= A(BC), and explain how a simple sequent calculus may account for some of its fascinating properties, such as the fact that the set of fully-bracketed words on n+1 letters forms a lattice Y_n under this order, as well as a remarkable formula counting the number of intervals in Y_n.
Then I will recall the definition of skew monoidal categories, and explain how a more refined sequent calculus may be used to solve two related coherence problems: deciding equality of maps and enumerating homsets in free skew monoidal categories. Closely related to recent work by Bourke and Lack, this sequent calculus may be considered as a canonical construction of the free left representable skew multicategory over a set of atoms.
Finally, I will briefly discuss variations of the sequent calculus capturing "partially skew" monoidal categories with different normality conditions.

References:
[1] https://arxiv.org/abs/1803.10080
[2] https://arxiv.org/abs/2003.05213
[3] https://arxiv.org/abs/2101.10487

The seminar on differential geometry will continue with this lecture:

June 7, 10am, online on MS Teams and the seminar room on the second floor

Join via this LINK.

Radek Suchanek (Masaryk University):

Some remarks on variational nature of Monge-Ampère equations in dimension four

Abstract:

I will present a necessary condition for the local solvability of the strong inverse variational problem in the context of Monge-Ampère partial differential equations and first-order Lagrangians. In contrast with the previous talk by Marcus Dafinger, this condition is given by comparing differential forms on the first jet bundle and is valid only for the aforementioned PDEs. To illustrate how this approach can be applied, we will examine the linear Klein-Gordon equation, first and second heavenly equations of Plebanski, Grant equation, and Husain equation.
I will also speak about the drawbacks of the method when trying to generalize it to a system of equations.