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IWFOS 2021: from 23rd to 25th June 2021 ONLINE PDF Print

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.

Last Updated on Friday, 11 June 2021 12:15
 
Online algebra seminar - June 10th, 1pm PDF Print

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

Last Updated on Wednesday, 09 June 2021 07:45
 
Online differential geometry seminar - June 7, 10am PDF Print

The seminar on differential geometry will continue with this lecture:

June 7, 10amonline 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.

Last Updated on Thursday, 03 June 2021 09:16
 
Online differential geometry seminar - May 31, 10am PDF Print

The seminar on differential geometry will continue with this lecture:

May 31, 10amonline on MS Teams and the seminar room on the second floor

Join via this LINK.

Marcus Dafinger (University of Jena):

On formal calculus of variations, Cartan formula and Noether's theorem

Abstract:

We give an introductory talk on the formal calculus of variations. Concepts from differential geometry, like Lie-derivative, exterior derivative and Cartan formula will be related to first variation, Helmholtz map and a kind of related Cartan formula. With the help of these operations we then formulate Noether's theorem and present some results on the so-called Takens' problem.

Last Updated on Monday, 31 May 2021 08:07
 
Online algebra seminar - May 13th, 1pm PDF Print

We will continue online on Thursday, May 13th, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Nathanael Arkor

Higher-order algebraic theories and relative monads

Abstract:
There have traditionally been two ways to reason about universal algebraic structure categorically: via algebraic theories, and via monads. It is well known that the two are tightly related: in particular, there is a correspondence between algebraic theories and a class of monads on the category of sets.


Motivated by the study of simple type theories, Fiore and Mahmoud introduced second-order algebraic theories, which extend classical (first-order) algebraic theories by variable-binding operators, such as the existential quantifier ∃x of first-order logic; the differential operators d/dx analysis; and the λ-abstraction operator of the untyped λ-calculus. Fiore and Mahmoud estab- lished a correspondence between second-order algebraic theories and a second-order equational logic, but did not pursue a general understanding of the categorical structure of second-order algebraic theories. In particular, the possibility of a monad–theory correspondence for second- order algebraic theories was left as an open question.

In this talk, I will present a generalisation of algebraic theories to higher-order structure, in particular subsuming the second-order algebraic theories of Fiore and Mahmoud, and describe a universal property of the category of nth-order algebraic theories. The central result is a correspondence between (n + 1)th-order algebraic theories and a class of relative monads on the category of nth-order algebraic theories, which extends to a monad correspondence subsuming that of the classical setting. Finally, I will discuss how the perspective lent by higher-order algebraic theories sheds new light on the classical monad–theory correspondence.

This is a report on joint work with Dylan McDermott.

Last Updated on Wednesday, 12 May 2021 15:57
 
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