The seminar on differential geometry will continue with this lecture:

October 21, 10am, lecture room M5.

Jan Slovák:

Non-holonomic equations in geometric control theory

Abstract:

The talk will remind my earlier exposition of a new approach to building non-holonomic equations equivalent to the hamiltonian formalism. In particular, I will reveal how to rewrite them as "nice" holonomic equations and present some examples.

Seminar of differential equations will continue on October 21, 2019 at 12pm in lecture room M5.

Mgr. Viera Štoudková Růžičková, Ph.D. (Ústav matematiky, FSI VUT Brno)

Discrete Riccati matrix equation and the order preserving property

The seminar on differential geometry will continue with this lecture:

October 14, 10am, lecture room M5.

Radoslaw Kycia:

The Poincare lemma, antiexact forms, and fermionic quantum harmonic oscillator

Abstract:

I will present the connection between Poincare lemma and homotopy operator defined by Edelen. This will be used to determine functional calculus (Bittner’s operator calculus), which, in the case of a homotopy operator, resembles quantum fermionic oscillator algebra.

I will also present a topological/chain complex version of a homotopy operator.

Finally, I will show how this operator calculus looks in the setup of complex manifolds and how it ‘interacts’ with the Dolbeault complex.

We will continue on Thursday, October 10, in M5 at 1pm by the talk

J. Adamek

Finitary functors

Abstract:
Every finitary functor F between locally finitely presentable categories is finitely bounded, i.e., finitely generated subobjects of each FX factorize through the image (under F) of finitely generated subobjects of X. Conversely, finitely bounded functors preserving monomorphisms are finitary.
We discuss conditions under which 'finitary = finitely bounded' holds for a l l functors. This is true e.g. for atomic Grothedieck toposes with finitely many finitely presentable atoms.
We also study the finitely presentable objects in the categories [Set,Set]_fin of all finitary set functors and Mnd_fin(Set) of all finitary monads over Set.