Seminarium 06.06.2024
Michał Pawlikowski
(Institute of Mathematics, Lodz University of Technology)
Seminarium 13.06.2024
Natalia Maślany
Seminarium 20.06.2024
Tomasz Żuchowski
(Uniwersytet Wrocławski)
Given a function $f \in \omega^{\omega}$, a set $A \in [\omega]^\omega$ is free for $f$ if $f[A] \cap A$ is finite. For a class of functions $\Gamma\subseteq\omega^{\omega}$, we define $\mathfrak{ros}_\Gamma$ as the smallest size of a family $\mathcal{A}\subseteq[\omega]^\omega$ such that for every $f\in\Gamma$ there is a set $A \in \mathcal{A}$ which is free for $f$, and $\Delta_\Gamma$ as the smallest size of a family $\mathcal{F}\subseteq\Gamma$ such that for every $A\in[\omega]^\omega$ there is $f\in\mathcal{F}$ such that $A$ is not free for $f$. We compare several versions of these cardinal invariants with some of the classical cardinal characteristics of the continuum. Using these notions, we partially answer some questions of the other author and Koszmider and of Banakh and Protasov.
This is joint work with Arturo Martinez-Celis.
Seminarium 27.06.2024
Francesco Giacosa
(Instytut Fizyki)
The use of symmetries is an important tool in theoretical physics, since it strongly constrains the interaction types among particles. Chiral symmetry refers to a certain symmetry that, mathematically, involves two distinct SU(3) groups and is commonly applied to study mesons (composite particles made of a quark and an antiquark, such as pions). Objects of two types are constructed: those that involve the traces of matrices, and those that involve the determinant. Both of them turn out to be 'chirally invariant'.
In the recent work PhysRevD.109.L071502, a certain extension of the determinant has been put forward. This extension reduces to the usual determinant if specific conditions are met, but is more general and appears quite naturally when studying interactions among mesons. Its definition and its properties, as well as possible connections to various other extensions of the determinant, shall be discussed.
