We will continue online on Thursday, 16th of September, at 13.00 CEST on ZOOM platform and M5 lecture room (for information how to acces seminar and next programme visit this page) by the talk:

Nicholas Meadows

Higher theories and monads

Abstract:
We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories, and exploit this to prove many classical theorems about monads in the $\infty$-categorical setting. Amongst other things, we prove that the category of algebras for an accessible monad on a locally presentable $\infty$ category is locally presentable. We also apply the result to construct examples of $\infty$-categorical monads from pretheories.

Record available HERE.

Semilinear elliptic equations with a singular potential

Phuoc Tai Nguyen
Wednesday, 15 September, 4 pm, in the M1 Lecture Hall and ONLINE on ZOOM

Pavol Quittner                              Jan Slovak
chairmen of the Board                Director of the department

We will continue online on Thursday, 19th of August, at 13.00 CEST on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Charles Walker

The nerve of a relative monad

Abstract:
In this talk we will consider an embedding of monads into double categories, which sends a monad P to its (concrete) double category of P-embeddings (also called P split monos), as well as generalizations of this embedding the setting of (well-behaved) relative monads. By considering a more general notion of monad morphism (motivated by the relative setting), we will understand this embedding as a fully faithful nerve which exhibits the terminal monad as 'dense' with respect to these more general morphisms.

We will then give two applications of this construction. Firstly, we will give another approach by which one arrives at the “decagon type” axioms of last time, and secondly we will give a simpler proof of the reduced form of pseudo-distributive laws involving lax-idempotent pseudomonads. Note that some parts are a work in progress.

Dear Friends of Hikes and Mathematics,

Extreme hike! The 32nd mathematical hike is planned on the 31st of July. Meet at 06:00 at the Main Train Station of Brno.

We go by train (leaves at 06:12), then approx. 53 km to get back to Brno. This means that there is no train to catch, no time pressure as at the 31st hike. This hike favours shorter options: you can leave at 19 and 36 km mark comfortably. Evaluate your strength and join us.

All information and photos can be found at https://conference.math.muni.cz/vylety/. (in CZ)

Have a nice summer, we look forward to you joining us.

Jana Bartoňová and Jonatan Kolegar, organizers
Jan Slovák, Director of the Department of Mathematics and Statistics