We will continue on Thursday, February 13, in M5 at 1pm by the talk

F. Pakhomov

Dilators and Ptykes

Abstract:
Dilators are endofunctors D:WO->WO preserving pullbacks and directed co-limits, where WO is the category of well-orderings and strictly monotone maps. This notion was introduced by J.-Y. Girard as one of central notions within his approach to certain problems in proof-theory (calculation of proof-theoretic ordinals). Some more sophisticated applications motivate higher-order generalizations of the notion of dilator, known as ptykes. For example, ptykes of the type (WO->WO)->WO are functors from the category of dilators Dil to WO that preserve pullbacks  and  directed co-limits (here Dil is the category of dilators and Cartesian natural transformations).

In the first part of the talk I plan to discuss dilators, some basic results about them, and give some idea about their applications in proof-theory.  Next I plan to talk about my approach to the theory of ptykes, where  types of ptykes are interpreted as classes of relational structures that are closed under substructures.

Call for research positions at the Department of Mathematics and Statistics, Masaryk University

Dear Friends of Hikes and Mathematics,

you are invited to our 28th mathematical hike planned on January 25th. Meet at 09:36 at the bus stop "Veverská Bítýška, náměstí" (bus number 303).

The hike is 18 km long - we will follow a green path to Lažánky and go a full circle by a yellow path to Bítýška. We will return to Brno by bus.

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

Have a nice January and successful exam period,

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

We will continue on Thursday, January 9, in M5 at 1pm by the talk

S. Henry

Polygraphs and homotopy polygraphs

Abstract:
Polygraphs (or computades) are the most general notion of diagram generating strict infinity categories. Some people have believed in the past that they were a presheaves category, but this was proved to be false by Makkai and Zawadowski.
After a quick introduction to polygraphs and why they are not a presheaves category, I'll show that if one defines a homotopy theoretic (or infinity categorical) version of polygraphs then they form an infinity presheaves category. More generally I'll associate to any strongly cartesian monad acting on an infinity topos an infinity category of polygraphs which is itself an infinity topos.