We will continue on Thursday, October 30, in boardroom (2nd floor) at 1pm by the talk

E. Lanari

Cartesian fibrations of (oo,2)-categories

Abstract:
The problem of dealing with infinitely many coherence constraints in oo-category theory when trying to define oo-functors has lead to a fibrational approach, in which one represents diagrams of the form B-->Cat_oo as a suitable kinds of fibrations over B. While this is a theorem, due to Lurie, in the case of oo-categories (i.e. (oo,1)-categories), so far there has been no combinatorial definition of a cartesian fibration of (oo,2)-categories.

In this talk, I will define cartesian fibrations in this context, prove some of their basic properties and show they are equivalent (under a suitable equivalence of (oo,2)-categories) to the counterpart in the context of categories enriched over marked simplicial sets (where the definition is given, mutatis mutandis, based on what happens with 2-categories). Furthermore, I will prove some statements made by Gaitsgory and Rozemblyum concerning locally cartesian fibrations and (oo,2)-categories fibred over (oo,1)-categories, thus substantiating the validity of our definition.

We will continue on Thursday, October 24, in M5 at 1pm by the talk

R. Stenzel

From Univalence to descent via "split indexed quasi-categories", part 2

Abstract:
In the last talk I sketched the definitions of univalent fibrations, complete Segal spaces and Grothendieck infinity-toposes.
On Thursday we will continue where we left off and relate these notions to one another, and, in that light, revisit the weak equivalence extension property and the fibration extension property of model categories.

Dear Friends of Hikes and Mathematics,

you are invited to our 26th mathematical hike planned on November 2nd. Start at 09:49 at the train station in Popice. You can join us in Brno - Dolní nádraží taking the train at 09:10.

We have planned an autumn 18 km hike visiting Pálava.  Return from Mikulov to Brno by bus.

We would love to see you there, please join us. It's a great opportunity for a meeting of students, graduates and employees of our department of all age or mathematical categories.

We are planning our next hike on 14th of December.

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

Looking forward to see you there,

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

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.