Seminar of differential equations will continue on November 18, 2019 at 12pm in lecture room M5.

doc. Mgr. Pavel Řehák, Ph.D. (Ústav matematiky, FSI VUT Brno)

Asymptotic analysis of differential and difference equations

We will continue on Thursday, November 7, in M5 at 1pm by the talk

T. Uemura

A General Framework for the Semantics of Type Theory

Abstract:
We propose an abstract notion of a type theory to unify the CwF-semantics of various type theories including Martin-Löf type theory, two-level type theory and cubical type theory. For each type theory, we establish a correspondence between theories and CwF-models: every theory generates a syntactic model; every model has an internal language.

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.