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Innolec lectures - Gian Maria Dall'Ara - An invitation to PDE methods in several complex variables PDF Tisk

Přednášky od 5. 11. do 8. 11. 2018, zasedací mistnost ÚMS (první patro u schodů), od 12:00 do 14:00

Gian Maria Dall'Ara (University of Vienna)

An invitation to PDE methods in several complex variables


In these lectures I will present the point of view on complex analysis in several variables originated in the '60s from the seminal work of Hörmander and Kohn (among others) on the d-bar problem and some of the most interesting applications. A tentative list of the topics I will discuss is:

1) one versus several complex variables: domains of holomorphy and failure of Riemann mapping theorem;

2) the problem of smooth extension to the boundary of biholomorphisms (Fefferman and Bell-Ligocka theorems);

3) existence and compactness in the d-bar problem: a review of some ideas of Hörmander, Kohn and Catlin;

4) Kohn-Nirenberg regularity and recent work on necessary and sufficient conditions for compactness.

The lectures will be suited (and hopefully interesting) for master students and researchers alike.

Aktualizováno Úterý, 06 Listopad 2018 16:33
Seminář z algebry - 8.11.2018 PDF Tisk

Další seminář z algebry se koná 8.11.2018 od 13.00 v posluchárně M5.

Jovana Obradović (Univerzita Karlova)

Categorified cyclic operads in nature


In this talk, I will introduce a notion of categorified cyclic operad and justify the need of such a notion by exhibiting its place and use “in nature”.
Categorified cyclic operads are like symmetric monoidal categories, in that they guide an interplay of commutativity and associativity, but they are more restrictive, as they allow less instances of these two isomorphisms. In particular, the coherence conditions of symmetric monoidal categories do not ensure coherence of categorified cyclic operads, the hexagon of Mac Lane not even being well-defined in the latter setting. The coherence conditions that we do take from Mac Lane are the pentagon and the requirement that the commutator isomorphism is involutive, but we need much more in order to ensure coherence: we need two more mixed coherence conditions, a hexagon (which is not the hexagon of Mac Lane) and a decagon, as well as three more conditions which deal with the action of the symmetric group.
I will first give an example of a categorified cyclic operad in the form of an easy generalisation of the structure of profunctors of Bénabou.
I will then show how to exploit the coherence conditions of categorified cyclic operads in proving that the Feynman category for cyclic operads, introduced by Kaufmann and Ward, admits an odd version.
I will finish with combinatorial aspects of categorified cyclic operads, i.e. with their possible characterisations in convex and discrete geometry. This investigation aims at finding polytopes which describe the coherences of categorified cyclic operads, in the same was as the geometry of symmetric monoidal categories is demonstrated by permutoassociahedra.

Aktualizováno Pondělí, 29 Říjen 2018 15:38