Mathematical Physics seminars at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SEMINAR
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"Categories of differential graded algebras and schemes"

The aim of these lectures is to understand the closed model category
structure on  DG-algebras and define and calculate the cotangent
complex using  dg-schemes.

We start form the basic definition of a Category  (no prerequisite are
required) and in fact the first three seminars are a short, elementary
introduction to category theory. They are suitable for mathematicians
in any field and for students, and also for the PhD or Laura
Magistrale level.

Program (Tentative Program)

Lecture 1: October 22nd (Monday) room C  at 11:00 am
Donatella Iacono
Introduction to Category Theory I.
(Definitions and Examples of Category and Functors.)


Lecture 2: October 24th (Wednesday) room C at 9:30 am
Donatella Iacono
Introduction to Category Theory II.
(Natural transformations and main properties).

Lecture 3: October 30th (Tuesday) room B at 2:30 pm
Donatella Iacono
Introduction to Category Theory III.
(Limit, colimit, fiber products.)

Then we will introduce the concept of Model Category, Dg-algebra, Dg-scheme,
Dg-manifold, and Cotangent Complex (about 10 Lectures in total, given by 
Barbara Fantechi and Donatella Iacono).