PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

PORTALE DELLA DIDATTICA

Elenco notifiche



Introduction to twistor geometry

01TIKUR

A.A. 2024/25

Course Language

Inglese

Degree programme(s)

Doctorate Research in Scienze Matematiche - Torino

Course structure
Teaching Hours
Lezioni 20
Lecturers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Antonelli Vincenzo   Ricercatore L240/10 MATH-02/B 10 0 0 0 1
Co-lectures
Espandi

Context
SSD CFU Activities Area context
*** N/A ***    
Twistor geometry, as it was introduced by R. Penrose, lies on the crossroads of Differential Geometry, Algebraic Geometry and Theoretical Physics. The essence of the twistor programme is to encode the differential geometry of a Minkowski or Euclidean manifold by holomorphic data on some auxiliary complex space (a twistor space). This approach has revealed itself very successful in order to solve problems arising in gauge theory, as it can be, to mention a celebrated one, Yang-Mills field equations. The main goals of this course are, at least, twofold: firstly, we will offer a general introduction to twistor geometry, conveying with elementary examples the spirit and scopes of this theory. Secondly, we will use twistor geometry as a framework in order to introduce some of the most basic objects that often appear in several areas of pure and applied mathematics.
Very basic knowledge of differential geometry and algebraic geometry. Depending on the requirements and necessities of the students, some introductory lessons will be added to the topics.
This is a tentative proposal of the contents of the course. The definitive program will be agreed with the students according to their interests and background. - Projective, Grassmannian and Flag manifolds. - Twistor manifolds and Klein correspondence. - Group actions, homogeneous structures and Lie groups. - Minkowski and Euclidian spaces. - Vector bundles, principal bundles and spinor bundles. - Construction of instantons.
On site
Oral presentation
P.D.2-2 - March
Course schedule: Tuesday 18 Marzo 14:30-17:30 Auletta Seminari (DISMA) Thursday 20 Marzo 14:30-17:30 Auletta Seminari (DISMA) Tuesday 25 Marzo 14:30-17:30 Auletta Seminari (DISMA) Thursday 27 Marzo 14:30-17:30 Auletta Seminari (DISMA) Tuesday 1 Aprile 14:30-17:30 Auletta Seminari (DISMA) Thursday 3 Aprile 14:30-17:30 Auletta Seminari (DISMA) Tuesday 8 Aprile 14:30-17:30 Auletta Seminari (DISMA) Thursday 10 Aprile 14:30-17:30 Auletta Seminari (DISMA)