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Oggetto:

Spazi di matrici, dalla teoria classica alle applicazioni in geometria differenziale, fisica matematica, analisi numerica

Oggetto:

Spaces of matrices, from classical theory to applications in differential geometry, mathematical physics, numerical analysis

Oggetto:

Academic year 2020/2021

Teacher
Prof. Ada Boralevi
Teaching period
Jan-Mar
Type
Basic
Course disciplinary sector (SSD)
MAT/03 - geometry
Delivery
Formal authority
Language
English
Attendance
Obligatory
Oggetto:

Sommario del corso

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Program

Program

The purpose of this course is twofold; on the one hand the basics on the problem of the study of linear systems of matrices will be given, from classical results to the state of the art. On the other hand, a series of connections with other fields and applications will be explained.

Contents:

  • Spaces of matrices of constant and bounded rank, compression spaces, primitive spaces.
  • Connection with the theory of sheaves and vector bundles, and use of their invariants (such as Chern and Segre classes).
  • Connection with secant varieties of Segre and Veronese varieties, and secants of Grassmannians.
  • Maximal dimension of spaces of matrices of constant and bounded rank, and classification problems (from the classical works of Westick and Eisenbud and Harris to today's research and open problems).
  • Applications to differential geometry (varieties with degenerate dual and second fundamental form from works of Ilic and Landsberg), mathematical physics (congruences of lines and hyperbolic systems of conservation laws from works of Agafonov and Ferapontov), numerical analysys (uniform determinantal representations from works of van Doornmalen, Draisma, Hochstenbach, Plesteniak and myself).

Here:

https://staff.polito.it/ada.boralevi/teaching.html

you can find some slides I prepared for a similar course.

Suggested readings and bibliography



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Notes

First meeting:

 

Thursday, January 14th, at 11am on Zoom:

https://polito-it.zoom.us/j/95376611493?pwd=aW5GbmR4d28rTUNwaUJtQjMyV3RrZz09

ID: 953 7661 1493
Passcode: 530019

During this first class we will also arrange next meetings, and settle some details, such as the language we will use and the number of introductory basic lectures.

Oggetto:
Last update: 11/01/2021 18:13
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