Perspectives in Lie Theory

INdAM Intensive Period - FIRB Project “Perspectives in Lie Theory”

9 December 2014 - 28 February 2015

Aims

Through the past century, Lie theory has developed in several directions, finding important applications in other areas of mathematics and physics.

There exist deep connections among these directions. First of all, techniques and tools are often very similar. Secondly some problems that arise in one context naturally induce questions that find their solution in another one. The combinatorics of root systems and Coxeter groups, for instance, is one of the fundamental ingredients in Lie theory, and some problems not directly connected with this language eventually amount to combinatorial statements.

This is the case, for instance, of the problem of classifying finite and infinite-dimensional Lie algebras, studying symmetric and spherical varieties, as well as topological properties of hyperplane arrangements. In the same vein, some of the most significant results in the combinatorics of Coxeter groups are handled via the geometry of the above varieties, or the representation theory of Lie algebras.

We believe that the collaboration between Lie theorists that have distinct education and interests may constitute a fundamental ingredient for our goals.

In this special period we would like to focus mainly on the following themes:

• Homogeneous varieties and their compactifications
• Wonderful models of subspace and toric arrangements.
• Configuration and loop spaces.
• Combinatorics and topology of toric and hyperplane arrangements and representations of Artin groups.
• Combinatorics of Coxeter groups and groups generated by pseudoreflections.
• Infinite-dimensional Lie algebras, their generalizations and applications.
• Representation theory and Kazhdan-Lusztig conjecture.
• Affine groups and algebras, geometrical aspects and representation theory.

The idea of the Intensive Period is to have some interesting mini courses for PhD students and researchers and regular talks, but also time for discussions and collaboration in the beautiful setting of the city of Pisa.

A workshop will take place during the third week of February.

Please also see Planned activities for more detailed information about the programme.

Some funds will be available to offer financial support to a limited number of selected young researchers and students. See the section Financial Support for more details and for applications. Priority will be given to applications submitted by September 7th, 2014.

In order to contact the organizers, please write to lie.theory.pisa@gmail.com.

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This research period is organized with the partecipation and support of the following institutions:

- INDAM.
- CMTP, Università di Roma Tor Vergata.
- Foundation Compositio Mathematica.
- . Università di Padova.
- Sapienza Università di Roma.
- Università di Bologna.
- . Università di Pisa.
- National Science Foundation.
-PRIN 2012 research project "Spazi di Moduli e Teoria di Lie":
- Dipartimento di Matematica, Università di Roma,Tor Vergata
- Dipartimento di Matematica, Università di Bologna.
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