A CIMPA Research School on the interaction between

mathematics and string theory.

Auditorio de la Biblioteca Central

Universidad de San Martín

San Martín, Buenos Aires, Argentina

28/10/2019 to 08/11/2019

For more than forty years, string theory has been able to impact in the development of several fields of mathematics. K-theory, algebraic and differential geometry, topology, infinite dimensional analysis, representation theory and derived categories, to mention a few, have been profoundly influenced by "stringy" ideas such as mirror symmetry, conformal field theory, D-branes and quantum cohomology. The main goal of this CIMPA Research School is to provide an introduction to many of these mathematical topics as well as some background on string theory.

**Courses and talks will cover the following subjects:**

- Courses and talks will cover the following subjects:
- Vertex Algebras and their modules.
- Representations of infinite dimensional Lie algebras.
- Calabi-Yau manifolds and Landau-Ginzburg models.
- Loday algebras and derived brackets.
- Hochschild homology and cohomology.
- Hopf algebras and quantum field theory.
- Quantum field theory on curved spacetimes.
- Generalized geometry and supersymmetric spaces.
- String compactifications and fluxes.
- Wess-Zumino-Novikov-Witten models.

The courses will not only provide the basic material but also some of the current research trends in the respective fields. The school is specially addressed to graduate and undergraduate students, both in mathematics and physics, but also to young researchers attracted by possible interactions with the topics previously described.