IDEA of the Round Table:
Modern Theoretical Physics and in particular String/Supergravity Theory has progressively included into a single texture the majority of most advanced mathematical structures pertaining to a spectrum of topics that ranges from algebraic topology to differential geometry, algebraic geometry, Lie algebra theory, integrable dynamical systems and even number theory. Pure Mathematics and Theoretical Physics not only cross each other’s way but in several instances have mutually benefited from such crossings. The excellence of French and Russian Mathematics is not only beyond any dispute but there is also a strong flow of interactions and collaborations between the two communities that finds a pivotal centre around the French Laboratoire Poncelet hosted by Moscow Independent University. The Italian Mathematical Physics community has also strong relations with France that have recently led to the creation of the Italo-French Laboratory Fibonacci at the Scuola Normale di Pisa. Similarly strong ties exist between Italy and France in Theoretical Physics and between Italy and Russia in several provinces of Math-Phys.
In view of this it is particularly interesting to unite at the same place for a three day meeting active scientists from the communities of the three countries with the goal of exchanging views on advanced topics of common interest having Fundamental Mathematics has the common denominator and central focus. The perspective is that of further expanding the existing collaborations and of exploring the possibilities for new ones. It would also be great if in the long run more stable and institutional connections could be built between the Italian and the Russian mathematically oriented communities on the model provided by the French-Russian experience of the Poncelet Institute.
The success of the series of Italian Russian Round Tables conducted in the last few years in Dubna suggested that the proper framework for this new trilateral event is once again the Joint Institute for Nuclear Research whose international prestige and proven expertise will contribute in an essential way to the success of the Round Table.
Ultimately the goal of the Round Table is to bring together Mathematical Physicists and Pure Mathematicians, who work on the corner of adjacent subjects but speaking somewhat “different languages”, so that there would be a deeper mutual understanding in the two communities and new ideas for a profitable exchange of views might arise. To this effect we will ask some of the senior distinguished participants to give a broad, overview talk on their field of expertise possibly in a simple language understandable by both communities.
Preliminary List of Topics:
The above goal will pursued establishing a list of four attraction points around which Pure Mathematicians and Mathematical Physicists can find common ground of interest and application. Specifically:
- Dynamical System Theory (classical and quantum) with applications in
- Integration of (super)gravity equations for Black Holes and Cosmology
- AdS/CFT correspondence, spin chains, solvability of Yang Mills theories, Omega deformations and the like
- Exact S matrix Quantum Field Theories, Liouville Theory, quantum gravity models, 2d CFT, AGT and the like
- Exact solutions of inflationary models
- The issue of Special Geometries, new Non Geometries, Non Kaehler Geometries, Non commutative geometries and the like, with applications to
- Gauge theories, instanton and monopoles
- Supergravity and String compactifications
- G-structures and flux compactifications
- Manifolds of restricted holonomy and all that
- Algebraic Geometry issues with applications in String Theory, Supergravity and Gauge Theories
- Mirror symmetry
- Issues of Number Theory that have found applications in Mathematical Physics like, for instance:
- Black Entropy, counting of microstates
- Feynman diagrams and new approach to finiteness, polylogs, multiple zeta values, Hurwitz numbers and matrix models
- Other …