New frontiers in algebra and geometry

A primary goal of this Meeting will be to witness and foster the existing close ties and cooperations between Korean and Italian mathematicians, in the fields related to Algebra and Geometry, with a particular emphasis on Algebraic Geometry, a major field of mathematical research and knowledge. A second goal, in a historical moment where scientific research is extremely specialized, also in mathematics, is to be a forum of frank and open interdisciplinary discussion in the field of mathematics, highlighting the interconnections of algebra, geometry and combinatorics, leading to a unified building of knowledge meant to reverberate on other disciplines, as Physics for instance. Algebra, geometry and combinatorics are all fields of exact calculations, as opposed to the numerical approximations and iterative methods: and the complexity of these calculations is overcome by the overarching principle of symmetry and geometrical representations. In the end, algebra may invoke the construction of combinatorial objects, or, as in the theory of linear series, and the theory of crystallographic groups, of convex geometry. In turn, algebro-geometric methods, as the hard Lefschetz theorems, may lead to the solution of long standing problems in commutative algebra and combinatorics (as witnessed by a recent Fields medal award). Groups of transformations are the key to the Symmetry principle, and here we encounter finite groups of symmetries, as well as infinite Lie Groups, and their differential geometric properties, and related differential equations. Complex geometry, but also positive characteristic and arithmetic geometry intertwine to lead to the solution to deep open problems: and the scenario is by and large still far from being fully uncovered.

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