Maps are discrete surfaces obtained by gluing polygons, and form a natural model of random geometry. Of particular interest is the study of their large-scale properties, which has been an active field of research for more than 25 years. A major open question is the geometry of maps which are “decorated” by a statistical physics model at a critical point. I will present some results about a...
Conformal blocks are essential objects to study in the 2d CFTs. They depend on the data of a vertex algebra CV, a punctured Riemann surface C, and possible decorations inserted at the punctures. The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. In particular, some very important Virasoro conformal blocks at c=1 are also...
Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. In this talk, I will show some examples of how the interplay between algebro-geometric methods and fundamental physics problems leads to advances in both disciplines. In particular, I will discuss vector spaces associated with a family of generalized Euler integrals and the study of their singular locus.
