I will give an overview of some recent progress in the computation and understanding of new structures of scattering amplitudes and related quantities in Quantum Field Theory, gravity and string theory, including all-loop geometries underlying amplitudes and correlators in maximally supersymmetric Yang-Mills theory, as well as a combinatorial formulation for real-world scattering of colored scalars, pions and gluons.

Biography:
Song He is mostly interested in fundamental questions in QFT, gravity and string theory, as well as applications to particle physics, cosmology and related topics in mathematics. He got his PhD from Peking University in 2009, and worked at Albert-Einstein Institute, Perimeter Institute and Institute for Advanced Study, before joining Institute of Theoretical Physics, Chinese Academy of Sciences in 2015.

Some highlights of his research include a new formulation for scattering of massless particles, the discovery of combinatorial geometries underlying real-world scattering, as well as higher-order/exact results in QFT and quantum gravity.

Heterotic string models in 4-dimensions are the hybrid theories of a left-moving $ N=1 $ fermionic string whose additional 6-dimensions are compactified on an $ N=2 $ SCFT with central charge 9, and a right-moving bosonic string, whose additional dimensions are also compactified on an $ N=2 $ SCFT with central charge 9, and the remaining 13 dimensions compactified on the torus of $ E(8) \times SO(10) $ Lie algebra.

The important class of exactly solvable heterotic string models considered earlier by D. Gepner corresponds to products of $ N=2 $ minimal models with total central charge $ c=9 $. These models are known to describe heterotic string models compactified on Calabi-Yau manifolds, which belong to a special subclass of general CY manifolds of Berglund-Hubsch type. We generalize this construction to all cases of compactifications on Calabi-Yau manifolds of general Berglund-Hubsch type, using the Batyrev-Borisov combinatorial approach. In particular, starting from the mirror pair of Batyrev lattices corresponding to a given CY manifold, we construct vertex operators of the complete physical theory as cohomology of Borisov differentials that correspond to points of reflexive Batyrev polyhedra. In particular, we show how the number of 27, 27 and singlet representations of $ E(6) $ is determined by the data of the reflexive Batyrev polytope that determines this CY manifold.

Biography:
Alexander Belavin, born on August 28, 1942, in Gorky (now Nizhny Novgorod) into an engineer's family, is a Russian theoretical physicist, Corresponding Member of the Russian Academy of Sciences, and Chief Researcher at the Landau Institute for Theoretical Physics. He specializes in quantum field theory and string theory, and is known for the discovery of instantons (1975), the development of conformal field theory (CFT), and his contributions to string theory. He graduated from MEPhI in 1967 and completed his postgraduate studies. Since 1976, he has been working at the Landau Institute for Theoretical Physics of the Russian Academy of Sciences. Together with his colleagues, he discovered instantons in gauge field theory, which became an important step toward understanding quark confinement. In 1984, he established the foundations of two-dimensional conformal field theory (jointly with A. A. Polyakov and A. B. Zamolodchikov).