Towards a bihamiltonian structure for the double ramification hierarchy

Tau-structure for the Double Ramification Hierarchies

In this paper we continue the study of the double ramification hierarchy of [Bur15]. After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of the) tau-function of the string solution and show that it satisfies various properties (string, dilaton and divisor equations plus some important degree constraints). We then formulate a stronger ver...

Towards Establishing a Hierarchy in the Japanese Sentence Structure

The Minami Hierarchy or the four-layers of embeddings within Japanese sentences has been known to give a convincing account of heterogeneous linguistic data in Japanese Grammar. However, the categorization of sentence constituents has faced serious problems. In this paper, we illustrate that the hierarchical sentential structure is on the whole tenable and attempt to represent it with Phrase St...

Hurwitz Theory and the Double Ramification Cycle

This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov-Witten theory, with a particular eye to the contributions made to the understanding of the Double Ramification Cycle, a cycle in the moduli space of curves that compactifies the double Hurwit...

Towards Explicit Description of Ramification

Bihamiltonian structure of the classical superstring in AdS5 × S⁵

We discuss the bihamiltonian structure of the Metsaev-Tseytlin superstring in AdS5 ×S 5. We explicitly write down the boost-invariant symplectic structure for the superstring in AdS5 × S 5 and explain its relation to the standard (canonical) symplectic structure. We discuss the geometrical meaning of the boost-invariant symplectic structure for the bosonic string.