"Algebraic properties of the quantum homology"
Abstract: The theory of quantum homology has been extensively studied in recent years, by mathematicians as well as physicists. The quantum homology algebra plays a fundamental role in symplectic geometry and has strong relations to many other fields such as algebraic geometry, integrable systems, and string theory. In this talk we will discuss certain algebraic properties of the quantum homology algebra of toric Fano manifolds. In particular, motivated by applications to symplectic geometry, we will focus on the semi-simplicity property of the quantum homology algebra, and describe an easily-verified condition for this property. (This is a joint work with Ilya Tyomkin.)