The paper surveys open problems and questions related to different aspects of integrable
systems with finitely many degrees of freedom. Many of the open problems were suggested …

The main purpose of this book is to present a complete self-contained explanation of the
virtual fundamental chain technique via the Kuranishi structure introduced by Fukaya–Ono …

Let XX be a smooth projective variety of dimension nn over CC equipped with a very ample
Hermitian line bundle L L. In the first part of the paper, we show that if there exists a toric …

In this paper, we tackle the problem of tiling a domain with a set of deformable templates. A
valid solution to this problem completely covers the domain with templates such that the …

Toric Degeneration and Nondisplaceable Lagrangian Tori in S2 × S2 Page 1 K. Fukaya et al.
(2012) “Lagrangian Tori in S2 × S2,” International Mathematics Research Notices, Vol. 2012, No …

Following the historical track in pursuing $ T $-equivariant flat toric degenerations of flag
varieties and spherical varieties, we explain how powerful tools in algebraic geometry and …

In this paper we first develop various enhancements of the theory of spectral invariants of
Hamiltonian Floer homology and of Entov-Polterovich theory of spectral symplectic quasi …

We study the algebraic combinatorics of monomial degenerations of Plücker forms which is
governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a …

arXiv:0801.2830v4 [math.SG] 1 Oct 2009 Page 1 arXiv:0801.2830v4 [math.SG] 1 Oct 2009
MIRROR SYMMETRY FOR TORIC FANO MANIFOLDS VIA SYZ TRANSFORMATIONS …

We set up a topological framework for degenerations of symplectic manifolds into singular
spaces paying a special attention to the behavior of Lagrangian manifolds and their …