Related papers: From primitive form to mirror symmetry
We show that under the hypotheses of Strominger, Yau and Zaslow's paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\"ahler…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the…
For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.
The paper is to classify irreducible integrable modules for the twisted full toroidal Lie algebra with some technical conditions. The twisted full toroidal Lie algebra are extensions of multiloop algebra twisted by sevaral finite order…
We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY double covers of \(\mathbb{P}^{3}\) branched along (1) a union…
A notion of rigidity with respect to an arbitrary semidualizing complex C over a commutative noetherian ring R is introduced and studied. One of the main result characterizes C-rigid complexes. Specialized to the case when C is the relative…
Parity nonconservation led Lee and Yang (1956) to the hypothesis of additional fermions with properties that mirror those of usual particles. It is shown here that the well-known observed qualitative structure of the quark mixing matrix…
We present a framework having the potential to unify the fundamental interactions in nature by introducing new degrees of freedom. An attempt is made to explain the hierarchy between the weak scale and the coupling unification scale, which…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system. The one dimensional equations of motion are integrated exactly for both systems and their solutions can be…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
This is an expanded version of the author's talk at the third annual meeting of International Consortium of Chinese Mathematicians held at USTC in December 2020. In this expository article, we give a survey on joint works with Hosono, Lian,…
Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that…
We analyze the recently proposed mirror superposition experiment of Marshall, Simon, Penrose, and Bouwmeester, assuming that the mirror's dynamics contains a non-unitary term of the Lindblad type proportional to -[q,[q,\rho]], with q the…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
We consider the Berglund-H\"ubsch-Henningson-Takahashi duality of Landau-Ginzburg orbifolds with a symmetry group generated by some diagonal symmetries and some permutations of variables. We study the orbifold Euler characteristics, the…
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
The introduction of mirror fermions with masses between the weak scale and 1 TeV could offer a dynamical origin to the standard-model electro-weak symmetry breaking mechanism. The purpose of this work is to study the dynamics needed in…
In this paper we study Seidel's mirror map for abelian and Kummer surfaces. We find that mirror symmetry leads in a very natural way to the classical parametrization of Kummer surfaces in $\P^3$. Moreover, we describe a family of embeddings…