Related papers: Mirror Symmetry And Some Applications
We use mirror symmetry to establish the first concrete arena of spacetime topology change in string theory. In particular, we establish that the {\it quantum theories} based on certain nonlinear sigma models with topologically distinct…
An overview of supersymmetry and its different applications is presented. We motivate supersymmetry in particle physics. We then explain how supersymmetry helps us analyze field theories exactly, and what dynamical lessons these solutions…
This article summarizes recent trends in mobile biometrics.
We study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a (super)manifold. We also show that in many cases these conditions guarantee exactness of the stationary phase…
Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, consequences for the associated diffraction spectra and the…
The author reports his recollections of what transpired. These may or may not prove consistent with the contributions to be published in the proceedings. Corrections are welcome.
The B-side of Kontsevich's Homological Mirror Symmetry Conjecture is discussed. We give first a self-contained study of derived categories and their homological algebra, and later restrict to the bounded derived category of schemes and…
This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the integral variations of Hodge structure which can underly…
Exploitation of symmetries is an indispensable approach to solve certain classes of difficult SAT instances. Numerous techniques for the use of symmetry in SAT have evolved over the past few decades. But no matter how symmetries are used…
This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of papers of the author and his collaborators Daniel Pomerleano…
For the past few decades, structured light has been gaining popularity across various research fields. Its fascinating properties have been exploited for both previously unforeseen and established applications from new perspectives. Crucial…
We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge…
In this talk I review recent developments in superstring theory. In the first half of the talk I discuss some of the earlier developments in this subject. This includes a review of the status of string theory as a unified theory of gravity…
General issues concerning the regularization of supersymmetric theories using dimensional regularization and dimensional reduction are reviewed. Recent progress on problems of dimensional reduction related to factorization, supersymmetry,…
This is a translation of an article appeared in Japanese in Suugaku 63 (2011), no. 1, 43-66 (MR2790665) and is a survey of Lagrangian Floer homology which the author studies jointly with Y.-G.Oh, H. Ohta, and K. Ono. It also contains some…
A summary of results on synchrotron radiation is presented along with notes on its properties and applications. Quantum aspects are briefly mentioned. Synchrotron radiation facilities are described briefly with a detailed coverage to the…
The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete…
We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. It is done in the so called attractor backgrounds (moduli) which can be far from the conventional large complex limits and are selected by…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
This is a written version of the invited lecture at the 9th European Congress of Mathematics in July 2024 in Sevilla. We review certain new symmetries of Grothendieck rings that have emerged in representation theory.