Related papers: Mirror Principle IV

This is the original version of my Ph.D. thesis. The main results have been divided up between papers arXiv:2111.09784 and arXiv:2204.10924. This paper has been kept on the arXiv to preserve some proofs of elementary lemmas that will be…

An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).

The reflection function of a smooth CR diffeomorphism between two minimal real analytic hypersurfaces is everywhere real analytic.

In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of coefficients preserving…

A much simpler proof of Theorem 1 from M.Burnashev "Code spectrum and reliability function: Binary symmetric channel" is presented.

We extend to orbifolds the quasimap theory of arXiv:0908.4446 and arXiv:1106.3724, as well as the genus zero wall-crossing results from arXiv:1304.7056 and arXiv:1401.7417. As a consequence, we obtain generalizations of orbifold mirror…

A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, is considered. This structure has a circulant matrix with respect to some basis, i.e. the structure is circulant, and it…

A Short Course on Frame Theory.

We consider the inverse refractor and the inverse reflector problem. The task is to design a free-form lens or a free-form mirror that, when illuminated by a point light source, produces a given illumination pattern on a target. Both…

This is a report on the recent work "Mirror symmetry for exceptional unimodular singularities" joint with Changzheng Li, Si Li and Yefeng Shen.

We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

This work is devoted to the proof of the statement about the existence of palindromic continued fractions in an arbitrary dimension. In addition, it is proved the criterion that an algebraic continued fraction has proper cyclic palindromic…

These notes deal with algebras equipped with an involution and related matters.

The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.

The geometric aspects of mirror symmetry are reviewed, with an eye towards future developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the best-understood mirror statements relate certain small corners of the moduli spaces of X…

In this paper we present a set of criteria for the choice of the shape parameter c contained in multiquadrics.

In this paper we outline a setup for Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical perspectives are considered.

This work presents a formalization of analogy on numbers that relies on generalized means. It is motivated by recent advances in artificial intelligence and applications of machine learning, where the notion of analogy is used to infer…