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In the last two decades there was a lot of progress in understanding the geometry of smooth Gaussian fields. This survey aims to cover one particular line of research: the large scale behaviour of level and excursion sets and their…
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.
It is argued that correlations and multiplicity distributions constitute one of the most characteristic properties of strong interactions. The progress made in the last years in our understanding of correlations is reviewed.
A new complete invariant for acyclic graphs is presented
This is a survey on coarse geometry with an emphasis on coarse homology theories.
A variety of possible extensions of mappings between posets to their Dedekind order completion is presented. One of such extensions has recently been used for solving large classes of nonlinear systems of partial differential equations with…
We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by…
A survey on the Greene-Kleitman correspondence, with complete proofs, many of which are new.
Recently, we have witnessed tremendous applications of algebraic intersection theory to branches of mathematics, that previously seemed very distant. In this article we review some of them. Our aim is to provide a unified approach to the…
This paper will be replaced later by a revised version.
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
In this current study, the most apparent aspect is to submit a new geometric sequence space. We investigate its topological properties , inclusion relations, Geometric statistical convergence and Geometric property of Orlicz function and .…
We prove that the automorphism group of a general complete intersection $X$ in a projective space is trivial with a few well-understood exceptions. We also prove that the automorphism group of a complete intersection $X$ acts on the…
We get sharp degree bound for generic smoothness and connectedness of the space of conics in low degree complete intersections which generalizes the old work about Fano scheme of lines on Hypersurfaces.
We prove a generalized mirror conjecture for non-negative complete intersections in symplectic toric manifolds. Namely, we express solutions of the PDE system describing quantum cohomology of such a manifold in terms of suitable…
Results are well-known
In this paper we study how certain symmetries of convex bodies affect their geometric properties. In particular, we consider the impact of symmetries generated by the block diagonal subgroup of orthogonal transformations, generalizing…
This expository article outlines the construction of De Concini-Procesi arrangement models and describes recent progress in understanding their significance from the algebraic, geometric, and combinatorial point of view. Throughout the…
In this paper, we give an explicit formula for the Futaki invariants of complete intersections. The result is new in the case where the variety is smooth or has orbifold singularities.
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,…