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This paper is devoted to the study of multigraded algebras and multigraded linear series. For an NsNs-graded algebra AA, we define and study its volume function FA:N+s -> RFA:N+s→R, which computes the ...
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...
It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension
A bipartite graph G is semi-algebraic in R-d if its vertices are represented by point sets P,Q subset of R-d and its edges are defined as pairs of points (p,q) epsilon P x Q that satisfy a Boolean combination of a fixed number of polynomial equations and i ...
We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...
We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR stategy co ...
Deformation twinning on a plane is a simple shear that transforms a unit cell attached to the plane into another unit cell equivalent by mirror symmetry or 180 degrees rotation. Thus, crystallographic models of twinning require the determination of the sho ...
We present a technique for the approximation of a class of Hilbert space--valued maps which arise within the framework of model order reduction (MOR) for parametric partial differential equations, whose solution map has a meromorphic structure. Our MOR str ...
We analyze the accuracy of the discrete least-squares approximation of a function u in multivariate polynomial spaces PΛ:=span{y↦yν:ν∈Λ} with Λ⊂N0d over the domain Γ:=[−1,1]d, based on the s ...
