相关论文: Newton-Okounkov bodies for Bott-Samelson varieties…

We construct the moduli space of finite dimensional representations of generalized quivers for arbitrary connected complex reductive groups using Geometric Invariant Theory as well as Symplectic reduction methods. We explicit characterize…

Motivated by the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO25], we consider a family of Newton--Okounkov polytopes of a complex smooth Fano variety $X$ related by a composition of…

We study the additivity of Newton-Okounkov bodies. Our main result states that on two-dimensional subcones of the ample cone the Newto-Okounkov body associated to an appropriate flag acts additively. We prove this by induction relying on…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

The generalized Kostka polynomials are the Poincare polynomials of isotypic components of certain graded GL(n)-modules. The former satisfy a monotonicity property arising from natural surjections of the corresponding modules. This…

We provide a general, homotopy-theoretic definition of string group models within an $\infty$-category of smooth spaces, and we present new smooth models for the string group. Here, a smooth space is a presheaf of $\infty$-groupoids on the…

We construct a generalized Witten genus for spin$^c$ manifolds, which takes values in level 1 modular forms with integral Fourier expansion on a class of spin$^c$ manifolds called string$^c$ manifolds. We also construct a mod 2 analogue of…

We review the theory of quiver bundles over a K\"ahler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group G. We first study the case when G=O(V) or Sp(V), interpreting them as orthogonal…

The notion of ball convexity, considered in finite dimensional real Banach spaces, is a natural and useful extension of usual convexity; one replaces intersections of half-spaces by suitable intersections of balls. A subset $S$ of a normed…

We establish simultaneous approximation properties of weighted first-order Sobolev orthogonal projectors onto spaces of polynomials of bounded total degree in the Euclidean unit ball. The simultaneity is in the sense that we provide bounds…

We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…

The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…

We study finitely generated projective modules over noncommutative tori. We prove that for every module $E$ with constant curvature connection the corresponding element $[E]$ of the K-group is a generalized quadratic exponent and,…

A cellular string of a polytope is a sequence of faces stacked on top of each other in a given direction. The poset of cellular strings, ordered by refinement, is known to be homotopy equivalent to a sphere. The subposet of coherent…

We construct new "standard modules" for the representations of general linear groups over a local non-archimedean field. The construction uses a modified Robinson-Schensted-Knuth correspondence for Zelevinsky's multisegments. Typically, the…

We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We…

We prove that each bounded polytope can be represented as a polynomial zonotope, which we refer to as the Z-representation of polytopes. Previous representations are the vertex representation (V-representation) and the halfspace…

Orthogonal decomposition of tensors is a generalization of the singular value decomposition of matrices. In this paper, we study the spectral theory of orthogonally decomposable tensors. For such a tensor, we give a description of its…

We generalize Kawamata's product formula for volumes of canonical divisors to arbitrary divisors using Okounkov bodies

Mirkovi\'c-Vilonen (MV) polytopes are a class of generalized permutahedra originating from geometric representation theory. In this paper we study MV polytopes coming from matroid polytopes, flag matroid polytopes, Bruhat interval…