Related papers: K-theory of Minkowski question-mark function

For a field $k$ we compute the $K$-theory of the exact category of $k[t_1,\dots,t_n]$-modules that are finite-dimensional over $k$, generalising the work of Kelley and Spanier.

We consider the problem $F=f(\nu)$ for strictly convex, closed hypersurfaces in $S^{n+1}$ and solve it for curvature functions $F$ the inverses of which are of class $(K)$.

The $K$-homology ring of the affine Grassmannian of $SL_n(C)$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory…

We prove that the trace of the Frobenius endofunctor of the category of automorphic sheaves with nilpotent singular support maps isomorphically to the space of unramified automorphic functions, settling a conjecture from [AGKRRV1]. More…

We give a systematic and thorough study of geometric notions and results connected to Minkowski's measure of symmetry and the extension of the well-known Minkowski functional to arbitrary, not necessarily symmetric convex bodies K on any…

The Funk--Minkowski transform ${\mathcal F}$ associates a function $f$ on the sphere ${\mathbb S}^2$ with its mean values (integrals) along all great circles of the sphere. Thepresented analytical inversion formula reconstruct the unknown…

In this work we show that the Riemann hypothesis for the Dedekind zeta--function $\zeta_{\mathrm{K}}(s)$ of an algebraic number field $\mathrm{K}$ is equivalent to a problem of the rate of convergence of certain discrete measures defined…

This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (its lambda-algebra structure), the relation to strict…

The J-function in Gromov-Witten theory is a generating function for one-point genus zero Gromov-Witten invariants with descendants. Here we give formulas for the quantum K-theoretic J-functions of type A flag manifolds and conjectural…

We prove a non-linear version of a theorem of Grayson which is an analogue of the Fundamental Theorem of Algebraic $K$-theory and identify the $K$-theory of the endomorphism category over a space $X$ in terms of reduced $K$-theory of a…

First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the…

We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph…

The tensor functor called $\alpha$-induction arises from a Frobenius algebra object, or a Q-system, in a braided unitary fusion category. In the operator algebraic language, it gives extensions of endomorphism of $N$ to $M$ arising from a…

Given a regular function $\phi$ on a smooth stack, and a $(-1)$-shifted Lagrangian $M$ on the derived critical locus of $\phi$, under fairly general hypotheses, we construct a pullback map from the Grothendieck group of coherent matrix…

The spectral problem for the q-Knizhnik-Zamolodchikov equations for $U_{q}(\widehat{sl_2}) (0<q<1)$ at arbitrary level $k$ is considered. The case of two-point functions in the fundamental representation is studied in detail.The scattering…

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show…

Bi-partite ribbon graphs arise in organising the large $N$ expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra $\mathcal{K}(n)$, with basis given by bi-partite…

Using Poincare duality, we formulate a formula of Lefschetz type which computes the Lefschetz number of an endomorphism of a separable, nuclear C*-algebra satisfying Poincare duality and the Kunneth theorem. (The Lefschetz number of an…

We present algorithms which, given a genus 2 curve $C$ defined over a finite field and a quartic CM field $K$, determine whether the endomorphism ring of the Jacobian $J$ of $C$ is the full ring of integers in $K$. In particular, we present…

We propose that geometric quantization of symplectic manifolds is the arrow part of a functor, whose object part is deformation quantization of Poisson manifolds. The `quantization commutes with reduction' conjecture of Guillemin and…