Related papers: Subdivision and Runner Removal Theorems

This revision contains some additional corrections and references, including a reference to Zeuthen suggested by Kleiman. For possible subsequent revisions, check http://math.ucr.edu/~ziv/papers/1nodal.pdf

Both boundary maps in K-theory are expressed in terms of surjections from projective C*-algebras to semiprojective C*-algebras.

We use reduction maps to study the minimal model program. Our main result is that the existence of a good minimal model for a klt pair $(X,\Delta)$ can be detected on the base of the $(K_{X}+\Delta)$-trivial reduction map. Thus we show that…

Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the $K$-theory of certain unital AF-algebras $A$ as (quotients of) polynomial rings. In this paper, we show that in each case the…

We interpret augmented racks as a certain kind of multiplicative graphs and show that this point of view is natural for defining rack homology. We also define the analogue of the group algebra for these objects; in particular, we see how…

Given a row-finite, source-free, graph of rank k, we extend the definition of reduction introduced by Eckhardt et al. This constitutes a large step forward in the extension of the geometric classification of finite directed graph…

The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.

We develop a unified framework to compute band-geometric quantities in multiband systems whose low-energy Hamiltonians realize arbitrary $SU(2)$ representations. Exploiting the presence of a quantization axis, we use the Wigner--Eckart…

This paper intends to lay the theoretical foundation for the method of functional maps, first presented in 2012 by Ovsjanikov, Ben-Chen, Solomon, Butscher and Guibas in the field of the theory and numerics of maps between shapes. We show…

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.

This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof…

We present a general scheme that allows for construction of scalar separability criteria from positive but not completely positive maps. The concept is based on a decomposition of every positive map $\Lambda$ into a difference of two…

In earlier work with C.~Monical, we introduced the notion of a K-crystal, with applications to K-theoretic Schubert calculus and the study of Lascoux polynomials. We conjectured that such a K-crystal structure existed on the set of…

We give an expansion in $1/N$ and $\beta$ of the cumulants of power sums of the particles of the $\beta$-ensemble. This new expansion is obtained using the tridiagonal model of Dumitriu and Edelman. The coefficients of the expansion are…

Let K \subset L be a field extension. Given K-subspaces A,B of L, we study the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain some lower bounds on the dimension of this subspace and on dim B^n in terms of dim A,…

The concept of relative sectional category expands upon classical sectional category theory by incorporating the pullback of a fibration along a map. Our paper aims not only to explore this extension but also to thoroughly investigate its…

Given a Legendrian knot $\Lambda \subset \mathbb{R}^3$ and a vertical line dividing the front projection of $\Lambda$ into two halves, we construct a differential graded algebra associated to each half-knot. We then show that one may obtain…

We compute a primary cohomological obstruction to the existence of an equipartition for j mass distributions in R^d by two hyperplanes in the case 2d-3j = 1. The central new result is that such an equipartition always exists if d=6 2^k +2…

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…

We develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus-1 curves. We use this approach to prove a purely elementary criterion for proving cases of…