Related papers: The Rost invariant has zero kernel for quasi-split…

We classify simple flops on smooth threefolds, or equivalently, Gorenstein threefold singularities with irreducible small resolution. There are only six families of such singularities, distinguished by Koll{\'a}r's {\em length} invariant.…

In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, \xi)…

We provide an explicit formula for all primary genus-zero $r$-spin invariants. Our formula is piecewise polynomial in the monodromies at each marked point and in $r$. To deduce the structure of these invariants, we use a tropical…

Let $\Gamma < \mathrm{GL}_n(F)$ be a countable non-amenable linear group with a simple, center free Zariski closure, $\mathrm{Sub}(\Gamma)$ the space of all subgroups of $\Gamma$ with the, compact, metric, Chabauty topology. An invariant…

We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other hand, finite group invariants, such as the…

This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…

This paper is focused on numerical semigroups and presents a simple construction, that we call dilatation, which, from a starting semigroup $S$, permits to get an infinite family of semigroups which share several properties with $S$. The…

We introduce two new general methods to compute the Chow motives of twisted flag varieties and settle a 20-year-old conjecture of Markus Rost about the Rost invariant for groups of type E7.

We show the heat kernel type variance decay $t^{-\frac{d}{2}}$, up to a logarithmic correction, for the semigroup of an infinite particle system on $\mathbb{R}^d$, where every particle evolves following a divergence-form operator with…

In this note we define three invariants of contact structures in terms of open books supporting the contact structures. These invariants are the support genus (which is the minimal genus of a page of a supporting open book for the contact…

We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invariance and generalized descent statements for categories of…

We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated…

In "A survey on the Turaev genus of knots," Champanerkar and Kofman propose several open questions. The first asks whether the polynomial whose coefficients count the number of quasi-trees of the all-A ribbon graph obtained from a diagram…

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith-Weston which…

We define the intersection complex for the universal cover of a compact weakly special square complex and show that it is a quasi-isometry invariant. By using this quasi-isometry invariant, we study the quasi-isometric classification of…

The complete positivity, i.e., positivity of the resolvent kernels, for convolutional kernels is an important property for the positivity property and asymptotic behaviors of Volterra equations. We inverstigate the discrete analogue of the…

We present a new smooth, Gaussian-like kernel that allows the kernel density estimate for an angular distribution to be exactly represented by a finite number of its Fourier series coefficients. Distributions of angular quantities, such as…

In a previous article by two of the present authors and S. Bonzio, \L ukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work…

Let $G$ be a semi-simple algebraic group over a perfect field $k$. A lot of progress has been made recently in computing the Chow motives of projective $G$-homogenous varieties. When $k$ has positive characteristic, a broader class of…

By twisted quantum invariants we mean polynomial invariants of knots in the three-sphere endowed with a representation of the fundamental group into the automorphism group of a Hopf algebra $H$. These are obtained by the Reshetikhin-Turaev…