Research
Research
Research
Research
19,811+ open-access research outputs.
Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial se…
We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of t…
J. Conway defined useful operations on the Class of combinatorial games and also introduced a notion of equivalence between games. Conway showed that, under his equivalence, games form a Group. Howeve…
We introduce the notions of $\mathbb{K}$-framings, based $\mathbb{K}$-framings and relative $\mathbb{K}$-framings of a compact connected oriented surface $\Sigma$ for any commutative ring $\mathbb{K}$…
We define a torus $U \subset T = (\mathbb{C}^\times)^K$ which acts on the $\Delta$-Springer varieties $Y_{n,\lambda,s}$ defined by Griffin-Levinson-Woo and give a Borel-style presentation for the equi…
Motivated by an optimal-matching problem (Leighton-Shor) and the random-field Ising model (Aizenman-Wehr, Ding-Wirth), we consider a variational problem for graphs in $1+1$ dimension maximizing an act…
Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphism…
In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.…
This paper explores the restriction behavior of silting-induced $t$-structures and co-$t$-structures on triangulated categories endowed with metrics. For compactly generated triangulated categories ad…
This paper presents a method for incorporating control analysis into design optimization for highly-maneuverable aircraft. By studying reachable sets for aircraft dynamics, we ensure that the optimize…
We prove that the unit group of a non-discrete irreducible, continuous ring, in the sense of John von Neumann, does not admit any non-trivial unitary representation continuous with respect to the stro…
In this paper, we define and study $S$-Noetherian lattices as a natural generalization of Noetherian rings. We prove that a ring $R$ is $S$-Noetherian if and only if its ideal lattice, $Id(R)$, is $S_…
We study moduli spaces of logarithmic stable maps to proper toric surfaces with prescribed tangency conditions to the toric boundary. Fixing a surface, we define a chamber decomposition on the space o…
We give a simple description of the coordinate ring of the universal centralizer associated to a simply connected semisimple group. To this end, we prove a general result on Weil restriction of affine…
Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base rin…
This paper presents various transcendence results in the ring of integers modulo infinitely large primes $\mathcal{A}$. In the ring $\mathcal{A}$, one can consider two notions of transcendence. One is…
We extend the classification results for torsion classes and torsion-free classes in the category of finitely generated modules over a commutative noetherian ring to suitable symmetric monoidal closed…
The continuous linear $P(k; N, w)$ and circular scan statistics $P_c(k; N, w)$ are fundamental tools in probability and spatial statistics, frequently used to detect clustering in uniform data. Let $X…
For a sequence $\gamma=(\gamma_n)_{n\ge 1}$, define \[ L_\gamma(z):=\sum_{n\ge 1}\gamma_n\frac{z^n}{1-z^n} =\sum_{n\ge 1}\Bigl(\sum_{d\mid n}\gamma_d\Bigr)z^n. \] We prove a short rigidity theorem: if…
We prove the Mukai conjecture on the characterisation of products of projective spaces among Fano varieties for a class of locally factorial Fano varieties defined in terms of their Cox rings. The Fan…
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