Research
Research
Research
Research
12,761+ open-access research outputs.
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 G\r{a}rding polynomials, a class of real multivariate polynomials defined via positivity regions invariant under translation by positive directions and closed under strictly positive affi…
In finance, portfolio management is a traditional yet difficult problem that has drawn attention from practitioners and researchers for many years. However, there are still difficult technological pro…
Let $ n \in \mathbb{N} $ with $ n \geq 3 $, and let $\mathcal{G} = \{G_i:i\in [n]\} $ be a family of $ n $-vertex graphs on a common vertex set $V$, where the graphs in the family do not need to be di…
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…
We develop a calculus for counting pseudoholomorphic disks with boundary in tropical Lagrangians contained in almost toric manifolds, using our previous work with Venugopalan. The results are mostly i…
Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some d…
We prove a necessary and sufficient condition for a $ C^1 $-hypersurface to have all parallel sets nowhere $ C^1 $-regular. As a corollary, we deduce that for a generic $ C^1 $-regular convex body all…
Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\m…
We study random matrices whose entries are obtained by applying consistent rank correlations, such as Hoeffding's $D$, pairwise to a high-dimensional random vector with mutually independent components…
Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$. Early work by Friedland and Stanley addressed so…
In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.…
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit exceptions when k < 4, ther…
Let $(M^4, g, f)$ be a four-dimensional complete noncompact gradient shrinking Ricci soliton with the equation $Ric+\nabla^2f= \frac{1}{2}g$. If its scalar curvature is $1$, Cheng-Zhou \cite{Cheng-Zho…
We study gradient descent for rank-1 matrix factorization through a certificate-based viewpoint. The central object is a parameterized quadratic certificate $I(\delta;\,\cdot)$ whose level sets shrink…
In this note we give generalizations and prove 'minimalistic' refinements of the t-birational Section Conjecture (t-BSC), cf. [Be], by doing both: First, by extending the class of base fields over whi…
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…
In this paper, we investigate arithmetical structures on Cartesian product graphs, particularly, ladder graph of the form P2\square Pm and grid graph of the form Pn \square Pm. An arithmetical structu…
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 introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sh…
Free open-access publishing with Google Scholar indexing.
Submission Guide →