Research
Research
Research
Research
3,237+ open-access research outputs.
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ prim…
Partially ordered patterns (POPs) generalize classical permutation patterns and have been extensively studied in the contexts of permutations, words, compositions, and partitions. Burstein, Han, Kitae…
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy K\"ahler moduli space on the derived category of an algebraic variety. For a toric variety, a model for this space …
Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations,…
Forward iteration of holomorphic self-maps generalizes the iteration of a single function in a natural way. This framework arises in complex dynamics, for instance in the study of wandering domains an…
Piatetski-Shapiro--Rallis discovered an integral representation construction, known as the doubling method, for the tensor product $L$-function of a cuspidal automorphic representation of $G \times \m…
In this article, we develop an efficient algorithm based on three special variants of the nonlinear conjugate gradient method, namely, the Polak--Ribiere--Polyak, Hestenes--Stiefel, and Liu--Story sch…
This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdor…
In this paper, we present an explicit and purely combinatorial characterization of the $m$-coloured quivers that appear within the $m$-coloured mutation class of a quiver of type $\mathbb{D}_n$. The $…
We present a domain decomposition formulation based on hybridization which is inspired by hybridized discontinuous Galerkin (HDG) methods, that enhance mixed domain decomposition methods by incorporat…
We propose a systematic method for constructing Wilf-Zeilberger (WZ) seeds and present seven WZ seeds. We also demonstrate how to construct WZ seeds from existing ones. With these WZ seeds, several hy…
This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the …
The Cram\'er-Wold device characterises weak convergence of probability measures on $\mathbb{R}^d$ through convergence of all one-dimensional projected laws. We prove that, if the target projected laws…
These personal reminiscences of the great Russian mathematician Sergey K. Godunov (1929-2023) arose from a request by his daughter, Ekaterina, to contribute a piece to a book she is writing about her …
For a smooth projective surface $S$, Johnson, Oprea, and Pandharipande defined cohomological descendent generating series for the Quot schemes of rank-$0$ quotients of $\mathcal{O}_S^{\oplus N}$. We p…
In this paper, we present a general framework for constructively proving the existence and of stationary localized solutions, spatially periodic solutions, and branches of spatially periodic solutions…
The heart of the a priori and a posteriori error control in convex minimization problems is the sharp control of the differences of discrete and exact minimal energy. Conforming finite element discret…
In this paper, we provide a class of domains in $\mathbb{C}^3$, such that every holomorphic self-map of that domain either has a fixed point or the sequence of iterates is compactly divergent. In part…
Ascent sequences form a central class of combinatorial objects, as they are in bijection with several important families such as (2+2)-free posets, Stoimenow matchings, and other Fishburn objects, and…
This paper analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition lattice, proving sharp…
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