Research
Research
Research
Research
421+ open-access research outputs.
We study contact 3-manifolds $Y$ with a special global frame inspired by Cartan's structure equations. This frame is dual to a generalized Finsler structure defined by Bryant. We present some examples…
In this paper we study the behavior of the scalar curvature at infinity on complete noncompact steady gradient Ricci solitons. In dimension four, we assume that the canonical Ricci flow induced by the…
The aim of these notes is to explain various enumerative results about $K3$ surfaces without assuming familiarity with Gromov--Witten theory. The enumerative results in question are due to Beauville, …
The goal of these lectures is to introduce the completion of the set of Lagrangian submanifolds of a symplectic manifold with respect to the spectral metric first introduced by V. Humili\`ere and rece…
We present a Bianchi-Calo type construction method for Bryant type linear Weingarten surfaces in hyperbolic space.…
A classical theorem in the theory of minimal surfaces establishes a correspondence between minimal surfaces in $\mathbb{R}^n$ and null holomorphic curves in $\mathbb{C}^n$. A hyperbolic version of thi…
The Zariski topology on a group G is the coarsest topology such that all sets of the form $\{x \in G | 1_G \neq g_0 x^{k_0} g_1 ... g_{l-1} x^{k_{l-1}} g_l\}$ are open. Originally introduced by Bryant…
In 2019, investigation of the so-called factor-invariant cubic graphs was initiated by Alspach, Khodadadpour and Kreher. For a cubic graph $\Gamma$ and a vertex-transitive subgroup $G$ of $\mathrm{Aut…
We construct, from a ground model of $ZFC$, a transitive symmetric model $M$ satisfying $ZF + DC + PP + AC_{wo} + \neg AC$. The construction starts with a Cohen symmetric seed model $N$ over $Add(\ome…
We introduce a notion of restricted pyramid configurations for computing the 1-leg Donaldson-Thomas $\mathbb{Z}_2\times\mathbb{Z}_2$-vertex. We study a special type of restricted pyramid configuration…
We provide a wall-crossing framework for operational enumerative invariants of equivariant 3-Calabi--Yau categories arising from virtual cycles. The strategy follows ideas of Joyce's ``universal'' wal…
Combining the methods of Brian and Stuart with the classical Dvoretzky theorem, we show that no infinite-dimensional Banach space contains a barrelled subspace of (algebraic) dimension $<\mbox{cov}(\m…
A bicirculant is a regular graph that admits a semi-regular automorphism with two vertex-orbits of the same size. By $m$ we denote the size of vertex-orbits and by $d$ the valence of a bicirculant. Fu…
In [52], Parmenter and Pollicott establish an abstract criterion that gives a geometric construction of equilibrium states for a class of partially hyperbolic systems. We refine their criterion to cov…
Suppose $J = (f_1, \dots, f_n)$ is an $n$-generated ideal in any ring $R$. We prove a general Brian\c{c}on-Skoda-type containment relating the integral closure $\overline{J^{n+k-1}}$ with ordinary pow…
Let $R$ be a noetherian commutative ring. Of great interest is the question whether one can find an explicit integer $k$ such that $\overline{I^{k+n}}\subseteq I^n$ for each ideal $I$ and each integer…
Large deviation principles for hyperbolic systems are well studied and provide exponential rates for the deviations of Birkhoff averages from their limit. This short article presents a local large dev…
In 2012, Peter Paule and Cristian-Silviu Radu proved an infinite family of Ramanujan type congruences for $2$-colored Frobenius partitions $c\phi_2$ introduced by George Andrews. Recently, Frank Garva…
A hypersurface $M$ in the unit sphere $S^n \subset {\bf R}^{n+1}$ is Dupin if along each curvature surface of $M$, the corresponding principal curvature is constant. If the number $g$ of distinct prin…
On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus…
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