Research
Research
Research
Research
445+ open-access research outputs.
We show how the circle method can be used to study rational points on a certain cubic fourfold, going beyond the square-root barrier.…
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…
Nevanlinna theory studies the value distribution of meromorphic functions and provides powerful results in the form of the First and Second Main Theorems. In this paper, we introduce quaternionic anal…
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, …
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…
In this paper, we define and investigate a connexive logic, called 'Connexive semi-Heyting logic' (\mathcal{CSH} for short) and a new subvariety CSH of the variety SH of semi-Heyting algebras. It is s…
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 recent result of Rickards states that the generating series of intersection numbers of real quadratic geodesics on indefinite Shimura curves are elliptic modular forms. We reinterpret this as a Kudl…
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…
It is proved that the roots of the derivative of a polynomial with quaternionic coefficients belong to the union of the intersections of sets defined in terms of certain projections of a polynomial. T…
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…
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…
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