Gonçalo Oliveira

activity

20132026

most citedMonopoles on the Bryant-Salamon

G_{2}

Manifolds

25 citations · 79 across the 23 of their papers we have counts for

collaborators

27 papers

math.DG2026

The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow

Jason D. Lotay, Goncalo Oliveira

We prove that at any nondegenerate neck pinch singularity of Lagrangian mean curvature flow of surfaces the mean curvature becomes unbounded, with control on the blow-up rate.

math.CA2026

Critical points of point charge potentials along lines

Goncalo Oliveira

We prove Conjecture 1.9 of Gabrielov-Novikov-Shapiro. More precisely, for every $p > 0$ , every nonconstant restriction to a line of a potential generated by $n$ point charges has at…

math.DG2026

Large mass limits of $G_{2}$ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Daniel Fadel, Goncalo Oliveira

We study large mass monopoles with structure group $SU (2)$ or $SO (3)$ on asymptotically conical $G_{2}$ -manifolds and Calabi--Yau $3$ -folds, with fixed asy…

cs.CG2025

Counting Equilibria of the Electrostatic Potential

Herbert Edelsbrunner, Christopher Fillmore, Gonçalo Oliveira

In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n - 1)^{2}$ isolated zeroes. The first (non-optimal) uppe…

cs.LG2024

The Positivity of the Neural Tangent Kernel

Luís Carvalho, João L. Costa, José Mourão +1

The Neural Tangent Kernel (NTK) has emerged as a fundamental concept in the study of wide Neural Networks. In particular, it is known that the positivity of the NTK is directly rel…

math.DG2023

Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry

Jason D. Lotay, Goncalo Oliveira

In this article we consider the Lagrangian mean curvature flow of compact, circle-invariant, almost calibrated Lagrangian surfaces in hyperkähler 4-manifolds with circle symmetry.…

cs.LG2023

Wide neural networks: From non-gaussian random fields at initialization to the NTK geometry of training

Luís Carvalho, João Lopes Costa, José Mourão +1

Recent developments in applications of artificial neural networks with over $n = 1 0^{14}$ parameters make it extremely important to study the large $n$ behaviour of such networks. Mo…

math.DG2023

Electrostatics and geodesics on $K 3$ surfaces

Goncalo Oliveira

Motivated by some conjectures originating in the Physics literature, we use Foscolo's construction of Ricci-flat Kahler metrics on K3 surfaces to locate, with high precision, sever…

math.DG2020★ 1 cited

The asymptotic geometry of $G_{2}$ -monopoles

Daniel Fadel, Ákos Nagy, Gonçalo Oliveira

This article investigates the asymptotics of $G_{2}$ -monopoles. First, we prove that when the underlying $G_{2}$ -manifold is nonparabolic (i.e. admits a positive Green's func…

math.DG2020★ 1 cited

Examples of deformed G_2-instantons/Donaldson-Thomas connections

Jason D. Lotay, Goncalo Oliveira

In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G…

math.DG2020

The DT-instanton equation on almost Hermitian 6-manifolds

Gavin Ball, Goncalo Oliveira

This article investigates a set of partial differential equations, the DT-instanton equations, whose solutions can be regarded as a generalization of the notion of Hermitian-Yang-M…

q-bio.PE2020

Early epidemic spread, percolation and Covid-19

Goncalo Oliveira

Human to human transmissible infectious diseases spread in a population using human interactions as its transmission vector. The early stages of such an outbreak can be modeled by…

q-bio.PE2020★ 9 cited

Refined compartmental models, asymptomatic carriers and COVID-19

Gonçalo Oliveira

The goal of this article is to analyze some compartmental models specially designed to model the spread of a disease whose transmission has the same features as COVID-19. The major…

math.DG2020

Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

Jason D. Lotay, Goncalo Oliveira

The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkaehler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conje…

math.DG2019★ 1 cited

The Kapustin--Witten equations on ALE and ALF gravitational instantons

Ákos Nagy, Gonçalo Oliveira

We study solutions to the Kapustin--Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates f…

math.DG2019

The Haydys monopole equation

Ákos Nagy, Gonçalo Oliveira

We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator; these monopoles can be interpreted as solutions to the Bogomolny equation w…

math.DG2018★ 2 cited

$G_{2}$ -instantons on noncompact $G_{2}$ -manifolds: results and open problems

Jason Lotay, Goncalo Oliveira

We survey the known existence and non-existence results for $G_{2}$ -instantons on non-compact cohomogeneity-1 $G_{2}$ -manifolds and their consequences, including an explicit example of…

math.DG2018

Yang-Mills flow on special-holonomy manifolds

Goncalo Oliveira, Alex Waldron

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curv…

math.DG2018★ 4 cited

The limit of large mass monopoles

Daniel Fadel, Goncalo Oliveira

In this paper, we consider finite energy $SU (2)$ monopoles on an asymptotically conical, oriented Riemannian $3$ -manifold with one end. The connected components of the mod…

math.DG2017

From vortices to instantons on the Euclidean Schwarzschild manifold

Ákos Nagy, Gonçalo Oliveira

The first irreducible solution of the $SU (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later…

math.PR2017★ 1 cited

Random Čech Complexes on Riemannian Manifolds

Omer Bobrowski, Goncalo Oliveira

In this paper we study the homology of a random Cech complex generated by a homogeneous Poisson process in a compact Riemannian manifold M. In particular, we focus on the phase tra…

math.DG2016★ 10 cited

Gauge theory on Aloff-Wallach spaces

Gavin Ball, Goncalo Oliveira

For gauge groups $U (1)$ and $S O (3)$ we classify invariant $G_{2}$ -instantons for homogeneous coclosed $G_{2}$ -structures on Aloff-Wallach spaces $X_{k, l}$ . As a consequence, we give ex…

math.DG2016★ 2 cited

$G_{2}$ -monopoles with singularities (examples)

Goncalo Oliveira

$G_{2}$ -monopoles are solutions to gauge theoretical equations on $G_{2}$ -manifolds. If the $G_{2}$ -manifolds under consideration are compact, then any irreducible $G_{2}$ -monopole must ha…

math.DG2016★ 1 cited

Gerbes on $G_{2}$ Manifolds

Goncalo Oliveira

On a projective complex manifold, the Abelian group of Divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a $G_{2}$ -manifold we use coassociative…

The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow

Critical points of point charge potentials along lines

Large mass limits of G2​ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Counting Equilibria of the Electrostatic Potential

The Positivity of the Neural Tangent Kernel

Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry

Wide neural networks: From non-gaussian random fields at initialization to the NTK geometry of training

Electrostatics and geodesics on K3 surfaces

The asymptotic geometry of G2​-monopoles

Examples of deformed G_2-instantons/Donaldson-Thomas connections

The DT-instanton equation on almost Hermitian 6-manifolds

Early epidemic spread, percolation and Covid-19

Refined compartmental models, asymptomatic carriers and COVID-19

Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

The Kapustin--Witten equations on ALE and ALF gravitational instantons

The Haydys monopole equation

G2​-instantons on noncompact G2​-manifolds: results and open problems

Yang-Mills flow on special-holonomy manifolds

The limit of large mass monopoles

From vortices to instantons on the Euclidean Schwarzschild manifold

Random Čech Complexes on Riemannian Manifolds

Gauge theory on Aloff-Wallach spaces

G2​-monopoles with singularities (examples)

Gerbes on G2​ Manifolds

Large mass limits of $G_{2}$ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Electrostatics and geodesics on $K 3$ surfaces

The asymptotic geometry of $G_{2}$ -monopoles

$G_{2}$ -instantons on noncompact $G_{2}$ -manifolds: results and open problems

$G_{2}$ -monopoles with singularities (examples)

Gerbes on $G_{2}$ Manifolds