Gonçalo Oliveira
Address:
Goncalo Oliveira,
Instituto Superior Tecnico, Lisboa, Portugal.
Office: 4.24
Email:
If you have tried to contact me at goliveir@ist.ac.at please contact me instead at galato97@gmail.com as I have no longer access to the first.
Short math Bio
Since February 2024, I have been an Associate Professor in the Department of Mathematics at Instituto Superior Tecnico in Lisbon, Portugal.
Previously, I had positions as an FCT Principal Investigator at Instituto Superior Técnico, a NOMIS Fellow at IST Austria, an Assistant Professor at Universidade Federal Fluminense (UFF) (2018-2021), a postdoc in IMPA (2017-2018) and as an Elliot Assistant Research Professor at Duke University (2014-2017). I also had a research membership at MSRI in the fall of 2022 and a visiting scientist position at the Max Planck Institute in Bonn (Germany), which I visited in the summer of 2015.
I completed my PhD in 2014 at Imperial College London, under the supervision of Sir Simon Donaldson.
Research Interests
I am interested in Differential Geometry and Mathematical Physics and my main research areas are special holonomy and gauge theory.
Publications and preprints
H. Edelsbrunner, C. Fillmore, G. Oliveira, Counting Equilibria of the Electrostatic Potential,
Preprint arXiv:2501.05315
G. Oliveira, and R. Sena-Dias, Hermitian, Ricci-flat toric metrics on non-compact surfaces à la Biquard-Gauduchon,
Preprint arXiv:2407.16843
G. Oliveira, R. Sena-Dias, Einstein metrics from the Calabi ansatz via Derdziński duality,
Preprint arXiv:2306.17328
Luís Carvalho, João Lopes Costa, José Mourão, Gonçalo Oliveira, Wide neural networks: From non-gaussian random fields at initialization to the NTK geometry of training,
Preprint arXiv:2304.03385 arXiv:2304.0338
G. Oliveira, Electrostatics and geodesics on K3 surfaces,
Preprint arXiv:2302.08354
Á. Nagy and G. Oliveira, Nonminimal solutions to the Ginzburg-Landau equations,
Preprint arXiv:2103.05613
J. D. Lotay, G. Oliveira, Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry, to appear in the Journal of the European Mathematical Society
Preprint arXiv:2305.05744
L. Carvalho, J. L. Costa, J. Mourão, G. Oliveira, The positivity of the Neural Tangent Kernel, to appear in SIMODS (SIAM Journal on Mathematics of Data Science )
Preprint arXiv:2404.12928
G. Oliveira, R. Sena-Dias, Scalar-flat Kahler metrics with varying cone angle singularities along a divisor, Proceedings of the American Mathematical Society 153 (2025), 331-339
Preprint arXiv:2312.17707
Á. Nagy and G. Oliveira, On the bifurcation theory of the Ginzburg-Landau equations, Proceedings of the American Mathematical Society 152.02 (2024): 653-664.
Preprint arXiv:2210.03271v1
J. Lotay and G. Oliveira, Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz, Journal of Differential Geometry, 126 (2024), 1121-1184
Preprint arXiv:2002.10391
D. Fadel, Á. Nagy and G. Oliveira, The asymptotic geometry of G_2-monopoles, Memoirs of the American Mathematical Society, 303, number 1521 (2024)
Preprint arXiv:2009.06788
A. Gómez, and G. Oliveira, New approaches to epidemic modeling on networks. Scientific Reports 13.1 (2023): 1-16.
J. Lotay and G. Oliveira, Examples of deformed G_2-instantons/Donaldson-Thomas connections, Annales de l'Institut Fourier, Volume 72 (2022) no. 1, pp. 339-366.
Preprint arXiv:2007.11304
G. Ball and G. Oliveira, The DT-instanton equation on almost Hermitian 6-manifolds, Communications in Mathematical Physics, vol 388, 819-844, (2021).
Preprint arXiv:2006.13399
G. Oliveira and Rosa Sena-Dias, Minimal Lagrangian tori and action-angle coordinates, Transactions of the American Mathematical Society, 7715-7742, vol 374, 11 (2021).
Preprint arXiv:2004.14697
Á. Nagy and G. Oliveira, The Kapustin--Witten monopole equation, accepted in Letters in Mathematical Physics (2021)
Preprint arXiv:1906.05435
Á. Nagy and G. Oliveira, The Haydys monopole equation, Selecta Mathematica 26, 58 (2020).
Preprint arXiv:1906.05432
G. Oliveira, Early epidemic spread, percolation and Covid-19, Journal of Mathematical Biology, 81, pages 1143–1168 (2020)
Preprint arXiv:2006.04905 also available in medRxiv here
A. Clarke, and G. Oliveira, Spin(7)-Instantons from evolution equations, The Journal of Geometric Analysis, 31, 4328-4355 (2021)
Preprint arXiv:1903.05526
G. Oliveira and A. Waldron, Yang-Mills flow on special-holonomy manifolds, Advances in Mathematics, vol 376, 107418 (2020).
Preprint arXiv:1812.10866
D. Fadel and G. Oliveira, The Limit of Large Mass Monopoles, Proceedings of the London Mathematical Society, Volume 119, Issue 6 (2019)
Also available at arXiv:1803.04117
Á. Nagy and G. Oliveira, From vortices to instantons on the Euclidean Schwarzschild manifold, Communications in Analysis and Geometry 30.2 (2022): 335-380.
Preprint arXiv:1710.11535
G. Ball and G. Oliveira, Gauge Theory on Aloff-Wallach spaces, Geometry & Topology 23, 685–743 , (2019)
Earlier version available at arXiv:1610.04557
O. Bobrowski and G. Oliveira, Random Cech Complexes on Riemannian Manifolds, Random Structures & Algorithms 15 of November 2018,
Earlier version available at arXiv:1704.07204
J. Lotay and G. Oliveira, SU(2)2-invariant G2-instantons, Mathematische Annalen, Volume 371, Issue 1–2, pp 961–1011, (2018).
Expanded version available at arXiv:1608.07789
G. Oliveira, Gerbes on G2 Manifolds, Journal of Geometry and Physics, Volume 114, April 2017, Pages 570--580 , (2017).
Also available at arXiv:1608.08949
G. Oliveira, G2-Monopoles with Singularities (Examples), Letters in Mathematical Physics, vol. 106, no. 11, pages 1479--1497, (2016).
Also available at arXiv:1609.05731
G. Oliveira, Monopoles on AC 3-manifolds, Journal of the London Mathematical Socitey, (2) 93, no. 3, 785--810, (2016).
Older version available at arXiv:1412.2252
G. Oliveira, Calabi-Yau Monopoles for the Stenzel metric, Communications in Mathematical Physics, Volume 341 (2), pages 699-728, (2015).
Older version available at arXiv:1411.0491
G. Oliveira, G2 Monopoles on the Bryant Salamon Manifolds, Journal of Geometry and Physics, Volume 86, 599-632, (2014).
Available at arXiv:1310.7392
G. Oliveira, Monopoles in Higher Dimensions, PhD Thesis, Imperial College London (2014).
Available at spiral
Reviews and articles in conference proceedings
G. Oliveira, Some useful facts on invariant connections, to appear in the ISAAC 2019 conference proceedings, in remembrance of Sir Isaac Newton and published by Springer (2020)
Available here
G. Oliveira, Pseudo-holomorphic curves: A very quick overview, Complex Manifolds, vol. 7, no. 1, 2020, pp. 215-229.
Available here
G. Oliveira, Concise notes on Special Holonomy with an emphasis on Calabi–Yau and G2-Manifolds, to appear in the proceedinds of the conference "Global Portuguese Mathematicians" published by the Buletim da Socieadade Portuguesa de Matemática (2020)
Available here
J. Lotay and G. Oliveira, G2-instantons on noncompact G2-manifolds: results and open problems, To appear in a forthcoming volume of the Fields Institute Communications, entitled "Lectures and Surveys on G2 manifolds and related topics" and published by Springer.
Available here.
G2-Gauge theory, extended abstract in Oberwolfach Reports Volume 12, Issue 1, 2015, (2015).
Available here
Other
Geometry and Quantization, Master Thesis at IST, Lisboa (2010) ,
Available here