Gonçalo Oliveira

Short math Bio

Since February 2024 I have been an Associate Professor of 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

• Luís Carvalho, João L. Costa, José Mourão, Gonçalo Oliveira, The positivity of the Neural Tangent Kernel, 

Preprint arXiv:2404.12928

• G. Oliveira, R. Sena-Dias, Scalar-flat Kahler metrics with varying cone angle singularities along a divisor, 

Preprint arXiv:2312.17707

• G. Oliveira, R. Sena-Dias, Einstein metrics from the Calabi ansatz via Derdziński duality,

Preprint arXiv:2306.17328

• J. D. Lotay, G. Oliveira, Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry,

Preprint arXiv:2305.05744

• 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 

• Á. Nagy and G. Oliveira, On the bifurcation theory of the Ginzburg-Landau equations,

Preprint arXiv:2210.03271v1

• J. Lotay and G. Oliveira, Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz, to appear in Journal of Differential Geometry

Preprint arXiv:2002.10391 

• D. Fadel, Á. Nagy and G. Oliveira, The asymptotic geometry of G_2-monopoles, to appear in Memoirs of the American Mathematical Society

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