Curriculum Vitae

Lucas Coelho Ambrozio

November 14th, 2019

Personal Information

Name: Lucas Coelho Ambrozio Date of Birth: March 17th of 1988 Nationality: Brazilian

Address

Department of Mathematics Zeeman Building University of Warwick Gibbet Hill Road Coventry CV4 7AL, UK E-mail: [email protected]

Education

2010 - 2014 Ph.D. in Mathematics IMPA, Rio de Janeiro/RJ Brazil Thesis Advisor: Fernando Cod´aMarques Title: Constant mean curvature foliations and scalar curvature rigidity of three-manifolds. Scholarship from: Conselho Nacional de Desenvolvimento Cient´ıficoe Tecno- l´ogico(CNPq)/ Funda¸c˜aoCarlos Chagas Filho de Amparo `aPesquisa do Estado do Rio de Janeiro (FAPERJ)

2008-2010 Mathematics M.S. IMPA, Rio de Janeiro/RJ Brazil Advisor: Marcos Dajczer Scholarship from: Conselho Nacional de Desenvolvimento Cient´ıficoe Tecno- l´ogico(CNPq)

2006-2008 Mathematics B.S. UFRJ - Universidade Federal do Rio de Janeiro/RJ Brazil

Employment history

2019 - Warwick Zeeman Lecturer, University of Warwick

2018 - 2019 Member, Institute for Advanced Study 2017 - 2018 Research Fellow, University of Warwick

2015 - 2017 Research Associate, Imperial College London

Academic Visits

2016 - 2017 University of Chicago (eight months)

2014 - 2015 Imperial College London (one year post-doc fellow- ship, CNPq-Brazil)

2014 IMPA (six months)

Research interests

Mathematics Differential Geometry Geometric Analysis

Accepted publications

- (with R. Montezuma), “On the two-systole of real projective spaces”, to appear at the Revista Matematica Iberoamericana, pre-print available at arxiv:1809.03636.

- (with R. Buzano, A. Carlotto and B. Sharp), “Bubbling analysis and ge- ometric convergence results for free boundary minimal surfaces”, Journal de l’Ecole´ polytechnique - Math´ematiques, 6 (2019), p. 621-664.

- (with A. Carlotto and B. Sharp), “Compactness analysis for free boundary minimal hypersurfaces”, Calculus of Variations and Partial Differential Equa- tions, 57 (2018), no. 1, 1-39.

- (with A. Carlotto and B. Sharp), “A note on the index of closed minimal hypersurfaces of flat tori”, Proceedings of the American Mathematical Society 146 (2018), no. 1, 335-344.

- (with I. Nunes), “A gap theorem for free boundary minimal surfaces in the three-ball”, to appear at the Communications in Analysis and Geometry, preprint available at arXiv:1608.05689.

- (with A. Carlotto and B. Sharp), “Index estimates for free boundary min- imal hypersurfaces”, Mathematische Annalen 370 (2018), no. 3-4, 1063-1078.

- (with A. Carlotto and B. Sharp), “Comparing the Morse index and the first Betti number of minimal hypersurfaces”, Journal of Differential Geometry, 108 (2018), no. 3, 379-410.

2 - (with A. Carlotto and B. Sharp), “Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue”, Journal of Geometric Analysis, 26 (2015), no. 4, 2591-2601.

- “On static three-manifolds with positive scalar curvature”, Journal of Dif- ferential Geometry, 107 (2017), no. 1, pp. 1-45.

- “On perturbations of the Schwarzschild Anti-de Sitter spaces of positive mass”, Communications in Mathematical Physics, 337 (2015), no. 2, 767-783.

- “Rigidity of area-minimizing free boundary surfaces in mean convex three- manifolds”, Journal of Geometric Analysis, 25 (2015), no. 2, 1001-1017.

Preprints

- (with R. Montezuma), “On the min-max width of unit volume three- spheres”, preprint available at arXiv:1809.03638.v2.

- (with R. Buzano, A. Carlotto and B. Sharp), “Geometric convergence re- sults for closed minimal surfaces via bubbling analysis”, preprint available at arXiv:1803.04956.

Invited talks at conferences

2019 2nd Encounter in Differential Geometry in Rio Grande do Sul, UFRGS, Porto Alegre, Brazil.

2019 1st Joint Meeting Brazil-France in Mathematics, IMPA, Rio de Janeiro, Brazil.

2019 RTG Conference on Geometric Analysis, Princeton University, USA.

2019 Mathematical Relativity: A Riemannian Approach, CIMAT, Guana- juato, Mexico.

2019 IX Workshop in Differential Geometry, UFAL, Maceio, Brazil.

2018 A Pan-Hemispheric Celebration of Mathematics in Miami, ICM satel- lite meeting, USA.

2018 Mass in General Relativity, Simons Center’s Workshop, USA.

2018 XX Brazilian School of Differential Geometry, Jo˜aoPessoa, Brazil.

2017 31th Brazilian Colloquium of Mathematics, Differential Geometry Section, Rio de Janeiro, Brazil.

2017 32nd Geometry Festival, Duke University, USA.

2016 XIX Brazilian School of Differential Geometry, Rio de Janeiro, Brazil.

3 2015 End of Year London Geometry Conference, UK.

2015 AMS/SPM International Meeting, Geometric Analysis Section, Porto, Portugal.

2014 Junior WIC Geometric Analysis Seminar, London, UK.

2014 XVIII Brazilian School of Differential Geometry, Bras´ılia,Brazil.

2014 IV Workshop in Differential Geometry, Mac´eio,Brazil.

2013 29th Brazilian Colloquium of Mathematics, Differential Geometry Section, Rio de Janeiro, Brazil.

Seminar talks

2019 Geometry Seminar - USP, Brazil.

2019 Geometry Seminar - IMPA, Brazil.

2019 Geometric Analysis Seminar - University of Notre Dame, USA.

2019 Geometric Analysis Seminar - University of Chicago, USA.

2019 Geometric Analysis Seminar - CUNY, USA.

2018 Variational Methods in Geometry Seminar - IAS, USA.

2018 Geometric Analysis Seminar - Rutgers University, USA.

2018 Geometry-Topology Seminar - UPenn, USA.

2018 Geometric Analysis Seminar - University of Chicago, USA.

2018 Seminario de Geometr´ıa- Universidad de Granada, Spain.

2018 PDE Seminar - Oxford University, UK.

2017 Geometry and Analysis Seminar - QMUL, UK.

2017 Differential Geometry Seminar - UC Irvine, USA.

2017 PDE and Differential Geometry Seminar - University of Connecticut, USA.

2017 Geometry and Topology Seminar - University of Wisconsin, USA.

2016 Semin´ariode Geometria - UFF, Niter´oi,Brazil.

4 2016 Geometry Seminar - Scuola Normale Superiore di Pisa, Italy.

2016 Differential Geometry and Geometric Analysis Seminar - Princeton Uni- versity, USA.

2015 Differentialgeometrie Oberseminar - Universit¨atM¨unster,Germany.

2015 S´eminairede G´eom´etrie- IMJ, Paris, France.

2015 Semin´ariode Geometria Diferencial - IMPA, Brazil.

2014 Semin´ariode Geometria - UFMA, Brazil.

2013 S´eminairede G´eom´etrie- IMJ, Paris, France.

Special Lectures and mini-courses

2019 Special Lecture “The Mathematics of Karen Uhlenbeck” - IMPA, Brazil.

2016 Lecture series “Minimal hypersurfaces: index and topology” - KIAS, South Korea.

Teaching

Advanced PDE, University of Warwick (2019/2020 Term I)

Geometry of Curves and Surfaces, University of Warwick (2017/2018 Term I)

Student orientation

Diego Soligon - Research project (Warwick MASt master program, 2017/2018)

Seminar organisation

- Warwick University, Analysis Seminar (2019/2020, Term 2)

- Institute for Advanced Studies, Variational Methods in Geometry Seminar (2018/2019, Term 2)

- Warwick University, Analysis Seminar (2017/2018, Term 3)

- University of Chicago, Geometric Analysis Seminar (2016/2017)

- Imperial College, Geometric Analysis Seminar (2015/2016)

Honours and Awards

2015 PrˆemioCAPES de Teses (Matem´atica/Probabilidadee Estat´ıstica).

2015 PrˆemioCarlos Gutierrez, USP-S˜aoCarlos.

5 2012 Bolsa Nota 10, FAPERJ.

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