Miguel Tribolet de Abreu

Research Interests

Preprints

• Periodic orbits of non-degenerate lacunary contact forms on prequantization bundles, (joint with Leonardo Macarini), preprint 2024 - pdf-file.

Publications

• Symmetric periodic Reeb orbits on the sphere, (joint with Hui Liu and Leonardo Macarini), Transactions of the AMS, 377 (2024), 6751-6770 - pdf-file.


• Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology, (joint with Leonardo Macarini and Miguel Moreira), Advances in Mathematics, 429 (2023), 50 pp. - pdf-file.


• Dynamical implications of convexity beyond dynamical convexity, (joint with Leonardo Macarini), Calculus of Variations and Partial Differential Equations, 61 (2022), 47 pp. - pdf-file.


• On contact invariants of non-simply connected Gorenstein toric contact manifolds, (joint with Leonardo Macarini and Miguel Moreira), Mathematical Research Letters, 29 (2022), 1-42 - pdf-file.


• Two closed orbits for non-degenerate Reeb flows, (joint with Jean Gutt, Jungsoo Kang and Leonardo Macarini), Mathematical Proceedings of the Cambridge Philosophical Society, 170 (2021), 625-660 - pdf-file.


• On the mean Euler characteristic of Gorenstein toric contact manifolds, (joint with Leonardo Macarini), International Mathematics Research Notices, 14 (2020), 4465-4495 - pdf-file.


• Dynamical convexity and elliptic periodic orbits for Reeb flows, (joint with Leonardo Macarini), Mathematische Annalen, 369 (2017), 331-386 - pdf-file.


• Multiplicity of periodic orbits for dynamically convex contact forms, (joint with Leonardo Macarini), Journal of Fixed Point Theory and Applications, 19 (2017), 175-204 - pdf-file.


• Toric constructions of monotone Lagrangian submanifolds in $\CP^2$ and $\CP^1 \times \CP^1$, (joint with Agnès Gadbled), Journal of Symplectic Geometry, 15 (2017), 151-187 - pdf-file.


• Displacing Lagrangian toric fibers by extended probes , (joint with Matthew Strom Borman and Dusa McDuff ), Algebraic & Geometric Topology, 14 (2014) 687-752 - pdf-file.


• Remarks on Lagrangian intersections in toric manifolds, (joint with Leonardo Macarini), Transactions of the AMS, 365 (2013), 3851-3875 - pdf-file.


• Contact homology of good toric contact manifolds, (joint with Leonardo Macarini), Compositio Mathematica, 148 (2012), 304-334 - pdf-file.


• Scalar-flat Kahler metrics on non-compact symplectic toric 4-manifolds, (joint with Rosa Sena-Dias), Annals of Global Analysis and Geometry, 41 (2012), 209-239 - pdf-file.


• Kahler-Sasaki geometry of toric symplectic cones in action-angle coordinates, Portugal. Math. (N.S.), 67 (2010), 121-153 - pdf-file.


• Toric Kahler Metrics: Cohomogeneity One Examples of Constant Scalar Curvature in Action-Angle Coordinates, Journal of Geometry and Symmetry in Physics, 17 (2010), 1-33 - pdf-file.


• Compatible complex structures on symplectic rational ruled surfaces, (joint with G. Granja and N. Kitchloo), Duke Math. Journal, 148 (2009), 539-600 - pdf-file.


• A personal tour through symplectic topology and geometry, Sao Paulo Journal of Mathematical Sciences (formerly Resenhas IME-USP), 2 (2008), 175-202 - pdf-file.


• Hearing the weights of weighted projective planes (joint with E. Dryden, P. Freitas and L. Godinho), Annals of Global Analysis and Geometry, 33 (2008), 371-395 - pdf-file.


• Moment maps, pseudo-holomorphic curves and symplectomorphism groups, in "Proc. XIV Fall Workshop on Geometry and Physics, Bilbao, September 14-16, 2005", Publ. de la RSME, Vol. 10 (2006), 1-31 - pdf-file.


• Moment maps, symplectomorphism groups and compatible complex structures, (joint with G. Granja and N. Kitchloo), Journal of Symplectic Geometry, 3 (2005), 655-670 - pdf-file.


• Kahler metrics on toric orbifolds, J. Differential Geom., 58 (2001), 151-187 - ps-file, pdf-file.


• Kahler geometry of toric manifolds in symplectic coordinates, in "Symplectic and Contact Topology: Interactions and Perspectives" (eds. Y.Eliashberg, B.Khesin and F.Lalonde), Fields Institute Communications 35, American Mathematical Society, 2003, pp. 1-24 - ps-file, pdf-file.


• On the invariant spectrum of $S^1$-invariant metrics on $S^2$, (joint with P. Freitas), Proc. London Math. Soc., 84 (2002), 213-230 - ps-file, pdf-file.


• Topology of symplectomorphism groups of rational ruled surfaces, (joint with D. McDuff), J. Amer. Math. Soc., 13 (2000), 971-1009 - ps-file, pdf-file.


• Kahler geometry of toric varieties and extremal metrics , Internat. J. Math., 9 (1998), 641-651 - ps-file, pdf-file.


• Topology of symplectomorphism groups of S^2 x S^2, Invent. Math., 131 (1998), 1-23 - ps-file, pdf-file.

Talks

• On the number of periodic orbits of non-degenerate lacunary contact forms on prequantizations - 2024.


• Symmetric periodic Reeb orbits on the sphere and contact homology of Lens spaces - 2023.


• Periodic orbits of Reeb flows on odd dimensional spheres - 2023, colloquium.


• Contact invariants of Q-Gorenstein toric contact manifolds and the Ehrhart (quasi-)polynomials of their toric diagrams - 2022.


• Contact invariants of Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology - 2019.


• A toric geometry road from Kahler metrics to contact topology - 2018.


• On the mean Euler characteristic of Gorenstein toric contact manifolds - 2016.


• Dynamical Convexity and Elliptic Orbits for Reeb Flows - 2013.


• Displacing Lagrangian Toric Fibers by Extended Probes - 2012.


• Remarks on Lagrangian Intersections in Toric Manifolds - 2011.


• Toric Kahler-Sasaki Geometry in Action-Angle Coordinates - 2008.


• A Personal Tour Through Symplectic Topology and Geometry - 2008.

Mini-Courses

• Toric contact manifolds - 2023.


• Toric Kahler-Sasaki Geometry - 2009.

Outreach

• 22 Centuries Measuring Area, (joint with Ana Cannas da Silva), January 2011 (updated January 2012), Klein vignette written in portuguese for Projeto Klein de Matemática em Língua Portuguesa - slides of corresponding talk in portuguese (September 2011) and english (February 2012).


• Introduction to Non-Euclidian Geometries, talk in portuguese for high school students - February 2012.


• The Fundamental Role of Mathematics, talk in portuguese for high school students - March 2004 (updated March 2011).

Some Local Activities

• Interactions of Poisson Geometry, Lie Theory and Symmetry - June 30 to July 04, 2025


• Workshop on Symplectic Dynamics - June 27 to July 01, 2022


• Geometric Analysis Conference - July 7-11, 2014


• VIII Workshop on Symplectic Geometry, Contact Geometry, and Interactions - January 30 to February 1, 2014


• X Lisbon Summer Lectures in Geometry - June 29 to July 3, 2009


• VIII Lisbon Summer Lectures in Geometry - June 2007


• SYMAT05 - Workshop on Symplectic Topology - July 2005


• Geometria em Lisboa


• Seminário Diagonal (IST student seminar on Mathematics)


• Conference on Poisson Geometry - September 2002


• Conference on Symplectic Geometry - June 1999

Teaching - Ensino (this is in portuguese)

• Cálculo Diferencial e Integral I (IST, Fall 2006, 2007, 2008, 2010, 2012, 2013, 2014, 2021, 2022, 2024 and 2025)


• Geometria Diferencial (IST, Fall 98, 2001, 2014 and 2025)


• Probabilidade e Estatística (IST, Spring 2022)


• Geometria Simpléctica (IST, Spring 2004, 2006, 2011, 2015 and 2021)


• Análise Matemática I (IST, Spring 2000, Fall 2002, 2003, 2004 and 2005)


• Análise Matemática IV (IST, Spring 2004)


• Análise Matemática II (IST, Spring 98, Fall 99, Spring 2002 and 2003)


• Geometria II (IST, Spring 2000)


• Álgebra Linear (IST, Fall 97 and Fall 98)