Miguel Tribolet de Abreu

Research Interests

Slides of Mini-Course

• Toric Kahler-Sasaki Geometry - 2009.

Talks

• 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.

Preprints

• Remarks on Lagrangian intersections in toric manifolds, (joint with Leonardo Macarini), preprint 2011 - pdf-file.

Publications

• Contact homology of good toric contact manifolds, (joint with Leonardo Macarini), to appear in Compositio Mathematica - pdf-file.


• Scalar-flat Kahler metrics on non-compact symplectic toric 4-manifolds, (joint with Rosa Sena-Dias), to appear in Annals of Global Analysis and Geometry - 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.

Some Local Activities

• 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)

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


• Cálculo Diferencial e Integral I (IST, Fall 2006, 2007, 2008 and 2010)


• 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 Diferencial (IST, Fall 98 and 2001)


• Geometria II (IST, Spring 2000)


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