Lino Grama

Research

I am a mathematician specializing in Differential Geometry at IMECC/UNICAMP. My research primarily focuses on the geometry of homogeneous spaces and Lie groups, invariant geometric structures, homogeneous geometric flows, as well as applications of Lie theory in Riemannian and symplectic geometry. Additionally, I co-organize the Sao Paulo Geometry Seminar (https://www.ime.unicamp.br/~geodif). Furthermore, I serve as a member of the Advisory Committee at the Institute of Mathematical Sciences of the Americas (IMSA) (https://www.imsa.miami.edu).

Teaching (in Portuguese)

Primeiro Semestre de 2024.

1. MM599 - Geometria Simplética 

   • Informações 

2. MA211 - Cálculo II (Licenciatura em Matemática) 

   • Informações 

Publications & Preprints

Preprints/Submitted for publication

• New look at Milnor spheres (with L.Cavenaghi and L.Katzarkov), preprint arXiv.

• Generalized toric varieties, LVMB manifolds and Lie groupoids (with L.Katzarkov and M.Costa), submitted.

• The complete dynamics description of positively curved metrics in the Wallach flag manifold SU(3)/T^2 (with L.Cavenaghi, R.M.Martins and D.D.Novaes), preprint arXiv.

• The Petersen--Wilhelm conjecture on principal bundles (with L.Cavenaghi and L.Sperança), preprint arXiv.

• A dual leaf approach to fatness: classifying results (with L.Cavenaghi), preprint arXiv.

• Twisted Kähler-Einstein metrics on flag varieties (with E.Correa), preprint arXiv.

Papers published/Accepted for publication

• Geodesics on adjoint orbits of  SL(n,R) (with R. do Prado e B.Grajales),  to appear in Communications in Contemporary Mathematics, 2024.

• Control sets of one-input linear control systems on solvable, nonnilpotent 3D Lie groups ( with A. Da Silva, A. Robles), to appear in Discrete and Continuous Dynamical Systems, 2024. 

• Equigeodesic vectors on compact homogeneous spaces with equivalent isotropy summnads (with B.Grajales), to appear in Annali di Matematica Pura ed Applicata, 2024. 

• Symmetric spaces as adjoint orbits and their geometries (with  L.Cavenaghi, C. Garcia e Luiz A.B. San Martin),  to appear in Revista Matemática Complutense, 2024.

• Gromoll-Meyer's actions and the geometry of (exotic) spacetimes (with  L.Cavenaghi), to appear in Differential Geometry and its Applications, 2024.

• On the dynamics of positively curved metrics on SU(3)/T^2 under the homogeneous Ricci flow (with L.Cavenaghi e R.M.Martins), to appear in Matemática Contemporânea, 2023.

• Scalar curvatures of invariant almost Hermitian structures on flag manifolds with two and three isotropic summands (with A.R. Oliveira),  The Journal of Geometric Analysis, 2023.

• The projected homogeneous Ricci flow and its collapses with an application to flag manifolds, Monatshefte für Mathematik, 2022 ( with R. M. Martins, M. Patrão, L. Seco, L. D. Sperança).

• The concept of Cheeger deformations on fiber bundles with compact structure group (with L.Cavenaghi e L.Sperança), São Paulo Journal of Math., 2022.

• Invariant Einstein metrics on real flag manifolds with two or three isotropy summands (with B.Grajales), Journal of Geometry and Physics, 2022.

• Lax formalism for Gelfand-Tsetlin integrable systems (with E. Correa), Bulletin des Sciences  Mathematiques, v. 170, p. 102999, 2021. 

• Scalar Curvatures of Invariant Almost Hermitian Structures on Generalized Flag Manifolds (with A.R Oliveira),  Symmetry Integrability and Geometry-Methods and Applications, 109, 2021. 

• Geodesic Orbit Spaces In Real Flag Manifolds (with C.J.C. Negreiros and B.Grajales), Communications in Analysis and Geometry, v. 28, p. 1933-2003, 2020. 

• Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on maximal flag manifolds (with K. Lima). Differential Geometry and its Applications, v. 73, p. 101684, 2020.

• Second Homotopy Group and Invariant Geometry of Flag Manifolds (with L.Seco). Results in Math, v.75, p.1-25, 2020. 

• Calabi-Yau metrics on canonical bundles of complex flag manifolds (with E. Correa). Journal of Algebra, v. 527, p. 109-135, 2019. 

• A Lie theoretical construction of a Landau-Ginzburg model without projective mirrors. (with E.Ballico, S.Barmeier, E.Gasparim e L.A.B. San Martin). Manuscripta Mathematica  v. 158, p. 85-101, 2019. 

• T-duality on nilmanifolds (with V.del Barco e L.Soriani). Journal of High Energy Physics, v. 2018, p. 153-177, 2018.

• On generalized G_2 structures and T-duality (with V.del Barco). Journal of Geometry and Physics, v. 132, p. 109-113, 2018. .

• On the stability of harmonic maps under the homogeneous Ricci flow (with R. do Prado).  Complex Manifolds, v. 5, p. 122-132, 2018.

• Variational aspects of homogeneous geodesics on generalized flag manifolds and applications (with R. do Prado). Annals of Global Analysis and Geometry, p. 451-477, 2018.

• Some Landau-Ginzburg models viewed as rational maps (with E.Ballico, E.Gasparim e L.A.B.San Martin). Indagationes Mathematicae v. 28, p. 615-628, 2017.  

• Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers (with C.J.C. Negreiros e A.R.Oliveira). Annali di Matematica Pura ed Applicata v. 196, p. 165-200, 2017. 

• Symplectic Lefschetz fibrations from a Lie theoretical viewpoint. Aceito em Proc. Langlands, TQFT and Mirror Symmetry, 2015 (with B.Callander, E.Gasparim e L.A.B.San Martin).

• A brief survey on the Ricci flow in homogeneous manifolds. Aceito em  São Paulo Journal of Mathematical Sciences (with R.M.Martins).

• Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds (with E.Gasparim e L.A.B.San Martin).  Proceedings of the Edinburgh Mathematical Society v. 60, p. 361-385, 2017. 

• Lefschetz fibration on adjoint orbits  (with E.Gasparim e L.A.B.San Martin).  Forum Mathematicum. v. 28, p. 967-979, 2016. 

• Equi-harmonic maps and Plücker formulae for horizontal-holomorphic curves on flag manifolds. Annali di Matematica Pura ed Applicata 193 (2014), no. 4, 1089–1102. (with C.J.C.Negreiros e L.A.B.San Martin).

• Global behavior of the Ricci flow on generalized flag manifolds with two isotropy summands. Indagationes Mathematicae 23 (2012) 95-104. (with R.M.Martins).

• Equigeodesics on Generalized Flag Manifolds with Two Isotropy Summands. Results in Mathematics 60 (2011) 405 - 421. (with C.J.C.Negreiros).

• Variational results on flag manifolds: Harmonic maps, geodesics and Einstein metrics. Journal of Fixed Point Theory and its Applications 10 (2011) 307 - 325. (with C.J.C.Negreiros e N.P.Silva).

• Invariant Hermitian structures and variational aspects of a family of holomorphic curves on flag manifolds. Annals of Global Analysis and Geometry 40 (2011) 105 - 123. (with C.J.C.Negreiros e L.A.B.San Martin).

• Equigeodesics on flag manifolds. Houston Journal of Mathematics 37 (2011) 113 - 125. (with C.J.C.Negreiros e N.Cohen).

• The Ricci flow of left invariant metrics on full flag manifold SU(3)/T from a dynamical systems point of view. Bull. Sci. math. 133 (5) (2009) 463 - 469. (with R.M.Martins).

Students 

In progress

• Giovane Neto (PhD, advisor)

• Otávio Cunha Oliveira (Master, advisor)

• Luiz Carazolli (Undergraduate, advisor)

Students supervised

• Matheus Silva Costa (PhD, advisor)

• Brian Grajales (PhD, advisor)

• Leonardo Soriani (PhD, advisor)

• Kennerson Nascimento de Sousa Lima (PhD, advisor)

• Ailton Ribeiro de Oliveira (PhD, co-advisor)

• Rafaela F. do Prado (PhD, advisor)

• Eder Moraes Correa (PhD, co-advisor)

• Francisco Vieira de Oliveira (PhD, advisor)

• Eder Moraes Correa (Master, co-advisor)

• Leonardo Soriani (Master, co-advisor)

• Bianca Fujita Castilho (Master, advisor)

• Ada Carolina Rojas (Master, advisor)

• Leonardo Schultz (Master, advisor)

• Otávio Cunha de Oliveira  (Undergraduate, advisor)

• Edson Cidral Filho  (Undergraduate, advisor)

• Diego Oliveira (Undergraduate, advisor)

• Renata Possobon (Undergraduate, advisor)

• Amanda Biscuola (Undergraduate, advisor)

• Leonardo Schultz (Undergraduate, advisor)

• Leonardo Mingrone Zan (Undergraduate, advisor)

Postdoctoral researchers mentored

• Kennerson Lima (2023 - current)

• Leonardo Cavenaghi (2021 -  current)

• Ailton R. Oliveira (2020 - 2021)