Daniel Posada-Buriticá

Research Interests:

My research interests lie in algebraic geometry, particularly in holomorphic foliations on projective varieties.

My research focuses on two intertwined directions:

• Understanding when a projective subvariety admits foliations that leave it invariant, following the modern formulation of the Poincaré problem.

• Studying when such foliations are uniquely determined by their singular scheme.

I am also interested in toric geometry, moduli spaces, and the Brill–Noether theory.

Preprints:

• J. Olivares and D. Posada-Buriticá. "Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces", 2026. (arXiv)

Publications:

• J. Olivares and D. Posada-Buriticá. "Foliations on projective complete intersection K3 surfaces" Forum Math., 38 (2026), no. 6, 2021-2035. (DOI) (arXiv)

Some Recorded Talks:

• Foliations by Curves on Smooth Projective Complete Intersection Varieties.
  (Foliaciones por curvas en variedades proyectivas suaves de intersección completa).
  Seminario de Álgebra Conmutativa y Geometría Algebraica, CIMAT, Guanajuato, México, 2026.

• From Dynamical Systems to Algebraic Geometry.
  (De los sistemas dinámicos a la geometría algebraica).
  CONVImaTE, Universidad del Valle, Cali, Colombia, 2025.

• Foliations on Projective K3 Surfaces.
  Foliations, Complex Geometry, and Painlevé Equations: Celebrating the 60th Birthday of Frank Loray, IMPA, Río de Janeiro, Brasil, 2025.

Curriculum Vitae:

You can download my CV here. (Updated October 2026)