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This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…

We consider holomorphic foliations by curves on compact complex manifolds, for which we investigate the existence of projective structures along the leaves varying holomorphically (foliated projective structures), that satisfy particular…

We investigate the notion of the $p$-divisor for foliations on a smooth algebraic surface defined over a field of positive characteristic $p$ and we study some of their properties. We present a structure theorem for the $p$-divisor of…

We prove weak approximation for isotrivial families of rationally connected varieties defined over the function field of a smooth projective complex curve.

We study codimension one foliations in projective space \PP^n over \CC by looking at its first order perturbations: unfoldings and deformations. We give special attention to foliations of rational and logarithmic type. For a differential…

We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…

The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds…

In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…

We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type…

We study non-isotrivial projective families of elliptic surfaces of Kodaira dimension one, over complex projective curves. If the base is an elliptic curve, we show that the family must have a singular fibre, and that over the projective…

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…

The theory of geometric structures on a surface with nonempty boundary can be developed by using a decomposition of such a surface into hexagons, in the same way as the theory of geometric structures on a surface without boundary is…

Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.

We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.

We consider singular holomorphic foliations on compact complex surfaces with invariant rational nodal curve of positive self-intersection. Then, under some assumptions, we list all possible foliations.

We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…

We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of…

In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made…