Related papers: Recent progress on the Minimal Model Program for f…
We show the validity of the relative dlt MMP over Q-factorial threefolds in all characteristics p>0. As a corollary, we generalise many recent results to low characteristics including: $W\mathcal{O}$-rationality of klt singularities,…
We survey our recent papers (some being joint ones) about the relation between the geometry of a compact K\"ahler manifold and the existence of automorphisms of positive entropy on it. We also use the language of log minimal model program…
We investigate a type of distance between triangulations on finite type surfaces where one moves between triangulations by performing simultaneous flips. We consider triangulations up to homeomorphism and our main results are upper bounds…
We establish the minimal model program (MMP) for generalized foliated threefolds $(X, \mathcal{F}, B, \mathbf{M})$ of rank 1, extending the result of Cascini and Spicer in [CS25d]. As an application of the generalized foliated MMP, we prove…
We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
In this paper we will survey some recent developments in the last decade or so on variation of Geometric Invariant Theory and its applications to Birational Geometry such as the weak Factorization Theorems of nonsingular projective…
In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.
Our aim is to illustrate how one can effectively apply the basic ideas and notions of topological entropy and dynamical degrees, together with recent progress of minimal model theory in higher dimension, for an explicit study of birational…
The division of compact Riemann surfaces into 3 cases K_C<0, g=0, or K_C=0, g=1, or K_C>0, g>=2 is well known, and corresponds to the familiar trichotomy of spherical, Euclidean and hyperbolic non-Euclidean plane geometry. Classification…
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis…
In this paper we discuss recent progress on the modularity of Calabi-Yau varieties. We focus mostly on the case of surfaces and threefolds. We will also discuss some progress on the structure of the L-function in connection with mirror…
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal…
In this article we prove the existence of pl-flipping and divisorial contractions and pl flips in dimension $n$ for compact K\"ahler varieties, assuming results of the minimal model program in dimension $n-1$. We also give a self contained…
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…
We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor…
We present new geometric formulations for the fractional spin particle models on the minimal phase spaces. New consistent couplings of the anyon to background fields are constructed. The relationship between our approach and previously…
This is the first of a series of papers studying real algebraic threefolds using the minimal model program. The main results are outlined in Part II. The present part I. contains the necessary preliminary work concerning terminal…