Hyperbolization, Cubulation, and Applications in Negative Curvature Geometry
Explore hyperbolization procedures, their impact on polyhedra, and the resulting manifolds' properties. Discover how fundamental groups interact with CAT(0) cube complexes in negatively curved spaces.
Grupo Fundamental e Espaços de Recobrimento - Aula 03
Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em aplicações e teoremas fundamentais da área.
Mestrado: Grupo Fundamental e Espaços de Recobrimento - Aula 01
Explore conceitos fundamentais de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprenda aplicações práticas e teoremas importantes nesta aula introdutória de mestrado.
The Fundamental Group - Algebraic Topology
Explore the fundamental group in algebraic topology, covering homotopic paths, loop multiplication, and equivalence classes. Understand key concepts for surfaces like disks and circles.
Homology Planes and Fundamental Groups
Explore homology planes and fundamental groups in complex surfaces, focusing on an algorithm for line arrangements and its applications to log-general type surfaces with infinite fundamental groups.
Higgs Bundles on Elliptic Surfaces and Logarithmic Transformations
Explore Higgs bundles on elliptic surfaces and their transformations, examining vector bundles' importance in mathematics and the impact of logarithmic transformations on these structures.
Pencils on Algebraic Surfaces with Prescribed Classes of Irreducible Components
Exploring bounds on reducible fibers in curve pencils on projective surfaces, with focus on irreducible components' classes in Neron-Severi group. Generalizes results on fundamental groups of line arrangement complements.
Braids and Configuration Spaces
Explore topology, homotopy, and braid groups in this talk on configuration spaces. Discover connections between fundamental groups, loop spaces, and unordered configurations in mathematics.
Persistent Homotopy Groups of Metric Spaces
Explore persistent homotopy groups of metric spaces, their stability, and advantages over persistent homology. Learn about tree-like structures and ultrametrics in fundamental groups.
Dejan Govc - Fundamental Groups of Small Simplicial Complexes
Explore minimal triangulations of manifolds and fundamental groups of small simplicial complexes, with insights on estimating vertex counts in minimal triangulations.
The Lower Semi-Continuity of Pi_1 and Nilpotent Structures in Persistence
Explore lower semi-continuity of π₁ in non-compact spaces, examining symmetries and nilpotent structures in persistence theory for compact geodesic space sequences.
Lower Multiplicity Bounds via Classifying Spaces
Explore equivariant methods and classifying spaces to analyze Lusternik-Schnirelmann category variations, focusing on open covers with fundamental group constraints and applications to amenable subgroups.
Braids and Line Arrangements - Old and New
Explore the interplay between braid groups, configuration spaces, and hyperplane arrangements, focusing on recent advances in understanding fundamental groups of complex line arrangement complements.
Perverse Sheaves on Varieties with Large Fundamental Group
Explore perverse sheaves on Kähler manifolds, focusing on a generalization of the Singer-Hopf conjecture and its proof using Shafarevich conjecture ideas. Joint work with Donu Arapura presented.
Hyperbolicity of Algebraic Varieties via Fundamental Groups
Explore hyperbolicity of algebraic varieties through fundamental groups, examining linear representations and their implications for complex quasi-projective varieties and the Green-Griffiths-Lang conjecture.
More Deformations of the Cohomology Ring of the Moduli Space of Representations
Explore deformations of cohomology rings in representation spaces of Riemann surfaces, examining algebraic, geometric, and physical perspectives on this rich mathematical topic.
Topology - Lecture 13
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
Topology - Lecture 20
Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.
Topology - Lecture 10
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
Topology - Lecture 4
Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.
Topology - Lecture 6
Explore fundamental concepts and advanced techniques in topological spaces, including continuity, compactness, and connectedness, with expert guidance from Bruno Zimmerman.