Fundamental Groups Courses and Certifications

ICTP Mathematics

Topology - Lecture 20

Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 10

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 4

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 6

Explore fundamental concepts and advanced techniques in topological spaces, including continuity, compactness, and connectedness, with expert guidance from Bruno Zimmerman.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 2

Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 3

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 16

Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 14

Explore advanced concepts in topology with Bruno Zimmerman, delving into complex mathematical structures and their properties in this comprehensive lecture.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 8

Explore fundamental concepts and advanced techniques in topological spaces, manifolds, and algebraic topology with expert guidance from Bruno Zimmerman.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore representations in Homeo_+(S^1) and their role in verifying left-orderability of 3-manifold groups, with applications to the L-space conjecture and taut foliations in various topological settings.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Conference Talk

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.

• YouTube
• 58 minutes
• On-Demand
• Conference Talk

Applied Algebraic Topology Network

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.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

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.

• YouTube
• 58 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 52 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video