Topology Courses and Certifications

Hausdorff Center for Mathematics

Dynamics - Topology and Numbers

Explore advanced mathematical dynamics through expert lectures on homogeneous dynamics, transfer operators, quantum modular forms, and spectral theory applications.

• YouTube
• 1 day 4 hours 54 minutes
• On-Demand
• Free Video

ICTP Mathematics

Frontiers in Geometry and Topology Summer School

Explore advanced topics in geometry and topology including Heegaard Floer homology, Dirac operators, pseudoholomorphic curves, and Seiberg-Witten equations through expert lectures.

• YouTube
• 15 hours 34 minutes
• On-Demand
• Free Video

ICTP Mathematics

Advanced School on Geometric Group Theory and Low-Dimensional Topology - Recent Connections and Advances

Explore cutting-edge connections between geometric group theory and low-dimensional topology through advanced lectures on virtually special groups, hyperbolic manifolds, and Teichmuller theory.

• YouTube
• 22 hours 54 minutes
• On-Demand
• Free Video

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

1 review

Explore taut foliations in 3-manifolds with Heegaard genus two, examining the connection between left-orderable fundamental groups and co-orientable taut foliations in closed, orientable, irreducible 3-manifolds.

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

Power Grids - Network Topology & Governance

Explore the complex network of power grids, their physical infrastructure, and regulatory intricacies. Learn about cascading failures, decision-making processes, and the challenges of maintaining our electrified world.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Community Detection and Data Topology in Network Science

Exploring network science and mathematical approaches to uncover hidden structures in complex data. Discusses community detection, data topology, and applications in social networks and opinion dynamics.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

USENIX

Diamond Miner - Comprehensive Discovery of the Internet's Topology Diamonds

Comprehensive Internet topology mapping system reveals hidden complexities, including load-balanced paths and frequent remapping events, offering deeper insights into network structure and resilience.

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

USENIX

NetHide - Secure and Practical Network Topology Obfuscation

NetHide: A framework for network topology obfuscation that mitigates link-flooding attacks while preserving debugging capabilities. Leverages programmable network devices to modify path tracing probes at line-rate, balancing security and usability.

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

Hausdorff Center for Mathematics

Notions of Booleanization in Pointfree Topology

Explores overlap algebras as a potential solution to retain features of Boolean locales while recovering classical properties in intuitionistic pointfree topology.

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

Hausdorff Center for Mathematics

Maurice Herlihy: Applying Combinatorial Topology to Byzantine Tasks

Explore combinatorial topology's application to Byzantine tasks in distributed systems, focusing on fault-tolerant algorithms and consensus protocols.

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

IMSA

Low Dimensional Topology and Circle-valued Morse Functions

Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.

• YouTube
• 1 hour 1 minute
• On-Demand
• Conference Talk

IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.

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

IMSA

An Application of Symplectic Topology to Algebraic Geometry

Explore symplectic topology's application to algebraic geometry, connecting Rouquier's triangulated category dimension to Krull dimension via homological mirror symmetry.

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

Hausdorff Center for Mathematics

Topology of Complexes Arising in Models for Distributed Computing

Explore simplicial models in distributed computing, focusing on chromatic subdivisions and their applications to problems like Weak Symmetry Breaking, leading to new mathematical questions.

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

USENIX

Lifting the Veil on Meta's Microservice Architecture - Analyses of Topology and Request Workflows

Comprehensive analysis of Meta's microservice architecture, revealing insights on topology, request workflows, and challenges in large-scale distributed systems. Implications for tool development and future research opportunities.

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