Computational Mathematics Courses and Certifications

Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.

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

Institute for Pure & Applied Mathematics (IPAM)

Computer-Assisted Proofs in the Arithmetic of Quadratic Forms - IPAM at UCLA

Explore computer-assisted proofs in quadratic forms arithmetic, covering equivalence, representation, local-global principles, and modular forms. Gain insights into complex computations across mathematics.

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

Institute for Pure & Applied Mathematics (IPAM)

Classical and Quantum Algorithms for Isogeny Problems

Explore classical and quantum algorithms for isogeny problems in post-quantum cryptography, focusing on computational challenges, path finding in isogeny graphs, and reductions to other problems in elliptic curve cryptography.

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

International Centre for Theoretical Sciences

The Power of Sampling by Peter W. Glynn

Explore sampling methods in statistics, computation, and engineering. Learn about their history, applications, and advantages in overcoming dimensional challenges and creating scalable algorithms.

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

IMSA

Spectrum of Singularities

Explore hypersurface singularity spectra: definition, properties, and computational techniques. Learn about Thom-Sebastiani theorem, semicontinuity, and applications in algebraic geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

IEEE

Pseudospectral Shattering the Sign Function and Diagonalization in Nearly Matrix Multiplication Time

Explore advanced matrix algorithms, including pseudospectral shattering and diagonalization techniques, for efficient computation in nearly matrix multiplication time.

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

IEEE

Towards Better Approximation of Graph Crossing Number

Explores advanced techniques for approximating graph crossing numbers, focusing on new frameworks and theorems for both general and bounded-degree graphs.

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

Applied Algebraic Topology Network

Homology Inference for the Degree-Rips Bifiltration

Explore density-sensitive degree-Rips bifiltration, its homology inference framework, and applications to annular point clouds with outliers. Analyze homotopy types and explanatory power in topological data analysis.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.

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

Applied Algebraic Topology Network

Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy

Explores efficient methods for approximating semi-algebraic sets, focusing on singly exponential complexity algorithms and their applications in algebraic geometry.

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

Applied Algebraic Topology Network

A Faithful Discretization of the Persistent Homology Transform

Explore a faithful discretization method for the Persistent Homology Transform, enhancing computational efficiency in topological data analysis and shape recognition.

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

Applied Algebraic Topology Network

The Persistence Mayer-Vietoris Spectral Sequence

Explore the persistent Mayer-Vietoris spectral sequence, its applications in parallelizing persistent homology computations, and its ability to provide locality-enriched persistence barcodes.

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

Applied Algebraic Topology Network

Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Explore efficient algorithms for approximating matching distance in 2-parameter persistence modules, focusing on quad-tree refinement and local adaptive bounds for improved computational performance.

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

Applied Algebraic Topology Network

Stability of 2-Parameter Persistent Homology

Explores stability results for 2-parameter persistent homology, covering multicover bifiltration, subdivision bifiltrations, and degree bifiltrations. Discusses computational aspects and implications for practical applications.

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

Applied Algebraic Topology Network

Don Sheehy - Persistent Homology of Lipschitz Extensions

Explore persistent homology of Lipschitz functions, analyzing sublevel set filtrations and barcodes from sample data. Learn about sub-barcodes and their theoretical guarantees in topological data analysis.

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