IMSA Courses

Rouquier Dimension Equals Krull Dimension for Toric Varieties

Explore the equality of Rouquier and Krull dimensions for toric varieties, delving into homological mirror symmetry and a multi-graded version of Hilbert's syzygy theorem.

• YouTube
• 57 minutes
• Self-Paced
• Free Video

On Some Aspects of Cosmological Fine-Tuning

Explore fine-tuning in cosmology through Bayesian and maximum entropy frameworks. Examine probabilistic measurements, distribution families, and the learnability of fine-tuning concepts.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Spinor-valued Higgs Bundles - Theory and Applications

Explore spinor-valued Higgs bundles with Nigel Hitchin, examining their unique properties and implications for Riemann surface geometry. Gain insights into Dirac equations and vector bundle theory.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

A New Perspective on Exotic Manifolds - Spherical Duality and Torus Links

Explore exotic manifolds through spherical duality and torus links. Discover new perspectives on homotopy spheres, O(3)-actions, and connections to singularity theory and mirror symmetry.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Spherical T-duality and Generalized Log Transform - Applications to Generalized Hopf Manifolds

Explore spherical T-duality and its connection to generalized log transform, with applications to generalized Hopf manifolds. Gain insights into advanced mathematical concepts and their interrelations.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Machine Learning Applications in Mathematical Research

Exploring machine learning's potential to assist mathematicians in research, proof verification, and problem-solving, highlighting innovative applications and future possibilities in mathematical discovery.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Knot Theory in Mathematics and AI Applications

Explore the fascinating world of knot theory and its connections to mathematics and AI in this engaging talk by Ernesto Lupercio from CINVESTAV.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Topos and Stacks for Understanding Semantic Functioning of Deep Neural Networks

Exploring topos theory and stacks to understand semantic functioning of deep neural networks, bridging advanced mathematics with AI for enhanced comprehension of machine learning processes.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Learning Short Proofs for Counting Planar Lattice Triangulations

Explore innovative techniques for generating concise proofs in counting planar lattice triangulations, blending mathematical theory with machine learning approaches.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

The Mathematics of Reliable AI

Exploring mathematical foundations for reliable AI systems, focusing on theoretical principles and practical applications to enhance AI trustworthiness and performance in real-world scenarios.

• YouTube
• 42 minutes
• Self-Paced
• Free Video

Discrete Curvature and Applications in Graph Machine Learning

Exploring discrete curvature in graph machine learning, focusing on applications and theoretical foundations for analyzing complex network structures and improving graph-based algorithms.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Formal Framework for Learning and Knowledge Acquisition

Explore a formal framework for learning and knowledge acquisition, examining theoretical foundations and practical applications in AI and mathematics.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Exact and Approximate Symmetries in Machine Learning Models

Explore exact and approximate symmetries in machine learning models, examining their impact on model performance and interpretability. Gain insights into leveraging symmetries for more efficient and robust AI systems.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

What Makes Solving Mathematics Problems Hard for Computers

Explore the challenges computers face in solving complex mathematical problems, examining the unique aspects of human mathematical reasoning and the limitations of current AI approaches.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

How AI/ML is Revolutionizing Weather and Climate Science

Explore how AI and machine learning are transforming weather and climate science, revolutionizing predictions and enhancing our understanding of complex atmospheric systems.

• YouTube
• 55 minutes
• Self-Paced
• Free Video