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In this video, we explore one of the most elegant and foundational ideas in differential geometry — the Maurer-Cartan form. You'll ...

Let's explore lie groupoup transformations at its core a lie group is a fascinating mathematical concept that marries two ...

In this video, we explore one of the most elegant and foundational ideas in differential geometry — the Maurer-Cartan Form. You'll ...

... 0:00 Introduction 2:26 Group Theory 5:23 Water Molecule 6:51 Space Groups 7:53 Lie Groups 10:10 Minkowski Space Escher's ...

These relate to Dynkin diagrams, exceptional Lie groups, and Coxeter groups. We illustrate our simple approach by computing ...

In this episode, we will introduce Lie groups as a foundation for various calculations in future discussions. I'll be uploading new ...

In a sense E8 is a structure in 8 dimensions, but since it corresponds to the largest exceptional Lie group it very mathematically ...

Applied Representation Theory | Episode 4 *^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^* We derive the symplectic condition on ...

What do a triangle, a spinning frisbee, and the laws of physics have in common? This video explains how symmetry is the hidden ...

Episode 28 of my series: One Hundred Years of Uncertainty, commemorating the centenary of Quantum Mechanics #iyq2025 ...

Applied Representation Theory | Episode 3 *^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^* We describe the subgroup of linear ...

The matrix Lie algebra of sp(2n,R) is derived from our knowledge of the Lie group Sp(2n,R).

"Quantum Control with Julia: Optimal Pulses and Lie Algebra Methods" by David Tinoco, presented at JuliaCon Local Paris 2025.

... the Exponential Map from the Lie algebra of functions over phase space to its associated Lie group that acts on that algebra.

You'll see classic examples like cyclic and dihedral groups, then progress to continuous Lie groups and their role in Noether's ...

Topics covered: * What Lie groups are and where they come from * How continuous symmetry describes motion * Why rotations ...

A structure M (group, Lie algebra, associative algebra, etc.) is ω-categorical if there is a unique countable model of its first-order ...

Applied Representation Theory | Episode 1 *^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^* From elementary mechanics, we ...