Discrete geometry

Related lectures (25)

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Explores the crystal packing of conjugated molecules, discussing shapes, structures, and packing arrangements in the solid state.

Crystal Packing of Conjugated Molecules

Explores the shapes and crystal structures of conjugated molecules, discussing packing arrangements, polymorphism, and the impact of substituents on crystal packing.

Supramolecular Organisation: Solid State

Explores the supramolecular organization of π-conjugated molecules in the solid state, covering crystal structures and packing preferences.

Supramolecular Organisation in Solid State

Explores supramolecular organization in the solid state, covering pi-conjugated molecules' shapes, crystal structures, and intermolecular interactions.

Crystallography: Describing Periodic Structures

Covers crystallography, lattice structures, vectors, and diffraction patterns.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Excitonic Coupling in Electron-rich Systems

Explores the excitonic coupling in electron-rich systems and the formation of neutral solitons in poly(acetylene) due to chemical oxidation.

Ceramic Materials: Structures and Properties

Explores atomic bonds, crystal structures, and polymorphism in ceramics, highlighting the importance of atomic size in crystal packing.

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Modeling Class: Vesta Software Visualization

Explores crystal structure visualization using Vesta software for CCP and HCP arrangements.

Extreme Problems in Diophantine Approximation and Dynamics

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

Sphere Packing

Covers the concept of sphere packing and its significance in time shifts and Nyquist criterion.

Vertex Operator Algebras: Conformal Vectors and Virasoro Algebra Log in to Mediaspace to watch this video

Explores conformal vectors, Virasoro algebra, and Heisenberg vertex algebra in the theory of vertex operator algebras.

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Lattices, Minkowski's Theorem Log in to Mediaspace to watch this video

Explores lattices, Minkowski's Theorem, and properties of symmetric convex sets.

Solid-Solid Interfaces: Grain Boundaries and Surface Energy Log in to Mediaspace to watch this video

Explores grain boundaries, surface energy, geometry parameters, and micelle formation.

Crystallography: Unit Cells, Lattices, and Reciprocal Lattice Log in to Mediaspace to watch this video

Introduces crystallography basics, covering unit cells, lattices, and reciprocal lattice concepts.

Monstrous Moonshine Log in to Mediaspace to watch this video

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.