Semimodular lattice

Mod-01 Lec-5ex Diffraction Methods For Crystal Structures - Worked Examples

Condensed Matter Physics by Prof. G. Rangarajan, Department of Physics, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course

Lattice Structures in Ionic Solids

We've learned a lot about covalent compounds, but we haven't talked quite as much about ionic compounds in their solid state. These will adopt a highly ordered and repeating lattice structure, but the geometry of the lattice depends entirely on the types of ions and their ratio in the chem

From playlist General Chemistry

Semi-coarse Spaces, Homotopy [Jonathan Treviño-Marroquín]

Semi-coarse spaces is an alternative to study (undirected) graphs through large-scale geometry. In this video, we present the structure and a homotopy what we worked on. In the final part, we look at the fundamental homotopy group of cyclic graphs.

From playlist Contributed Videos

Inner & Outer Semidirect Products Derivation - Group Theory

Semidirect products are a very important tool for studying groups because they allow us to break a group into smaller components using normal subgroups and complements! Here we describe a derivation for the idea of semidirect products and an explanation of how the map into the automorphism

From playlist Group Theory

Crystal lattice and unit cell

All crystalline materials have 3D, long range, periodic order. Therefore, they have a lattice which is a grid of repeating atomic positions. We can pick a small repeating area in this grid and it becomes a unit cell. The primitive unit cell should be the smallest repeatable unit cell.

From playlist Materials Sciences 101 - Introduction to Materials Science & Engineering 2020

Gregory Henselman-Petrusek (9/28/22): Saecular persistence

Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric

From playlist AATRN 2022

Inner Semidirect Product Example: Dihedral Group

Semidirect products explanation: https://youtu.be/Pat5Qsmrdaw Semidirect products are very useful in group theory. To understand why, it's helpful to see an example. Here we show how to write the dihedral group D_2n as a semidirect product, and how we can describe that purely using cyclic

From playlist Group Theory

What Are Allotropes of Metalloids and Metals | Properties of Matter | Chemistry | FuseSchool

What Are Allotropes of Metalloids and Metals Learn the basics about allotropes of metalloids and metals, as a part of the overall properties of matter topic. An allotrope is basically a different form of the same element, each with distinct physical and chemical properties. For example

From playlist CHEMISTRY

John R. Parker: Complex hyperbolic lattices

Lattices in SU(2,1) can be viewed in several different ways: via their geometry as holomorphic complex hyperbolic isometries, as monodromy groups of hypergeometric functions, via algebraic geometry as ball quotients and (sometimes) using arithmeticity. In this talk I will describe these di

From playlist Geometry

Ionic Solids, Molecular Solids, Metallic Solids, Network Covalent Solids, & Atomic Solids

This chemistry video tutorial provides a basic introduction into solids. It explains how to classify a solid as ionic solids, molecular solids or atomic solids. There are 3 different types of atomic solids that you need to be familiary with - metallic solids, Group 8A solids, and network

From playlist New AP & General Chemistry Video Playlist

Introduction to Solid State Physics, Lecture 8: Reciprocal Lattice

Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host

From playlist Introduction to Solid State Physics

Introduction to Solid State Physics, Lecture 7: Crystal Structure

Upper-level undergraduate course taught at the University of Pittsburgh in the Fall 2015 semester by Sergey Frolov. The course is based on Steven Simon's "Oxford Solid State Basics" textbook. Lectures recorded using Panopto, to see them in Panopto viewer follow this link: https://pitt.host

From playlist Introduction to Solid State Physics

Phong NGUYEN - Recent progress on lattices's computations 1

This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...

Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He

From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

History of science 7: Did Witt discover the Leech lattice?

In about 1970 the German mathematician Witt claimed to have discovered the Leech lattice many years before Leech. This video explains what the Leech lattice is and examines the evidence for Witt's claim. Lieven Lebruyn discussed this question on his blog: http://www.neverendingbooks.org/w

From playlist History of science

A simple proof of a reverse Minkowski inequality - Noah Stephens-Davidowitz

Computer Science/Discrete Mathematics Seminar II Topic: A simple proof of a reverse Minkowski inequality Speaker: Noah Stephens-Davidowitz Affiliation: Visitor, School of Mathematics Date: April 17, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Elliptic Curves - Lecture 14b - Elliptic curves over the complex numbers

This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/

From playlist An Introduction to the Arithmetic of Elliptic Curves

Counting points on the E8 lattice with modular forms (theta functions) | #SoME2

In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT

From playlist Summer of Math Exposition 2 videos

Nihar Gargava - Random lattices as sphere packings

In 1945, Siegel showed that the expected value of the lattice-sums of a function over all the lattices of unit covolume in an n-dimensional real vector space is equal to the integral of the function. In 2012, Venkatesh restricted the lattice- sum function to a collection of lattices that h

From playlist Combinatorics and Arithmetic for Physics: Special Days 2022

Lattice relations + Hermite normal form|Abstract Algebra Math Foundations 224 | NJ Wildberger

We introduce lattices and integral linear spans of vexels. These are remarkably flexible, common and useful algebraic objects, and they are the direct integral analogs of vector spaces. To understand the structure of a given lattice, the algorithm to compute a Hermite normal form basis is

From playlist Math Foundations