Modular forms: Theta functions in higher dimensions
This lecture is part of an online graduate course on modular forms. We study theta functions of even unimodular lattices, such as the root lattice of the E8 exceptional Lie algebra. As examples we show that one cannot "her the shape of a drum", and calculate the number of minimal vectors
From playlist Modular forms
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
Lecture 9.1 Periodic functions
Periodic functions are functions that repeat themselves at regular intervals. In this lecture, we discuss the properties of periodic functions.
From playlist MATH2018 Engineering Mathematics 2D
Etale Theta - Part 02 - Properties of the Arithmetic Jacobi Theta Function
In this video we talk about Proposition 1.4 of Etale Theta. This came out of conversations with Emmanuel Lepage. Formal schemes in the Stacks Project: http://stacks.math.columbia.edu/tag/0AIL
From playlist Etale Theta
Calculus - Find the limit of a function using epsilon and delta
This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. This particular video uses a linear function to highlight the process and make it easier to understand. Later videos take care of more complicated functions and using epsilon and delta
From playlist Calculus
Modular forms: Theta functions
This lecture is part of an online graduate course on modular forms. We show that the theta function of a 1-dimensional lattice is a modular form using the Poisson summation formula, and use this to prove the functional equation of the Riemann zeta function. For the other lectures in th
From playlist Modular forms
We calculate the functional form of some example spherical harmonics, and discuss their angular dependence.
From playlist Quantum Mechanics Uploads
Trig Functions on the Unit Circle
How do these 6 trigonometric functions fit together on the unit circle? Downloadable copy for your refridgerator: http://bit.ly/YT-TrigFunctions
From playlist Trigonometry
The Lambert W Function Introduction
This function comes up as a solution to equations ranging from pure math to quantum physics to biology. In this video, I introduce the concepts behind the function and give some sample calculations. There's lots more to this function, so explore it on your own if you're interested.
From playlist Math
Sphere packings in 8 dimensions (after Maryna Viazovska)
The is a math talk about the best possible sphere packing in 8 dimensions. It was an open problem for many years to show that the best 8-dimensional sphere packing is given by the E8 lattice. We describe the solution to this found by Maryna Viazovska, building on work of Henry Cohn and Noa
From playlist Math talks
Melting of three-sublattice and easy-axis antiferromagnets on triangular and kagome lattices
New questions in quantum field theory from condensed matter theory Talk Title : Melting of threesublattice order in easyaxis antiferromagnets on triangular and kagome lattices by Kedar Damle URL: http://www.icts.res.in/discussion_meeting/qft2015/ Description:- The last couple of decade
From playlist New questions in quantum field theory from condensed matter theory
Arithmetic theta series - Stephan Kudla
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Arithmetic theta series Speaker: Stephan Kudla Affiliation: University of Toronto Date: March 8, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
CTNT 2022 - Definite orthogonal modular forms in rank 4 (by Eran Assaf)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Sylvia Serfaty - 1/4 Systems with Coulomb Interactions: Mean-Field Limits and Statistical (...)
We will discuss large systems of particles with Coulomb-type repulsion. The first part of the course will mention the question of mean-field for the dynamics of such systems via a modulated energy approach. The second part will be more expanded and concern the statistical mechanics of suc
From playlist Sylvia Serfaty - Systems with Coulomb Interactions : Mean-field Limits and Statistical Mechanics
Multiple Phase Transitions in a System of Hard Core Rotors on a Lattice (Lecture 3) by Deepak Dhar
INFOSYS-ICTS CHANDRASEKHAR LECTURES MULTIPLE PHASE TRANSITIONS IN A SYSTEM OF HARD CORE ROTORS ON A LATTICE SPEAKER: Deepak Dhar (Distinguished Emeritus Professor and NASI-Senior Scientist, IISER-Pune, India) VENUE: Ramanujan Lecture Hall and Online DATE & TIME: Lecture 1: Monday, D
From playlist Infosys-ICTS Chandrasekhar Lectures
Random Walks (Lecture - 02) by Abhishek Dhar
Bangalore School on Statistical Physics - VIII DATE: 28 June 2017 to 14 July 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru This advanced level school is the eighth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics in s
From playlist Bangalore School on Statistical Physics - VIII
Introduction to the Dirac Delta Function
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Introduction to the Dirac Delta Function
From playlist Differential Equations
J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)
In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field k. Then the arithmetic counterpart of the dimension h0(C,V)=dimkΓ(C,V) of the space of section
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes