Genus of a multiplicative sequence

Recent progress in multiplicative number theory – Kaisa Matomäki & Maksym Radziwiłł – ICM2018

Number Theory Invited Lecture 3.5 Recent progress in multiplicative number theory Kaisa Matomäki & Maksym Radziwiłł Abstract: Multiplicative number theory aims to understand the ways in which integers factorize, and the distribution of integers with special multiplicative properties (suc

From playlist Number Theory

Math 131 Lecture #04 091216 Complex Numbers, Countable and Uncountable Sets

Recall the complex numbers: the plane with addition and multiplication. Geometric interpretation of operations. Same thing as a+bi. Complex conjugate. Absolute value (modulus) of a complex numbers; properties (esp., triangle inequality). Cauchy-Schwarz inequality. Recall Euclidean sp

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis

Multiplicative order of a congruence class

In this video we introduce the concept of multiplicative order and we prove several properties and go over some examples. The content of this video corresponds to Section 8.1 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-

From playlist Number Theory and Geometry

Maria Charina: Algebraic multigrid and subdivision

Abstract: Multigrid is an iterative method for solving large linear systems of equations whose Toeplitz system matrix is positive definite. One of the crucial steps of any Multigrid method is based on multivariate subdivision. We derive sufficient conditions for convergence and optimality

From playlist Numerical Analysis and Scientific Computing

Theory of numbers: Multiplicative functions

This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.

From playlist Theory of numbers

Dynamical generalizations of the Prime Number Theorem and...disjointness of... -Florian Richter

Joint IAS/Princeton University Number Theory Seminar Topic: Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions Speaker: Florian Richter Affiliation: Northwestern University Date: June 4, 2020 For more video please visit http://vi

From playlist Mathematics

Multivariable Calculus | What is a vector field.

We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

Algorithms for Multiplicative Inverses in Primitive/Basic Fields - Field Theory - Lecture 03

In this video we describe how to compute the multiplicative inverse of an element in a "basic extension". Note that I use the word "simple extension" but I want to reserve that terminology for something else later --- extensions corresponding to simple groups.

From playlist Field Theory

On the algebraic fundamental group of surfaces of general type by Margarida Lopes

Algebraic Surfaces and Related Topics PROGRAM URL : http://www.icts.res.in/program/AS2015 DESCRIPTION : This is a joint program of ICTS with TIFR, Mumbai and KIAS, Seoul. The theory of surfaces has been the cradle to many powerful ideas in Algebraic Geometry. The problems in this area

From playlist Algebraic Surfaces and Related Topics

Holomorphic Curves and the ADHM Vortex Equations by Aleksander Doan

PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie

From playlist Vortex Moduli - 2023

On the existence of minimal Heegaard splittings - Dan Ketover

Variational Methods in Geometry Seminar Topic: On the existence of minimal Heegaard splittings Speaker: Dan Ketover Affiliation: Princeton University; Member, School of Mathematics Date: Oct 2, 2018 For more video please visit http://video.ias.edu

From playlist Variational Methods in Geometry

Categories 6 Monoidal categories

This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super

From playlist Categories for the idle mathematician

Wei Ho: Explicit models of genus one curves and related problems

CIRM HYBRID EVENT We discuss various explicit models of genus one curves, some classical and some a little less so, with an eye towards applications in number theory and arithmetic geometry. In particular, we will talk about how understanding such models has shed light on many kinds of pro

From playlist Algebraic and Complex Geometry

Counting embedded curves in symplectic 6-manifolds - Aleksander Doan

Symplectic Dynamics/Geometry Seminar Topic: Counting embedded curves in symplectic 6-manifolds Speaker: Aleksander Doan Affiliation: Columbia University Date: February 03, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Mikhail Khovanov: Universal construction in ultra low dimensions

We'll explain the notion of the universal construction, which can be viewed as a weakening of the TQFT axioms, and demonstrate how it works in dimensions one and two.

From playlist Workshop: Monoidal and 2-categories in representation theory and categorification

Quantum Cohomology and WDVV equation (Lecture 1) by Ritwik Mukherjee

Program : Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics ORGANIZERS : Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE & TIME : 16 July 2018 to 10 August 2018 VENUE : Ramanujan L

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

Andrew Lobb: Quantum sln knot cohomology and the slice genus

Abstract: We will give an overview of the information about the smooth slice genus so far yielded by the quantum 𝔰𝔩n knot cohomologies. Recording during the thematic meeting "Knotted Embeddings in Dimensions 3 and 4" the February 15, 2017 at the Centre International de Rencontres Mathémat

From playlist Topology

Andrew Sutherland: Introduction to Sato-Tate distributions

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Jean-Morlet Chair - Shparlinski/Kohel

C. T. McMullen - Billiards, quadrilaterals and moduli spaces

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Multilinear Algebra

Multilinearity of the determinant In this video, I define the notion of a multilinear function and I show that the determinant is multilinear. Come and get a taste of the beauty of multilinear algebra :) Check out my Determinants Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIr

From playlist Determinants