Compact group

Math 101 Fall 2017 112917 Introduction to Compact Sets

Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi

From playlist Course 6: Introduction to Analysis (Fall 2017)

Quotient group example

Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.

From playlist Abstract algebra

Simple Groups - Abstract Algebra

Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order

From playlist Abstract Algebra

Symmetric Groups (Abstract Algebra)

Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in

From playlist Abstract Algebra

Quotient groups

The idea of a quotient group follows easily from cosets and Lagrange's theorem. In this video, we start with a normal subgroup and develop the idea of a quotient group, by viewing each coset (together with the normal subgroup) as individual mathematical objects in a set. This set, under

From playlist Abstract algebra

301.2 Definition of a Group

A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.

From playlist Modern Algebra - Chapter 15 (groups)

Definition of a group Lesson 24

In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el

From playlist Abstract algebra

GT2. Definition of Subgroup

Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-

From playlist Abstract Algebra

Product groups

Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.

From playlist Abstract algebra

Group Actions and Power Maps by C. R. E. Raja

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

Proper Actions and Representation Theory Part 2

Professor Toshiyuki Kobayashi, University of Tokyo, Japan

From playlist Distinguished Visitors Lecture Series

The Embedding Problem of Infinitely Divisible Probability Measures on Groups by Riddhi Shah

PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis

From playlist Ergodic Theory and Dynamical Systems 2022

Conformal Dynamics in Pseudo-Riemannian Geometry: a Question of A. Lichnerowicz - Charles Frances

Charles Frances Universite Paris-Sud 11; Member, School of Mathematics April 1, 2013 In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The

From playlist Mathematics

The orbit method for (certain) pro-p groups (Lecture 1) by Uri Onn

PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund

From playlist Group Algebras, Representations And Computation

Parallel session 4 by Jens Heber

Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma

From playlist Geometry Topology and Dynamics in Negative Curvature

Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems

Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8

From playlist Dynamical Systems and Ordinary Differential Equations

Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha

From playlist Toposes online

Monica Nevins: Representations of p-adic groups via their restrictions to compact open subgroups

SMRI Algebra and Geometry Online 'Characters and types: the personality of a representation of a p-adic group, revealed by branching to its compact open subgroups' Monica Nevins (University of Ottawa) Abstract: The theory of complex representations of p-adic groups can feel very technical

From playlist SMRI Algebra and Geometry Online

Nigel Higson: Isomorphism conjectures for non discrete groups

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I shall discuss aspects of the C*-algebraic version of the Farrell-Jones conjecture (namely the Baum-Connes conjecture) for Lie groups and p-adic groups. The conj

From playlist HIM Lectures: Junior Trimester Program "Topology"

Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra