Representation theory: Introduction
This lecture is an introduction to representation theory of finite groups. We define linear and permutation representations, and give some examples for the icosahedral group. We then discuss the problem of writing a representation as a sum of smaller ones, which leads to the concept of irr
From playlist Representation theory
RT6. Representations on Function Spaces
Representation Theory: We note how to transfer a group action of a group G on a set X to a group action on F(X), the functions on X. Because F(X) is a vector space, we obtain a representation of the group, and we can apply previous techniques. In particular, the group acts on itself in
From playlist Representation Theory
Representation Theory as Gauge Theory - David Ben-Zvi [2016]
Slides for this talk: https://drive.google.com/file/d/1FHl_tIOjp26vuULi0gkSgoIN7PMnKLXK/view?usp=sharing Notes for this talk: https://drive.google.com/file/d/1BpP2Sz_zHWa_SQLM6DC6T8b4v_VKZs1A/view?usp=sharing David Ben-Zvi (University of Texas, Austin) Title: Representation Theory as G
From playlist Number Theory
RT1: Representation Theory Basics
Representation Theory: We present basic concepts about the representation theory of finite groups. Representations are defined, as are notions of invariant subspace, irreducibility and full reducibility. For a general finite group G, we suggest an analogue to the finite abelian case, whe
From playlist *** The Good Stuff ***
RT4.1. Constructions from Linear Algebra (Expanded)
Representation Theory: We apply techniques from linear algebra to construct new representations from old ones. Constructions include direct sums, dual spaces, tensor products, and Hom spaces. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/U
From playlist Representation Theory
Representation theory: Induced representations
We define induced representations of finite groups in two ways as either left or right adjoints of the restriction functor. We calculate the character of an induced representation, and give an example of an induced representation of S3.
From playlist Representation theory
Representation Theory: We explain unitarity and invariant inner products for representations of finite groups. Full reducibility of such representations is derived. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/UR-RepTheory.html
From playlist Representation Theory
RT7.2. Finite Abelian Groups: Fourier Analysis
Representation Theory: With orthogonality of characters, we have an orthonormal basis of L^2(G). We note the basic philosophy behind the Fourier transform and apply it to the character basis. From this comes the definition of convolution, explored in 7.3. Course materials, including pro
From playlist Representation Theory
Ellie Pavlick: "Should we care about linguistics?"
New Deep Learning Techniques 2018 "Should we care about linguistics?" Ellie Pavlick, University of Pennsylvania Abstract: There are countless examples of how deep learning has shattered previously state-of-the-art results on language processing tasks, including machine translation, quest
From playlist New Deep Learning Techniques 2018
Representations of finite groups of Lie type (Lecture - 3) by Dipendra Prasad
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
Linguistically informed NLP for healthcare experience data | Healthcare NLP Summit 2021
Get your Free Spark NLP and Spark OCR Free Trial: https://www.johnsnowlabs.com/spark-nlp-try-free/ Register for NLP Summit 2021: https://www.nlpsummit.org/2021-events/ Watch all Healthcare NLP Summit 2021 sessions: https://www.nlpsummit.org/ Investigation of attention mechanisms of BER
From playlist Healthcare NLP Summit 2021
Representation theory: Abelian groups
This lecture discusses the complex representations of finite abelian groups. We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality). We check the orthogonality relations for the
From playlist Representation theory
How do we convert the conceptual representation into a linguistic structure? What are the internal levels of "linguistic encoding".This short E-lecture provides the main answers to these questions.
From playlist VLC301 - Psycholinguistics
Comprehension 1 - Situation Models & Mental Simulations according to Zwaan (2016)
In this video, I review Zwaan's (2016) review article on Situation Models & Mental Simulations.
From playlist What is Listening?
Macdonald polynomials and decomposition numbers for finite unitary groups - Olivier Dudas
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Macdonald polynomials and decomposition numbers for finite unitary groups Speaker: Olivier Dudas Affiliation: Institut de mathématiques de Jussieu–Paris Rive Gauche Date: November 20, 2020 For more video pl
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Broué’s Abelian Defect Group Conjecture II - Daniel Juteau
Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture II Speaker: Daniel Juteau Affiliation: Centre National de la Recherche Scientifique/Université Paris Diderot; Member, School of Mathematics Date: September 16, 2020 For more video please
From playlist Seminar on Geometric and Modular Representation Theory
Decomposition numbers in defining characteristic - Andrea Dotto
SL2 Seminar Topic: Decomposition numbers in defining characteristic Speaker: Andrea Dotto Affiliation: Member, School of Mathematics Date: November 3, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
The Philosophy of Language - John Searle & Bryan Magee (1978)
In this program, John Searle discusses the philosophy of language with Bryan Magee. This is from a 1978 series on Modern Philosophy called Men of Ideas. #Philosophy #BryanMagee #Searle
From playlist Bryan Magee Interviews - Modern Philosophy: Men of Ideas (1977-1978)
This E-lecture first draws a distinction between dictionaries and lexicons and then discusses the role of the lexicon in linguistics. It shows how lexical entries are specified linguistically.
From playlist VLC206 - Morphology and Syntax
RT7.3. Finite Abelian Groups: Convolution
Representation Theory: We define convolution of two functions on L^2(G) and note general properties. Three themes: convolution as an analogue of matrix multiplication, convolution with character as an orthogonal projection on L^2(G), and using using convolution to project onto irreduci
From playlist Representation Theory