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Representation Theory: A First Course

William Fulton
TLDR
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras.
Abstract: 
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation theory of finite groups, the text explains how to work out the representations of classical groups.

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Enumerative Combinatorics

Charalambos A. Charalambides
TL;DR: This review of 3 Enumerative Combinatorics, by Charalambos A.good, does not support this; the label ‘Example’ is given in a rather small font followed by a ‘PROOF,’ and the body of an example is nonitalic, utterly unlike other statements accompanied by demonstrations.
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Topological quantum chemistry

Barry Bradlyn, +9 more
- 20 Jul 2017 - 
TL;DR: A complete electronic band theory is proposed, which builds on the conventional band theory of electrons, highlighting the link between the topology and local chemical bonding and can be used to predict many more topological insulators.
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Galois theory of linear differential equations

Marius van der Put, +1 more
TL;DR: In this paper, a large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, inverse problem and linear differential equations in positive characteristic.
Book

A First Course in Modular Forms

Fred Diamond, +1 more
TL;DR: Modular forms, elliptic curves, and modular curves as Riemann surfaces have been used to define the Eichler-Shimura Relation and L-functions.
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Classifying quantum phases using matrix product states and projected entangled pair states

Norbert Schuch, +2 more
- 31 Oct 2011 - 
TL;DR: In this article, Chen, Gu, and Wen give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states and in both the absence and the presence of symmetries.