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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notion
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Tag(s):
- mathematics
- perturbative quantum field theory
- classical field theory
- free quantum theories
- feynman diagrams
- renormalization theory
- local operators
- operator product expansion
- renormalization group equation
- classical
- field
- theory
- feynman
- diagrams
- free
- quantum
- theories
- local
- operators
- product
- expansion
- perturbative
- renormalization
- gr
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
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Tag(s):
- mathematics
- finite dimensional algebras
- quiver representations
- series representations
- finite groups
- representation theory
- lie algebras
- tensor products
- density theorem
- jordan-h?older theorem
- krull-schmidt theorem
- maschke?s theorem
- frobenius-schur indicator
- frobenius divisibility
- burnside?s theorem
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their re
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Tag(s):
- mathematics
- dunkl operators
- cherednik
- affine algebra
- representation theory
- hecke
- knizknik-zamoldchikov
- orbifolds
- calogero-moser space
- hilbert scheme
- algebra
- macdonald-mehta integral
- integrable system
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Published by: Massachusetts Institute of Technology | Language: English
Published by: Massachusetts Institute of Technology | Language: English
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This course will give a detailed introduction to the theory of tensor categories and review some of its connections to other subjects (with a focus on representation-theoretic applications). In particular, we will discuss categorifications of such notions from ring theory as: module, morphism of modules, Morita equivalence of rings, commuta
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Tag(s):
- mathematics
- monoidal functors
- tensor
- pivotal
- spherical
- maclane's
- grthendieck
- module categories
- braided tensor
- muger centralizer
- symmetric categories
- deligne's theorem
- radford formula
- squared norms
- global dimensions
- cohomology
- oceanu ridigity
- robenius-perron
- lifting theory
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