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   Content  Â
Schedule: Tuesdays & Thursdays 13-15 GMT-4Â
Definitions & Introduction to Commutative Algebra
Roots of Commutative Algebra
Localization
Associated Primes and Primary Decomposition
Integral Dependence and The Nullstellensatz
Filtation and the Artin-Rees Lemma
Completions and Hensel's LemmaÂ
Dimension Theory
Modules of Differentials
Applications to Algebraic Geometry (Guest Speakers)
The course is evaluated with assignments (60%), seminars (10%) and a final exam (30%).
Applications are now closed
Lecture Notes
Guest Talk
Chiu-Chu Melissa Liu [A-Model: Topological String Theory]
Yukinobu Toda [Gopakumar-Vafa Invariants]
Rachel Webb [GIT, Stacks, and Quasimap Theory]
Miles Reid [Simpler Algebraic Groups]Â
Alexander Givental [Quantum Riemann-Roch]
LITERATUREÂ
David Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry.
Michael Atiyah and Ian Grant Macdonald, Introduction To Commutative Algebra.
Miles Reid, Undergraduate Commutative Algebra.
Nicolas Bourbaki, Commutative Algebra: Chapters 1-7.
Jean-Pierre Serre, Local Algebra.
successfully passed students
Gerardo Anguis  🇵🇪
(Ponticia Universidad Católica del Perú, PE)
Kevin Chavez 🇪🇨
(Universidad Yachay Tech, EC)
Allan Hurtado 🇬🇹
(University of San Carlos of Guatemala, GT)
Rubén Túquerrez 🇪🇨
(Escuela Politécnica Nacional, EC)
Dayana Zhigue 🇪🇨
(Universidad Yachay Tech, EC)
Guest SPEAKERs
Barbara Fantechi
SISSA
Alexander Givental
UC Berkeley
Chiu-Chu Melissa Liu
Columbia University
Miles Reid
University of Warwick
Yukinobu Toda
kavli IPMU, Univeristy of Tokyo
Rachel Webb
Cornell University
Teaching assistanTS
Christian Forero Pulido
SISSA
