VII Escuela IMCA: Algebraic Geometry

Minicourses:

• Fernando Cukierman (Universidad de Buenos Aires)

  Introduction to representations of complex semisimple Lie algebras

  • Lecture 1: Definitions and first examples of groups and linear representations. Finite groups, symmetric groups, Young diagrams and Weyl's construction.
  • Lecture 2: Representations of \(\mathfrak{sl}(\mathbb{C})\). Nilpotent, soluble and semi-simple Lie algebras.
  • Lecture 3: Weights, roots, Cartan decomposition. Classification of simple Lie algebras. Classification of linear representations.

  References:

  • W. Fulton and J. Harris: Representation theory, a first course.
  • J. Humphreys: Introduction to Lie algebras and representation theory.

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• Sergey Gorchinskiy (Steklov Mathematical Institute of RAS)

  Chow motives and their applications

  • Lecture 1: Decompositions of Chow motives
  • Lecture 2: Transcendence of zero-cycles and generation of modules
  • Lecture 3: Chow motives of Lefschetz type

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• Vladimir Guletskii (University of Liverpool)

  Motivic obstruction to rationality in dimension 4

  • Lecture 1: Integral (in)decomposability of transcendental motives of surfaces over a field
  • Lecture 2: The transcendental motive of the Fermat sextic in \( \mathbb{P}^3 \)
  • Lecture 3: Mod p > 0 reduction of transcendental motives, an arithmetic view

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Conferences:

• Lucas das Dores (University of Liverpool)

  Rational curves on symmetric powers of surfaces

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• Richard Gonzales (Pontificia Universidad Catolica del Peru)

  Equivariant Chow groups, localization and applications

  • Part 1: Algebraic rational cells and equivariant Chow groups
  • Part 2: Localization in equivariant operational Chow groups and applications

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• Alberth Nuñez (Instituto de Matemáticas y Ciencias Afines)

  Cotangent complex of infinite symmetric powers of algebraic spaces

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