Algebraic GeometryÂ
Lecturer: Daniel Galviz & Francisco Villacis
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   Content  Â
Week 1:
   - Lecture 1: Introduction and basics of category theory
   - Lecture 2: Zariski Topology and Affine Varieties
   - Lecture 3: Algebraic Varieties and Projective Varieties
Week 2:
   - Lecture 4: Sheaves and Stalks
   - Lecture 5: Abelian sheaves
   - Lecture 6: Sheaves of modules & Coherent SheavesÂ
Week 3:
   - Lecture 7: SchemesÂ
   - Lecture 8: Morphisms of schemes
   - Lecture 9: Projective morphisms
Week 4:
   - Lecture 10: Differentials and Divisors on curves
   - Lecture 11: Vector Bundles
   - Lecture 12: Sheaf cohomology
This mini course is evaluated with assignments.
Applications are now closed
Lecture Notes
Guest Speakers
Dennis Gaitsgory [Geometric Langlands Correspondence]
Richard Thomas [Spec and Proj] [Slides]
Daniel Galviz [Gromov-Witten Theory and String Theory] [Slides]
Daniel Huybrechts [Algebraic Geometry of Kähler manifolds] [Slides]
Artan Sheshmani [Super Gromov-Witten invariants on almost Kähler varieties]Â
Lothar Göttsche [Hilbert schemes of points on surfaces] [Slides]Â
Martinj Kool [Algebraic geometry and Vafa-Witten theory] [Slides]
Claire Voisin [Variations of Hodge structures and geometric applications] [Slides]
Yalong Cao [Gopakumar-Vafa type invariants of Calabi-Yau 4-folds] [Slides]
Catherine Cannizzo [Homological Mirror symmetry] [Slides]
Exercise sheetsÂ
LITERATUREÂ
Robin Hartshorne, Algebraic GeometryÂ
D. Galviz and F. Villacis, Physics Latam: Lectures on Algebraic Geometry
Alexander Grothendieck, Elements of Algebraic Geometry
Ravi Vakil, The Rising Sea: Foundations of Algebraic Geometry
Harris and Phillip Griffiths, Principles of Algebraic Geometry
Igor Shafarevich, Basic Algebraic Geometry 1 & 2
successfully passed students
Allan Hurtado 🇬🇹
(University of San Carlos of Guatemala, GT)
Isaac Mendez 🇲🇽
(Universidad Autónoma del Estado de Mexico, MX)
Juan Morales 🇨🇴
(Universidad de los Andes, CO)
Franco Rufolo 🇦🇷
(Universidad de Buenos Aires, AR)
Daniel Reyes 🇲🇽
(Universidad Nacional Autónoma de México, MX)
Ronald Urrutia 🇧🇷
(Universidade de São Paulo, BR)
Heldert Villegas 🇨🇴
(Universidad Nacional de Colombia, CO)
Guest SPEAKERs
Catherine Cannizzo
UC- Berkeley
Yalong Cao
RIKEN Institute
Alexander CruzÂ
UNAL
Dennis Gaitsgory
Harvard U.
Lothar Göttsche
ICTP
Mark Gross
Cambridge U.
Daniel Huybrechts
Bonn University
Martijn Kool
Utrecht University.
Pranav Pandit
ICTS-TIFR
Richard Thomas
Imperial College London
Artan Sheshmani
Harvard U. & BIMSA Tsinghua U.
Claire Voisin
IMJ-Paris Rive Gauche
Lecturers
(Pure Mathematics University of Waterloo, CA)
Lecturer & Organizer
Daniel Galviz
YMSC (Tsinghua University)
ICTS (Tata Institute of Fundamental Research, IN)