Algebraic Geometry
Lecturer: Daniel Galviz & Francisco Villacis
Content
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 Sheaves
Week 3:
- Lecture 7: Schemes
- 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]
Lothar Göttsche [Hilbert schemes of points on surfaces] [Slides]
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]
Exercise sheets
LITERATURE
Robin Hartshorne, Algebraic Geometry
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
students
30 Students were accepted
We will publish the list of students who have successfully approved the course.
30 Students were accepted
We will publish the list of students who have successfully approved the course.
Guest SPEAKERs
Catherine Cannizzo
UC- Berkeley
Yalong Cao
RIKEN Institute
Alexander Cruz
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)