Lectures and Courses
Decoding Dimensions
Description: This long-term program hosted at IPM’s School of Mathematics delves into the intriguing realms of Algebraic Geometry and Number Theory. For a description of the program, click here.
The courses for the Spring semester 2025: Algebraic Geometry III, Algebraic Number Theory, Class Field Theory, Derived Algebraic Geometry, Essentials, Group Schemes (for more details, please see the poster).
The courses for the Spring semester 2024: Algebraic Geometry, Advanced Commutative Algebra, Category Theory and Homological Algebra (for more details, please visit here).
The courses for the Fall semester 2023: Galois Theory, Commutative Algebra, Algebraic Number Theory, Elliptic Curves and Modular Forms.
Poster: here
Seminars: here
Elliptic Surfaces
Date and Time: March 2-March 5, 2025.
Description: This is a mini-course. For more details, please visit here.
Location: Lecture Hall 1 at IPM School of Mathematics.
Topics in Moduli Spaces
Description: The theory of schemes has significant limitations when it comes to study moduli problems. This is mainly because they essentially fail to address the symmetries inherent in the classified objects. Parametrizing algebraic/geometric objects, while keeping track of their automorphisms led mathematicians to discover the category of algebraic stacks. In this regard, they provide a capable language for describing the geometry delegated to moduli problems.
Prerequisite: Some background knowledge of scheme theory (second and third chapters of Hartshorne’s Algebraic Geometry).
Date and Time: Thursdays, 9:30-1:30 Tehran local time, Spring and Fall semesters 2024.
Location: Lecture Hall 2 at IPM School of Mathematics.
References: R. Hartshorne, Algebraic Geometry; B. Fantechi, L. Göttsche, L. Illusie, S. L. Kleiman, N. Nitsure and A. Vistoli, FGA explained; G. Laumon and L. Moret-Bailly, Champs alg'ebriques; M. Olsson, Algebraic Spaces and Stacks; J.S. Milne, 'Etale Cohomology; W. Waterhouse, Introduction to Affine Group Schemes.
Fermat's Last Theorem
Description: This is an advanced reading course. For more details, please visit here.
Reference: T. Saito, Fermat's last theorem: Basic Tools, American Mathematical Society, 2013.
Location: Hybrid course: in Lecture Hall 2 at IPM School of Mathematics; and online with Google Meet (please contact us to receive the link).
Higher Hida Theory
Description: This is a reading seminar on higher Hida theory, presented by students.
Location: Lecture Hall 2 at IPM School of Mathematics.
Toric Geometry
Reference: W. Fulton, Introduction to toric varieties, Princeton University Press, 1993.
Supplementary References: D. Cox, Lectures on toric varieties; V. Alexeev, Complete moduli in the presence of semiabelian group action.
Prerequisite: Algebraic geometry (first chapter of Hartshorne’s Algebraic Geometry).
Date and Time: Wednesdays, 14:00-15:00 Tehran local time, Fall semester 2023.
Location: Hybrid seminar: in Lecture Hall 2 at IPM School of Mathematics; and online (please send an email to takusi@gmail.com to receive the link).
Introduction to Intersection Theory
Reference: D. Eisenbud, J. Harris, 3264 and All That: A Second Course in Algebraic Geometry, Cambridge University Press, 2016.
Prerequisites: A basic knowledge in classical algebraic geometry; an acquaintance with the language of schemes; an acquaintance with coherent sheaves and their cohomology. (Equivalently, the first 3 chapters of Hartshorne’s Algebraic Geometry).
Date and Time: Wednesdays, 14:00-16:00 Tehran local time, Spring semester 2023.
Location: Hybrid class: in Lecture Hall 2, School of Mathematics; and online (please send an email to taladpoosh@gmail.com to receive the link).
Poster: here
Classes: here
Hida Theory
Description: This is a reading seminar on Hida theory, presented by students.
Reference: H. Hida, Elementary Theory of L-Functions and Eisenstein Series, London Mathematical Society Student Texts, 1993.
Location: Hybrid seminar: in Lecture Hall 2 at IPM School of Mathematics; and online (please send an email to amir.ekhlasi@gmail.com to receive the link).
Topics in Arithmetic Geometry
Description: This is an advanced (thematic) reading course. Currently, we are studying Clausen-Scholze theory of Condensed Mathematics.
Last semester, we studied perverse sheaves and simplicial methods in algebraic geometry.
Reference: P. Scholze, Lectures on Condensed Mathematics, 2019.
Location: Lecture Hall 2, School of Mathematics.
Elliptic Curves
Descripton: This is a reading course on elliptic curves, run by postdocs and students. For more details, please send an email to a.marefparvar@ipm.ir.
Reference: J. H. Silverman, The Arithmetic of Elliptic Curves, 2nd Edition, Springer, Dordrecht, 2009.
Location: Online (Skype).