On Saturdays the seminar meets from 9:00 PM to 11:00 PM Tehran's time (12:30 PM to 2:30 PM U.S. Eastern Time) on Zoom. We also have informal talks by the participants on Wednesdays from 8:45 PM to 10:00 PM Tehran's time (12:15 PM to 1:30 PM U.S. Eastern Time) on Zoom.
Talk #23: Saturday, Mehr 3, 1400 (September 25, 2021):
Speaker: Amir Jafari, Topics: Grothendieck's Riemann-Roch Theorem
Video. Here is the link to the video recording of talk #23 on YouTube.
The third part of the seminar will review various cohomology theories such as Čech cohomology, étale cohomology, etc.
Talk #20: Saturday, Shahrivar 13, 1400 (September 4, 2021):
Speaker: Amir Jafari, Topics: Introduction to cohomology (Part III)
Video. Here is the link to the video recording of talk #20 on YouTube.
Talk #18: Saturday, Mordad 30, 1400 (August21, 2021):
Speaker: Amir Jafari, Topics: Introduction to cohomology (Part II)
Video. Here is the link to the video recording of talk #18 on YouTube.
Talk #16: Saturday, Mordad 16, 1400 (August 7, 2021):
Speaker: Amir Jafari, Topics: Introduction to cohomology (Part I)
Video. Here is the link to the video recording of talk #16 on YouTube.
The second part of the seminar will include selected topics from commutative algebra such as unramified, smooth and etale morphisms, regularity, flatness, completion, Hilbert series, etc.
Talk #22: Saturday, Shahrivar 27, 1400 (September 18, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and etale morphisms: local theory VI: Unramified algebras over a field, and an introduction to Zariski's Main Theorem
Video. Here is the link to the video recording of talk #22 on YouTube.
Notes. Here is the link to the notes for talk #22.
Talk #21: Saturday, Shahrivar 20, 1400 (September 11, 2021):
Speaker: Amir Jafari, Topics: An informal talk on faithfully flat descent.
Video. Here is the link to the video recording of talk #21 on YouTube.
Talk #19: Saturday, Shahrivar 6, 1400 (August 28, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and etale morphisms: local theory V: Faithfully flat descent
Video. Here is the link to the video recording of talk #19 on YouTube.
Notes. Here is the link to the notes for talk #19.
Talk #17: Saturday, Mordad 23, 1400 (August 14, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and etale morphisms: local theory IV: Base change for the module of Kähler differentials, further properties of unramified morphisms.
Video. Here is the link to the video recording of talk #17 on YouTube.
Notes. Here is the link to the notes for talk #17.
Talk #15: Saturday, Tir 12, 1400 (July 3, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and étale morphisms: local theory III: The second exact sequence of the module of Kähler differentials, The standard étale algebra.
Video. Here is the link to the video recording of talk #15 on YouTube.
Notes. Here is the link to the notes for talk #15.
Talk #14: Saturday, Tir 5, 1400 (June 26, 2021):
Speaker: Amir Jafari, Topics: The Riemann-Roch Theorem for algebraic curves (Part II)
Video. Here is the link to the video recording of talk #14 on YouTube.
Talk #13: Saturday, Khordad 29, 1400 (June 19, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and étale morphisms: local theory II: Examples and some properties of unramified, smooth and étale morphisms, localization of the module of Kähler differentials.
Video. Here is the link to the video recording of talk #13 on YouTube.
Notes. Here is the link to the notes for talk #13.
Talk #12: Saturday, Khordad 22, 1400 (June 12, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Unramified, smooth, and étale morphisms: local theory I: Derivations and the module of Kähler differentials, the first exact sequence of the module of Kähler differentials, definitions of unramified, smooth and étale morphisms.
Video. Here is the link to the video recording of talk #12 on YouTube.
Notes. Here is the link to the notes for talk #12.
The first part of the seminar will begin with the definition of categories and functors and will end with the construction of the derived category of an abelian category and the definition and various examples of derived functors. For some references please check here.
Talk #11: Saturday, Khordad 15, 1400 (June 5, 2021):
Speaker: Amir Jafari, Topics: Derived functors and hypercohomology
Video. Here is the link to the video recording of talk #11 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Khordad 19, 1400 (June 9, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Khordad 19, 1400 (June 2, 2021).
Talk #10: Saturday, Khordad 8, 1400 (May 29, 2021):
Speaker: Amir Jafari, Topics: Localization in triangulated categories, and the derived category
Video. Here is the link to the video recording of talk #10 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Khordad 12, 1400 (June 2, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Khordad 12, 1400 (June 2, 2021).
Talk #9: Saturday, Khordad 1, 1400 (May 22, 2021):
Speaker: Amir Jafari, Topics: Triangulated categories and localization.
Video. Here is the link to the video recording of talk #9 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Khordad 5, 1400 (May 26, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Khordad 5, 1400 (May 26, 2021).
Talk #8: Saturday, Ordibehesht 25, 1400 (May 15, 2021):
Speaker: Amir Jafari, Topics: Introduction to derived categories (Part 3).
Video. Here is the link to the video recording of talk #8 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Ordibehesht 29, 1400 (May 19, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Ordibehesht 29, 1400 (May 19, 2021).
Talk #7: Saturday, Ordibehesht 18, 1400 (May 8, 2021):
Speaker: Amir Jafari, Topics: Introduction to derived categories (Part 2).
Video. Here is the link to the video recording of talk #7 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Ordibehesht 22, 1400 (May 12, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Ordibehesht 22, 1400 (May 12, 2021).
Talk #6: Saturday, Ordibehesht 11, 1400 (May 1, 2021):
Speaker: Amir Jafari, Topics: Introduction to derived categories (Part 1).
Video. Here is the link to the video recording of talk #6 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Ordibehesht 15, 1400 (May 5, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Ordibehesht 15, 1400 (May 5, 2021).
Talk #5: Saturday, Ordibehesht 4, 1400 (April 24, 2021):
Speaker: Amir Jafari, Topics: Additive functors, Injective and projective objects, and DG-categories.
Video. Here is the link to the video recording of talk #5 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Ordibehesht 8, 1400 (April 28, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Ordibehesht 8, 1400 (April 28, 2021).
Talk #4: Saturday, Farvardin 28, 1400 (April 17, 2021):
Speaker: Mahdi Majidi-Zolbanin, Topics: Additive and Abelian categories.
Video. Here is the link to the video recording of talk #4 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Ordibehesht 1, 1400 (April 21, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Ordibehesht 1, 1400 (April 21, 2021).
Talk #3: Saturday, Farvardin 21, 1400 (April 10, 2021):
Speaker: Dr. Amir Jafari, Topics: Enriched categories, Higher categories, Properties and examples of adjointness.
Video. Here is the link to the video recording of talk #3 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Farvardin 25, 1400 (April 14, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Farvardin 25, 1400 (April 14, 2021).
Talk #2: Saturday, Farvardin 14, 1400 (April 3, 2021):
Speaker: Dr. Amir Jafari, Topics: Limits and colimits, Yoneda's Embedding Theorem, Adjoint functors, Additive categories.
Video. Here is the link to the video recording of talk #2 on YouTube.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Farvardin 18, 1400 (April 7, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Farvardin 18, 1400 (April 7, 2021).
Talk #1: Saturday, Farvardin 7, 1400 (March 27, 2021):
Speaker: Dr. Amir Jafari, Topics: Definitions and examples of categories and functors, Natural transformations, Universal constructions in categories (products, coproducts, equilizers, limits, etc.).
Video. Here is the link to the video recording of talk #1 on YouTube.
Exercises. Here are a set of exercises for the first talk.
Questions. If you have any questions about the material presented in this talk, please submit your questions here before Wednesday Farvardin 11, 1400 (March 31, 2021). Any question that is received will be discussed in the informal meeting on Wednesday Farvardin 11, 1400 (March 31, 2021).