Pavel Sechin

Teaching

Current (Winter Semester 2025)

• Exercises for the course Algebraic Geometry I (Prof. M. Hoyois)

External webpage     Internal webpage (GRIPS)

Selected materials from previous semesters

• Elementary Number Theory     Script (in German, PDF)    Exercises (in German, PDF)
     
  In summer 2025, I taught the course called "Elementare Zahlentheorie (LG, LM, LR)". It included topics from basic number theory, like the Euclidean algorithm and the Fundamental Theorem of Arithmetic, but explained them in a way that was easier for people without a maths background to understand. This course is part of the training for future teachers in elementary and middle schools in Germany, who may or may not teach maths.
  
  
• Algebraic Topology II

  YouTube playlist Lecture notes (Pröls, 223 pages, PDF) Lecture notes (Götzfried, 151 pages, PDF)

  
  In the summer of 2021, during the pandemic, I created and recorded an original course, "Algebraic Topology II".
  The course explores topics such as higher homotopy groups, 2-categories and homotopy pullbacks/pushforwards in them, the Blakers–Massey and Mather’s Cube theorems, Brown representability, as well as principal G-bundles and characteristic classes.

Alexandra Pröls has typed the lecture notes of this course based on the video recordings.
In summer 2022, I taught this course again, now in the usual format.
Linus Götzfried has typed the lecture notes, and also kindly made the TeX-source available here: TeX-files .
Please note that the lecture notes above have not been proof-read, so you should use them at your own risk.


• Introduction to the enumerative geometry     Exercises (in German, PDF)
  
  As a part of the QED-Seminar in Regensburg (May 30 — June 2, 2025) I gave two talks aimed at high school students and first and second year undergraduates, explaining the basic problems of enumerative geometry and their solutions.
  
  
• Algebraic cobordism of Levine–Morel     YouTube playlist    Exercises (PDF)
  
  In summer 2023 I gave a course on oriented cohomology theories in algebraic geometry, with the focus on the algebraic cobordism of Levine–Morel.
  
  
• Seminar on the Brauer group and Severi–Brauer varieties
  
  
• Seminar on the algebraic surfaces     Program (PDF)
  
  
• Research seminar on the Grothendieck ring of varieties and birational geometry

Back to the main page