Lectures&Exercises

Invariants of classical groups

• Linear Algebraic Groups, Invariant functions, Covariants, First fundamental theorem for GL, Endomorphisms of tensors, Polarization and restitution I, Polarization and restitution II, Character theory GL and S_m I, Character theory GL and S_m II, FFT for O_n/SO_n, FFT for Sp_n, Basic examples of classical invariants, Classical groups and their representations, Invariants of finite groups.

Introduction to differential topology

• Sard's theorem, Morse theory, Intersection theory.

Seminar on Fundamentals of Algebraic Geometry I:

• Lecture notes (scan).

Riemann surfaces:

• Lecture notes (scan).

Heat flow and the holographic Laplace operator:

• Lecture notes (scan)

(Locally) Symmetric spaces:

• Motivated introduction to (locally-)symmetric spaces, Lectures notes on symmetric spaces

Harmonic Analysis:

• Introduction to Harmonic Analysis (Lectures)

Riemannian Geometry:

• Introduction to Riemannian geometry (Lectures)

Seminar on Invariants of knots and Khovanov homology (notes):

• Invariants of knots, Khovanov coh. 1., Khovanov coh. 2., Vassiliev knot invariants, KZ equation, quantum groups and monodromy I., KZ equation, quantum groups and monodromy II., KZ equation, quantum groups and monodromy III., Verlinde formula I.,

Seminar on Quantum groups (notes):

• Sem. 1, Sem. 2, Sem. 3, Sem. 4, Sem. 5, Sem. 6, Sem. 7, Sem. 8, Sem. 9,

Algebraic geometry, Elliptic curves:

• Algebraic geometry (Lectures)
  
• Elliptic curves (Lectures)
  

Algebraic topology:

• Algebraic Topology I. (Lectures)
• Algebraic Topology II. (Lectures)
• Algebraic topology I.,II. - You can download the lectures of A.Hatcher (1.+2. semestr).
• Spektrální posloupnosti, fibrace (J.Vanžury) (ps-verze) (use "gunzip all_lectures.tar.gz" and then "tar -xvf all_lectures.tar")

Algebraic geometry:

• Algebraic geometry (Lectures)