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Symplectic geometry

Semester: 

Spring

Offered: 

2024
e-class
This is an elected course taught 3 hours a week. The book by da Silva is used.

Curves and Surfaces

Semester: 

Spring

Offered: 

2024
e-class
(Athens, undergraduate, every year, 6 hrs/week) Following Marfredo do Carmo's classical book on the subject.

Geometry 1 (Coordinates Geometry)

Semester: 

Winter

Offered: 

2024
e-class
This is an obligatory course for first year students. It is taught 6 hours per week. It covers the introduction of coordinates in Geometry, algebra of vectors, the classical theorems of Geometry (Menelaus, Pappus, Ceva, Desargues), inner product, exterior product, mixed triple product, lines, planes, parallelism and orthogonality, areas, volumes, conic sections and the basic theorems (Dedenlin, Apollodorus), ending with a complete study of the second order equation.

Differential Geometry 1

Semester: 

Winter

Offered: 

2024
(Athens, MSc, 4 hrs/week) Manifolds, tangent vectors, vector fields, Lie bracket, Frobenius theorem, Lie groups and Lie algebras

Singular Foliations

Semester: 

Spring

Offered: 

2023
This is a graduate course offered in Zurich, to the graduate students of UZH and ETH. 

Differential Geometry 2

Semester: 

Spring

Offered: 

2022
e-class
(MSc course, 4 hours per week) Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow theorem, Jacobi fields.

Linear Algebra

Semester: 

Spring

Offered: 

2018
(Athens, every year to Physics students, 3 hrs/week) Systems of linear equations, matrices, vector spaces and linear maps, eigenvalues/vectors/spaces, linear systems of differential equations with constant coefficients.

Differential Forms

Semester: 

Winter

Offered: 

2017
e-class
(Athens, 3 hrs/week) Followed the book "Calculus on Manifolds", by M. Spivak.

Geometric Quantization

Semester: 

Spring

Offered: 

2013
(Athens, MSc, 4 hrs/week) Discussed the orbit method. Kirillov's book is a good guide on the subject.

The Atiyah-Singer index theorem

Offered: 

2012
(Athens, seminar) Introduced K-theory of C*-algebras, pseudodifferential calculus, Fredholmness, ellipticity and analytic index, Lie groupoids, and finally gave the proof of the Atiyah-Singer index theorem.

K-theory

Offered: 

2007
(University of Crete, seminar) Introduced topological K-theory and explained its relation with algebraic K-theory and C*-algebras. Presented Both periodicity, 6-terms exact sequence and Kunneth theorem.

History of Geometry

Semester: 

Spring

Offered: 

2007
(University of Crete, undergraduate, 3 hrs/week)