# Symplectic geometry

## Semester:

Spring

## Offered:

2020

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

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Spring

2020

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

Winter

2020

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.

Winter

2019

MSc course offered in the winter semester 2019-20. Followed the book of A. Treves. Here are the students' assignments:

Spring

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.

Spring

2018

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

Winter

2018

(Athens, undergraduate, every year, 3 hrs/week) Fundamental group, covering spaces, Singular Homology. The online book by A. Hatcher (https://pi.math.cornell.edu/~hatcher/AT/AT.pdf) is quite useful.

Winter

2017

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

Spring

2013

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

Winter

2013

(Athens, MSc, 4 hrs/week) Followed the book by Duistermaat and Kolk.

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.

Spring

2012

(Athens, MSc, 4 hrs/week) Manifolds, tangent vectors, vector fields, Lie bracket.

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.

Spring

2007

(Crete, undergraduate, 3 hrs/week) Followed "Calculus on manifolds" by M. Spivak.

Spring

2007

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

Winter

2007

(University of Crete, undergraduate, 4 hrs/week)

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National and Kapodistrian University of Athens,

Department of Mathematics

(+30) 210-7276423

Panepistimiopolis Zografou

Athens, ZipCode 157-84

iandroul@math.uoa.gr