Found 9 relevant results in 0.61s where lecturer="Paul Biran"
This is an introductory course in algebraic topology, which is the study of algebraic invariants of topological spaces. Topics covered include:singular homology, cell complexes and cellular homology, the Eilenberg-Steenrod axioms.
This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including:homology with coefficients, cohomology, homological algebra and universal coefficient theorems, Poincaré duality, ring structure of cohomology.
This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including:cohomology of spaces, operations in homology and cohomology, duality.
Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.
Linear Algebra I
Lineare Algebra I
Introduction to the theory of vector spaces for students of mathematics or physics: Basics, vector spaces, linear transformations, solutions of systems of equations, matrices, determinants, endomorphisms, eigenvalues, eigenvectors.
Linear Algebra II
Lineare Algebra II
Eigenvalues and eigenvectors, Jordan normal form, bilinear forms, euclidean and unitary vector spaces, spectral theorem, multilinear algebra, tensor product
In this seminar, we will define quasimorphisms and use them as an algebraic tool to study various automorphism groups of manifolds. After a short introduction to symplectic geometry, we will mainly focus on the group of Hamiltonian diffeomorphisms and Calabi quasimorphisms.
In this seminar we will define quasimorphisms and use them as an algebraic tool to study various automorphism groups of manifolds. After a short introduction to symplectic geometry, we will mainly focus on the group of Hamiltonian diffeomorphisms and the Calabi quasimorphism.
This will be an introductory course in symplectic geometry and topology.We will cover the simplest instances of symplectic rigidity phenomena, and techniques to detect and study them. The last part of the course will be devoted to more advanced techniques such as Floer theory.