Found 16 relevant results in 3.69s where lecturer="Manfred Einsiedler"
Introduction and development of some basic algebraic structures - groups, rings, fields including Galois theory, representations of finite groups, algebras.The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
Selected topics concerning fields, including Galois theory.
Analysis I: One Variable
Analysis I: eine Variable
Introduction to the differential and integral calculus in one real variable: fundaments of mathematical thinking, numbers, sequences, basic point set topology, continuity, differentiable functions, ordinary differential equations, Riemann integration.
Definition and basic property of measure theoretic dynamical entropy (elementary and conditionally). Ergodic theorem for entropy. Topological entropy and variational principle. Measures of maximal entropy. Equidistribution of periodic points. Measure rigidity for commuting maps on the circle group.
This course equips doctoral students with knowledge and tools to recognize, discuss and address ethical issues of their research.
We will build the theory of homogeneous dynamics and discuss applications to number theory, e.g. counting results concerning quadratic forms. We will assume (the willingness to learn the) basics of dynamics, but will build the theory of homogeneous dynamics from scratch.
We continue our development of homogeneous dynamics by discussing Ratner's measure classification theorems and corollaries thereof. We will also discuss various applications of the general theory. However, a big portion of the course will focus on the Margulis strategy for proving arithmeticity of lattices and the more recent result by Bader-Fisher-Miller-Stover.
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
Assignment-based course on stylistic, technical and cultural aspects of mathematical writing.
The reading course will focus on some basics of Ergodic Theory and homogeneous dynamics with the aim to understand the proofs of (special cases) of Ratner's theorems.
The students will understand the basic theory of unitary representations as well as the classification of a few unitary duals.
This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R).
This course will introduce unitary representations of Lie groups, discuss spectral gap in general, and discuss concrete unitary representations of SL(2,R).