## Alessandro Carlotto: Catalogue data in Spring Semester 2020 |

Name | Dr. Alessandro Carlotto |

Field | Mathematics |

alessandro.carlotto@math.ethz.ch | |

Department | Mathematics |

Relationship | Assistant Professor |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-2554-00L | Topology | 6 credits | 3V + 2U | A. Carlotto | |

Abstract | Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces. | ||||

Objective | An introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures. | ||||

Literature | We will follow these, freely available, standard references by Allen Hatcher: i) http://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf (for the part on General Topology) ii) http://pi.math.cornell.edu/~hatcher/AT/ATch1.pdf (for the part on basic Algebraic Topology). Additional references include: "Topology" by James Munkres (Pearson Modern Classics for Advanced Mathematics Series) "Counterexamples in Topology" by Lynn Arthur Steen, J. Arthur Seebach Jr. (Springer) "Algebraic Topology" by Edwin Spanier (Springer). | ||||

Prerequisites / Notice | The content of the first-year courses in the Bachelor program in Mathematics. In particular, each student is expected to be familiar with notion of continuity for functions from/to Euclidean spaces, and with the content of the corresponding basic theorems (Bolzano, Weierstrass etc..). In addition, some degree of scientific maturity in writing rigorous proofs (and following them when presented in class) is absolutely essential. | ||||

401-5350-00L | Analysis Seminar | 0 credits | 1K | M. Struwe, A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, L. Kobel-Keller, T. Rivière, University lecturers | |

Abstract | Research colloquium | ||||

Objective | |||||

Content | Research seminar in Analysis | ||||

406-2554-AAL | TopologyEnrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement. Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit. | 6 credits | 13R | A. Carlotto | |

Abstract | Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces. | ||||

Objective | An introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures. | ||||

Lecture notes | See lecture homepage: https://metaphor.ethz.ch/x/2017/fs/401-2554-00L/ | ||||

Literature | James Munkres: Topology | ||||

Prerequisites / Notice | The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material. |