# Giordano Favi

##### Matériel Cours

- Analyse I pour Sciences et Technologies du Vivant. - Mathématiques pour Architectes. - Mathématiques Générales I pour Biologistes et Pharmaciens UNIL.
**EPFL SB SMA-GE **

MA A2 365 (Bâtiment MA)

Station 8

CH-1015 Lausanne

Unité: SMA-ENS

## Mission

My vision in teaching mathematics is to provide simple explanations for complex concepts. I also like to explain mathematical theories using analogy and comparison with everyday's life situations.

My goal is to give a broader approach to mathematics, that is not only focused on particular topics (like geometry, analysis, etc.) but that is also devoted to the study of the existing bridges between the different areas of study.

## Current work

My current work at EPFL is fully dedicated to teaching mathematics for 1st year students.

It is very important to give satisfactory introductory courses to first year students: future engineers need solid basis in mathematics and that is the purpose of my courses.

I also share with passion my vision of mathematics which is a beautiful tool for expressing elaborate constructions.

## Parcours professionnel

Scientific Collaborator | SMA | EPFL | September 2014 -- today |

Lecturer | Cours Euler | EPFL | August 2012 -- August 2014 |

Freelance Mathematician | February 2011 -- July 2012 | ||

Lecturer | MATHGEOM | EPFL | September 2010 -- January 2011 |

Scientific Collaborator | Mathematisches Institut | Universität Basel | April 2006 -- August 2010 |

Lecturer | DMA - EGG | EPFL | September 2009 -- February 2010 |

Guest researcher | Mathematisches Institut | Universität Bielefeld | January 2006 -- March 2006 |

Guest researcher | Mathematics section | Forschungsinstitut Zürich | November 2005 -- December 2005 |

Post-doc | Mathematics Department | ETHZ | April 2005 -- October 2005 |

Post-doc | Mathematisches Institut | Universität Basel | October 2004 -- March 2005 |

Post-doc | Département de Mathématiques | EPFL | January 2004 -- September 2004 |

Doctoral Assistant | Institut de Mathématiques | Université de Lausanne | September 1998 -- December 2003 |

## Education

Ph.D | Mathematics | Universite de Lausanne | 2003 |

Master | Mathematics | Universite de Lausanne | 1999 |

Bachelor | Mathematics | Universite de Lausanne | 1998 |

## Publications

#### Publications

Paul Balmer, Giordano FaviProceedings of the London Mathematical Society (3), 102, no.6 (2011), 1161-1185 |
Generalized tensor idempotents and the Telescope Conjecture. |

Giordano Favi, Mathieu FlorenceJournal of Algebra, Volume 319, (2008), 3885-3900. |
Tori and essential dimension. |

Paul Balmer, Giordano FaviQuarterly Journal of Mathematics, Volume 58, (2007), 415-441 |
Gluing techniques in triangular geometry. |

Grégory Berhuy, Giordano FaviJournal of Algebra, Volume 278, (2004), 199-216. |
Essential dimension of cubics. |

Grégory Berhuy, Giordano FaviDocumenta Math. Vol. 8 (2003), 279-330 |
Essential dimension: A functorial point of view (After A. Merkurjev). |

## Enseignement & Phd

#### Enseignement

- Mathematics,

#### Programmes doctoraux

#### Doctorants

## Cours

#### Analyse I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

#### Mathématiques

Ce cours présente les objets et outils de base de l'analyse du point de vue infinitésimal: polynômes, exponentielles, logarithmes, fonctions trigonométriques, séries de Taylor, différentiation et intégration, dans le but de représenter les courbes et surf...

#### Mathématiques 1A (pour MAN)

(Fiche de cours pas encore validée par la section)

#### Mathématiques 2A (pour MAN)

(Fiche de cours pas encore validée par la section)

#### Mathématiques générales I (pour BIO+PHA)

Introduction aux notions de probabilités, calcul différentiel et intégral, Systèmes linéaires, Equations différentielles

## Past courses

-Analyse 2 -Algebra -Topology -Group Theory -Linear Algebra -Algebraic Topology -Commutative Algebra -Introduction to Category Theory## Recherche

## Category Theory

My main research interest is in Category Theory and its generalizations to higher dimensions. This branch of mathematics has the potential to be applied to all kind of science. It even has an entry in the Stanford Encyclopedia of Philosophy:"Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science, and is also applied to mathematical physics. Roughly, it is a general mathematical theory of structures and of systems of structures. As category theory is still evolving, its functions are correspondingly developing, expanding and multiplying. At minimum, it is a powerful language, or conceptual framework, allowing us to see the universal components of a family of structures of a given kind, and how structures of different kinds are interrelated. Category theory is both an interesting object of philosophical study, and a potentially powerful formal tool for philosophical investigations of concepts such as space, system, and even truth. It can be applied to the study of logical systems in which case category theory is called "categorical doctrines" at the syntactic, proof-theoretic, and semantic levels. Category theory is an alternative to set theory as a foundation for mathematics. As such, it raises many issues about mathematical ontology and epistemology. Category theory thus affords philosophers and logicians much to use and reflect upon. [...]"

To quote one of my favorite mathematicians:

"In the years between 1920 and 1940 there occurred, as you know, a complete reformation of the classification of different branches of mathematics, necessitated by a new conception of the essence of mathematical thinking itself, which originated from the works of Cantor and Hilbert. From the latter there sprang the systematic axiomatization of mathematical science in entirety and the fundamental concept of mathematical structure. What you may perhaps be unaware of is that mathematics is about to go through a second revolution at this very moment. This is the one which is in a way completing the work of the first revolution, namely, which is releasing mathematics from the far too narrow conditions by 'set'; it is the theory of categories and functors, for which estimation of its range or perception of its consequences is still too early..." (Jean Dieudonné, 1961)