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Universität Basel
Departement Mathematik und Informatik

Spiegelgasse 1

CH-4051 Basel


Activities and Links

Every Tuesday from 10:30 to 12:00

The weekly seminar takes place every Tuesday from 10:30 to 12:00 a.m. on the ground floor of Spiegelgasse 1, with a tea in the "Eulerzimmer" (6th floor) at 10:10 a.m., prior to the talk. 

Das Bernoulli-Euler-Zentrum ist ein interdisziplinäres und interfakultäres Dokumentations- und Forschungszentrum. Seine Aufgabe ist es, das umfangreiche Quellenmaterial im Umfeld der Mathematiker und Physiker aus der Familie Bernoulli und Leonhard Eulers zu erschliessen und die wissenschaftshistorische Forschung zu unterstützen. Das BEZ wurde 2010 durch Beschluss des Rektorats der Universität Basel gegründet.

Die Bernoulli-Euler-Gesellschaft hat die Aufgabe, die Erschliessung und Auswertung des umfangreichen Quellenmaterials im Umfeld der Bernoulli und Eulers zu unterstützen und zu fördern, deren Lebensleistungen der Öffentlichkeit nahezubringen und die wissenschafts-historische Forschung zu stärken.

Talks and Lectures

June 8, 2021

October 24-28, 2016 in Grenoble (FR)

Automorphism Groups of Affine Varieties

Affine Geometry, Hyperbolicity, Complex Analysis – A Conference in Honor of Mikhail Zaidenberg
Insitut Fourier, Saint-Martin-d'Hères, Grenoble, France

October 24-28, 2016

September 12, 2016

The Cremona Group – A Historical Survey

Talk at the Cremona Conference Basel 2016
In two fundamental papers from 1863 and 1865 Luigi Cremona introduced and studied birational transformations of the projective plane. The group of all these transformations was later called Cremona Group. Because of its strong interaction with the geometry of rational surfaces–e.g., the automorphism group of every rational surface is contained in the Cremona Group–it became a central object in classical algebraic geometry.
What do we know today about this group, after 150 years of research? Many interesting results can be found in the classical literature, although some of the proofs appear to be incomplete. We will also see that several basic questions have only been answered in the last 20 years.

June, 2012

Conference in Levico Terme, June 2012

June 8-11, 2011

Conference in Honor of Claudio Procesi, Rome, June 8-11, 2011

16./17. Mai 2011

Vortrag an der Senioren-Uni, 16./17. Mai 2011 –> Notizen

June 1995

Séminaire BOURBAKI, 47ème année, 1994-95, n 802

Course Notes
Notes from Courses

Version from July 2014

Notes from several courses on "Algebraic Geometry". The text will eventually become the first appendix of a book "Algebraic Transformation Groups". Other chapters are also available on this site.

Version from January 2017

These are some notes from several courses on "Algebraic Transformation Groups and Invariant Theory". They are still incomplete, but should eventually be published as a book.

October 2015

These are notes from some lectures I gave in the Fall 2015.

Version from July 1996

These are notes from courses given in Basel, based on some lecture notes of Claudio Procesi

More Notes
More Notes


We discuss and prove some results about the Lie algebra of

vector fields Vec(X) on an affine variety X which are due to

J. Grabowski and T. Siebert, e.g. that two normal varieties 

X and Y are isomorphic if and only if the vector fields Vec(X) and Vec(Y) are isomorphic Lie algebras.


We give a modern proof of the Regularization Theorem of A. Weil which says that for every rational action of an algebraic group G on a variety X there exist a variety Y with a regular G-action and a G-equivariant birational map X ---> Y. Moreover, we show that a rational G-action on an affine variety X with the property that each g from a sense subgroup of G induces a regular automorphism of X, is a regular action.

arXiv:1808.08729 [math.AG]


Eine nicht ganz ernste "mathematische" Kurzgeschichte!

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