In the year 2000, the Clay Foundation proclaimed the seven most important problems in mathematics – the so-called Millennium Prize Problems. Each of these problems promises an award of 1 million US dollars to the person(s) solving them. On this occasion of the 22nd anniversary of these Millennium Prize problems, there will be celebration events – at seven locations throughout Germany in this summer of 2022.

In Heidelberg University, we will celebrate the Poincaré Conjecture, the only millennium problem that has been solved so far. We are organizing a variety of public lectures, events, and workshops to share with the world these fascinating new developments in the world of mathematics.

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Public Lecture (in German)

Prof. Dr. Sebastian Hensel (Ludwig-Maximilians-Universität München)

22. July 2022, 16:30
Hörsaal Mathematikon, Berliner Straße 41 (INF 205)

“Von Sphären, Schleifen und Flüssen: die Poincaré-Vermutung und die Form des Raums”

Inhalt: Es ist anschaulich klar, dass man die Oberfläche einer Kugel nicht (ohne zu schneiden oder zu reißen) in einen Donut verformen kann. Immerhin hat letzterer ein Loch, und die Kugeloberfläche hat keins. Schon lange wussten Mathematiker, dass die Kugeloberfläche die einzige geschlossene Fläche ist, die kein Loch hat.

Die Poincaré-Vermutung fragt, ob man eine dreidimensionale Sphäre — also den Rand einer vierdimensionalen Kugel — auch daran erkennen kann, dass sie “kein Loch hat”. Diese vielleicht einfach klingende Frage hat Mathematiker für fast hundert Jahre beschäftigt, und wurde erst Anfang des 21. Jahrhunderts geklärt.

In diesem Vortrag werde ich einen Überblick über die Geschichte und Bedeutung dieses Problems geben, und dabei auch einen verständlichen ersten Einblick in die Topologie bieten: den Teilbereich der Mathematik, die sich mit den Formen von Räumen beschäftigt.

This talk is aimed at everyone who is curious about topology and at high school students (Oberstufe).

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Open HEGL (in German and English)

After the Public Lecture on 22 July 2022, approx 17:45
Heidelberg Experimental Geometry Lab (Basement of Mathematikon)

After the lecture, there will be the opportunity to talk to the lecturer and other scientific experts while enjoying snacks and drinks in the inner courtyard and foyer of the Mathematikon.

Then we invite you to join us for a hands-on exploration of geometry and topology at the Heidelberg Experimental Geometry Lab. You will get an opportunity to:

• Step into virtual reality worlds and experience unusual phenomena in unfamiliar geometries.
• Marvel at our exhibition of 3D printed and fabricated geometry and mathematical art models.
• Meet with mathematicians who will accompany you on your geometry trip and answer all your questions.

The event is open for all.

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Mathematical Lecture (in English)

Prof. Dr. Markus Banagl (Heidelberg University)
15. July 2022, 15:30
Hörsaal Mathematikon, Berliner Straße 41 (INF 205)

“Introduction to the Generalized Poincaré Conjecture”

Abstract: The generalized Poincaré conjecture aims for recognizing a sphere based on certain local and global assumptions on a space: It should locally be modelled on n-dimensional Euclidean space, it should be compact, simply connected and have the homology of an n-dimensional sphere.

We will give a first introduction to these questions and, after sketching the genesis of the conjecture, focus on the influential topological methods that lead to a proof in high dimensions.

The talk is aimed at math students, scientists and the mathematically interested public.

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Workshop for School Students: “The Euler Characteristic and Topology”
(in German, if not arranged otherwise individually)

We invite you to an interactive workshop about the Euler characteristic and topology - the area of math that lies behind the Poincaré Conjecture. The workshop is aimed at classes or individuals from the 9th grade. Snacks and drinks will of course also be offered.

The workshop will be given in German, if not arranged otherwise individually.

See the (German) workshop page for further details and application.