September 1 - December 12, 2025
Organizers: Valentina Harizanov, Philipp Hieronymi, Jennifer Park, Florian Pop, Alexandra Shlapentokh
Description: Gödel’s Incompleteness Theorems reveal the fundamental complexity of arithmetic, both in negative sense, i.e., the undecidability of the theory of the natural numbers, but also in positive sense that first-order language of fields is far more expressive than one might think. The structures born from the interaction of logic and number theory/arithmetic
geometry are at the center of extensive and intensive study at the frontier of computability theory, model theory, number theory and arithmetic geometry.
Among the topics at the core of the program, the focus will be on:
- Decidability and computability, e.g. Hilbert Tenth Problem over arithmetically significant domains.
- Definability, e.g., definability of valuations, definability in arithmetic geometry.
- Computability, e.g., effectiveness and complexity of countable structures.
The program will include an introductory school, a workshop and a conference. For further information concerning these events, please follow the links on the righthand side to the corresponding pages.
In addition to the activities listed above, there will be a weekly seminar with speakers from the participants and/or short-term visitors as well as possibly ad-hoc talks on “hot topics”.
The online application platform to participate in this trimester program is open until March 2, 2025 (CET).
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September 8 - 12, 2025
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Valentina Harizanov, Philipp Hieronymi, Jennifer Park, Florian Pop, Alexandra Shlapentokh
Lecturers:
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Sylvy Anscombe (Université Paris Cité)
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Franziska Jahnke (Münster)
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Bjorn Poonen (MIT)
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Ted Slaman (UC Berkeley)
Description: Definability has a far-reaching impact in mathematics, far beyond model theory. In this workshop, experts not only from definability, but in other areas of mathematics (number theory, computability theory, arithmetic geometry, etc.) will give an expository overview of the impact of definability in their fields, as well as the state of the current research in their fields. These talks are accessible to graduate students and experts from other fields, to facilitate the discussions that will follow during the trimester.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.
The online application platform to participate in the school will open on March 3, 2025 (CEST).
October 20 - 24, 2025
Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Franziska Jahnke, Florian Pop, Sasha Shlapentokh, Jakob Stix
Description: The goal of this workshop is to bring all leading experts in the world at HIM to discuss the important open problems in number theory to which model theory might have an application, and to bridge the gap that always seems to exist between number theory and model theory. Number theorists and model theorists whose works have natural applications to number theory will present their work.
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.
December 8 - 12, 2025
Venue: Lipschitz-Saal (Endenicher Allee 60, Bonn)
Organizers: Wesley Calvert, Valentina Harizanov, Philipp Hieronymi, Angus Macintyre, Umberto Zannier
Description: TBA
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event. Beyond this, researchers from the HCM, in particular, early-career researchers, are welcome upon request.
5 minute walk from Bonn central train station to HIM
Leave the station through the back exit into the street called Quantiusstrasse. Cross at the zebra crossing and turn left. Walk to the corner: the cross-street is the Poppelsdorfer Allee. Cross (careful of traffic from your left) and walk to the right up the Poppelsdorfer Allee, towards the Poppelsdorfer Castle in the distance. At the next intersection, continue straight on up the avenue. HIM is building No. 45 on the left side of Poppelsdorfer Allee behind the wrought iron gate.
The airport shuttle drops you in front of the central train station. Cross at the traffic light nearest you and take the escalator down to the underground passage. Go straight to the end of the passageway until you reach the street (Quantiusstrasse) and follow the directions above.
If you are coming to a Workshop or School, go straight to Poppelsdorfer Allee 45 and sign-in.
If you are coming for a (Junior) Trimester Program, come first to the HIM Administration at Poppelsdorfer Allee 82, diagonally across the street from the Institute proper.