תאריך:
ה', 12/01/202314:30-15:30
Title: Sharply o-minimal structures
Abstract: O-minimality is an axiomatic framework of "tame geometry". The sets definable in an o-minimal structure admit a nice geometric theory such as a good notion of dimension, finite triangulation, smooth stratifications, etc. Over the past couple of decades a powerful link has been developing between o-minimality and Diophantine geometry. However, the full generality of o-minimal geometry appears to be too broad to capture the full potential of this link: certain important conjectures are believed to hold in the o-minimal structures arising from Diophantine geometry, but not in all o-minimal structures. I will talk about a relatively new refinement of the o-minimal formalism called "sharp o-minimality" that attempts to capture these finer arithmetic tameness properties, and discuss some results that we recently obtained in this context.
Recording will be available at: https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=a6e6beab-eb0e-47c6-9d5d-aeb500acb5ad
Abstract: O-minimality is an axiomatic framework of "tame geometry". The sets definable in an o-minimal structure admit a nice geometric theory such as a good notion of dimension, finite triangulation, smooth stratifications, etc. Over the past couple of decades a powerful link has been developing between o-minimality and Diophantine geometry. However, the full generality of o-minimal geometry appears to be too broad to capture the full potential of this link: certain important conjectures are believed to hold in the o-minimal structures arising from Diophantine geometry, but not in all o-minimal structures. I will talk about a relatively new refinement of the o-minimal formalism called "sharp o-minimality" that attempts to capture these finer arithmetic tameness properties, and discuss some results that we recently obtained in this context.
Recording will be available at: https://huji.cloud.panopto.eu/Panopto/Pages/Sessions/List.aspx?folderID=a6e6beab-eb0e-47c6-9d5d-aeb500acb5ad