a virtual math seminar on open conjectures in

number theory and arithmetic geometry

VaNTAGe started in January 2020, as one of the first international virtual seminars about number theory and arithmetic geometry (NT&AG).  The seminar provides open access to world class mathematics, with a focus on progress on unsolved problems in NT&AG.  The purpose of the seminar is to provide a viable way for researchers to connect with cutting-edge research in NT&AG without the expense and environmental impact of travel.  Another aim of the seminar is to advance understanding on the most exciting open problems in this field.  As the goal of the seminar is to build communication among researchers developing the fields of NT&AG,  speakers and participants are expected to uphold the highest standards for clear exposition and respectful interactions.

The seminar is organized by Rachel Pries and Andrew Sutherland.  

The intended audience includes graduate students and faculty with some background in NT&AG; for practical reasons the seminar will be presented in English at (1 pm Eastern US)=(noon Central US) = (11 am Mountain US) = (10 am Pacific US), every other Tuesday.  Live access links are posted here and on the night before each talk, and also sent to our mailing list.  Video recordings of prior talks can be found on our YouTube channel.

2024: The 18th topic is TBA

2024: The 17th topic is Heights and Diophantine Geometry

Jan 23: Hector Pasten  A criterion for algebraic degeneracy of integral points (slides, video)

Feb 6: Philipp Habegger Conjectures on Unlikely Intersections: What is known and what is open? (slides, video)

Feb 20: Ziyang Gao Sparsity of rational points on curves: What is known and what is expected? (slides, video)

Feb 27: Sara Checcoli On fields with finitely many points of bounded height: around property (N)

For information (including slides and videos) about VaNTAGe talks on earlier topics,  click here.

Video recording: Most VaNTAGe meetings are recorded and posted to our YouTube channel a week after the talk (this gives us time to add high quality captions, which are included with all our video recordings).  Participants should be aware that if they join the live meeting both the audio and video will be recorded.  Participants who do not wish to be recorded should keep their video camera and microphone off and use the chat to ask questions.

VaNTAGe is currently using Zoom.  At other times, we used BlueJeans.

If you have suggestions for topics, please send them to or

Rachel Pries would like to thank the National Science Foundation DMS-22-00418 for its support of the VaNTAGe math seminar, and  Andrew Sutherland is grateful to the Simons Foundation (grant 550033) for its support.  We thank MIT for hosting the virtual zoom platform.