a virtual math seminar on open conjectures in
number theory and arithmetic geometry
In spring 2020, a new math seminar was started: VaNTAGe, a virtual seminar on open conjectures in 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 be involved 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 will be expected to uphold the highest standards for clear exposition and respectful interactions.
The 7th topic is Manin conjectures and rational points.
The following survey paper provides background for this topic: Algebraic varieties with many rational points
5/4 Will Sawin The freeness alternative to thin sets in Manin's conjecture
5/11 Yuri Tschinkel Height zeta functions
5/18 Damaris Schindler Campana points on toric varieties
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)=(10 am Pacific US), every other Tuesday. Live access links are posted the night before each talk and also sent to the seminar mailing list which you can subscribe to via
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 the 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.
Rachel Pries would like to thank the National Science Foundation DMS-19-01819 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 and the ACNS video conference services at Colorado State University for hosting the virtual BlueJeans platform and Chris Chagnon for providing technical support.
The first topic of the seminar was Class groups of number fields. The following survey paper provides background for this topic:
Jan 21: Lillian Pierce. On some questions in number theory, from the perspective of moments (video not available)
The second topic was the Sato-Tate conjecture for abelian varieties. The following survey paper provides background for this topic:
We would like to thank Jun Bo Lau for editing the closed captions for the videos in this series.
The third topic was Arithmetic dynamics. The following survey paper provides background for this topic:
July 7: Nicole Looper. The ABC conjecture and arithmetic dynamics
The fourth topic was Rational points on elliptic curves . A good survey paper to prepare for this series of talks is:
The fifth topic was An update on ICERM workshop on Arithmetic Geometry, Number Theory, and Computation .
Some of the postdocs involved with the June ICERM workshop will give updates about their group's research project.
We are sorry we could only accommodate six such talks because there were many postdocs at this conference.
The sixth topic was K3 surfaces.
The following survey paper provides background for this topic: Arithmetic of K3 surfaces