VaNTAGe is a virtual seminar on open conjectures in number theory and arithmetic geometry, with a focus on progress on unsolved problems. The purpose of the seminar is to provide a viable way for researchers to be involved with cutting-edge research without the expense and environmental impact of travel, and to advance understanding and interest in some of the most exciting open problems. Speakers and participants will be expected to uphold the highest standards for clear exposition and respectful interactions. Zoom meeting links are posted here and on the external website the night before each talk and also e-mailed to those on our mailing list . No required, but we do use a waiting room. Everyone in the waiting room will be admitted when the talk starts. Late arrivals will be admitted as soon as the host is available to do so, as will anyone who loses their connection and rejoins the meeting (but please be patient). Video recording: Most lectures in this seminar are recorded and posted to our YouTube channel one week after the lecture. Participants who do not wish to be recorded should keep their video camera and microphone turned off (you can still ask questions via the chat).