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AGNES Goes To School (remotely)
May 4-5, 2021
Conference Administrator: Lori Nascimento (Brown University)
Funding provided by the National Science Foundation and Brown University.
Organizers: Dan Abramovich, Madeline Brandt, Brendan Hassett
Registered participants: please fill our feedback form here.
Registration has ended.
Links were sent to registered participants on Monday evening, May 3, 2021, and to newly registered participants at noon Tuesday May 4. We'll try to send further links periodically if we notice new registrations.
The mini conference constitutes three introductory lectures, each with ample breaks for problem sessions or socialization, generally aimed at graduate students, some even for advanced undergraduates, interested in algebraic geometry.
Schedule of Events:
Tuesday, May 4, at 2-5 pm EDT:
Kenny Ascher (Princeton): Hyperbolicity of varieties of log general type.
Lectures are based on the expository notes: https://arxiv.org/abs/2001.10475
Lecture segments: 2-2:30 (video), 3-3:30 (video), 4-4:30 (video)
Breaks: 2:30-3:00, 3:30-4; Additional social time: 4:30-5.
Abstract: The goal of these lectures is to present an introduction to problems concerning arithmetic and geometric hyperbolicity properties of algebraic varieties. The first lecture will motivate the overarching circle of ideas via celebrated results for curves, and then move on to conjectural generalizations for higher dimensional varieties. In the second lecture we will introduce a few notions from birational geometry. Using these notions, in the third lecture we will discuss some results and pose some questions that remain open in higher dimensions.
Tuesday, May 4 evening, at 6:30-8pm: Game night.
Organizer and coordinator: Madeline Brandt
Abstract: we will play codenames online using this:
Codenames is a game where you split into two teams. Each team has a "leader" who has some secret information that they are trying to convey to their team using hints. Whichever team solves their hints first wins!
Wednesday May 5, at 9:30am-12pm EDT:
Brendan Hassett (Brown): Rationality criteria for complex varieties
Lecture segments: 9:30-10 (video), 10:30-11 (video), 11:30-12 (video)
Breaks: 10-10:30, 11-11:30.
Abstract: We study when complex varieties admit parametrizations by rational functions. In the first segment, we will focus on curves and surfaces where explicit criteria have been known for over a century. Threefolds will be the topic of the second segment, with a view toward demonstrating geometric techniques and identifying open questions. Finally, we will discuss what is known in higher dimensions, focusing on results obtained in the last five years.
By way of preparation, students could look at the notes I prepared for an invited lecture at Boston College: http://www.math.brown.edu/bhassett/BClecture.pdf
Prepared slides here, annotated slides here.
Wednesday May 5, at 12-2 pm: lunch break
Our Zoom session will take a break, but our online common room will be open to all. Challenges include: find portals, maze, and sleeping giant. Discuss math. Voice your view on future AGNES events.
Wednesday May 5, at 2-5 pm EDT:
Jonathan Wise (University of Colorado): The moduli space of triangles.
Lecture segments: 2-2:30 (video), 3-3:30 (video), 4-4:30 (video)
Breaks: 2:30-3:00, 3:30-4; Additional social time: 4:30-5.
Abstract: I will give a gentle introduction to stacks in the context of moduli spaces. In the first part, we will discuss the utility of deformation as a tool for solving geometric problems. In the second part, we will see how stacks are implicated in the study of moduli problems, with the moduli space of triangles as an example. Finally, we will look at some examples of moduli stacks arising in algebraic geometry in the third part. The talks will be accompanied by interactive visualizations that can be run in a Python environment. The first two parts at least should be accessible to advanced undergraduates.
Jonathan's google drive folder with notes and python demos here. Triangles demo here.
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