Experimental Talks in AG - Exploring ways to virtually communicate math

The recent shift from in-person to online talks provides us with an
opportunity to explore new and interesting ways to communicate and
learn things related to algebraic geometry. The goal of this seminar
is to provide a space for speakers and audience members to do this
exploration.

Each speaker will be given 50 minutes to create and lead an
environment where topics related to algebraic geometry can be
communicated and learned. How the speaker uses their time and
creates such an environment is entirely up to them. They may try
mixing pre-recorded and live aspects of a talk, they might try
leading group work, who knows, it is entirely up to the speaker. The
only request made of speakers is that they think critically about
new ways to best use their time to promote the communication and
learning of math. After the 50 minutes, a short group discussion
will be held discussing how this form of online math communication
went, and how it might be built upon. Everyone participating is
asked to keep in mind that this is a place for experimentation.

This event is being organized by Juliette Bruce in association with the Algebraic Geometry Syndicate (AGS) discord server.
Updates about the talks will be posted both here and on the AGS discord server. If you would like to join the AGS discord
server please email juliette.bruce 'at' math.wisc.edu.

Date (2:00pm (CST) - 3:00pm (CST)) | Speaker | Title |
---|---|---|

May 27, 2020 | Sachi Hashimoto - Boston University | An obstruction to weak approximation on a Calabi-Yau threefold |

June 3, 2020 | Soumya Sankar - UW Madison | Counting elliptic curves with a rational N-isogeny |

June 10, 2020 | #ShutDownSTEM | N/A |

June 17, 2020 | Kristin DeVleming - UC San Diego | Moduli spaces of plane curves |

June 24, 2020 | Takumi Murayama - Princeton University | Every variety is birational to a weakly normal hypersurface |

July 1, 2020 | Andrew Kobin - UC Santa Cruz | Zeta functions in number theory, algebraic geometry and beyond |

July 8, 2020 | Madeline Brandt - UC Berkeley | Limits of Voronoi and Delaunay Cells |

In this talk, we investigate the arithmetic structure of a class
of Calabi-Yau threefolds. These threefolds were constructed over the
complex numbers by Hosono and Takagi as a linear section of a double
quintic symmetroid, and have a beautiful and simple story in the
geometry of quadrics over the rational numbers. In forthcoming work
with Honigs, Lamarche, and Vogt, we exhibit an obstruction to weak
approximation on these threefolds. For the "experimental" nature of
this seminar, we will conclude by working through a demonstration in
cocalc. Attendees are asked to make cocalc accounts to participate fully; no prior coding
experience necessary!

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

The problem of counting elliptic curves over Q with a rational N
isogeny can be rephrased as a question of counting rational points
on the moduli stacks X_0(N). In this talk, I will discuss heights on
projective varieties and a generalization to stacks of certain
kinds, based on upcoming work of Ellenberg, Satriano and
Zureick-Brown. We will then use this to count points on X_0(N) for
low N. This is joint work with Brandon Boggess.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

Compactifying moduli spaces has been a fundamental problem in
algebraic geometry that has been richly developed in the past 50
years. In that time, many different perspectives have been studied
and these have resulted in many different compactifications.
Starting from an audience discussion, we will consider the moduli
space of plane curves of fixed degree, some potential
compactifications, and how they fit together. Based on that
discussion, I will mention a few of my favorite proper moduli spaces
of plane curves, discuss their relationships, and pose some open
questions.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

Classically, it is known that every variety is birational to a
projective hypersurface. For curves and surfaces, this hypersurface
can be taken to have at worst nodal and at worst ordinary
singularities, respectively. We will prove that in arbitrary
dimension, this hypersurface can be taken to be weakly normal, and
for smooth projective varieties of dimension at most five, this
hypersurface can be taken to have semi-log canonical singularities.
These results are due to Roberts and Zaare-Nahandi and to Doherty in
characteristic zero, respectively, and to Rankeya Datta and myself
in positive characteristic. Attendees will be asked to do some
concrete computations with polynomials.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

Participants will have a chance to fondly recall their favourite
zeta functions. Together, we will discuss how different examples
relate to/generalize each other. Then I will describe a general
framework for studying zeta functions using decomposition spaces
from homotopy theory.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

Voronoi diagrams of finite point sets partition space into regions. Each region contains all points which are
nearest to one point in the finite point set. Voronoi diagrams (and their generalizations and variations)
have been an object of interest for hundreds of years by mathematicians spanning many fields, and they
have numerous applications across the sciences. Recently, Cifuentes, Ranestad, Sturmfels, and Weinstein
defined Voronoi cells of varieties, in which the finite point set is replaced by a real algebraic variety. Each
point y on the variety has a cell of points in the ambient space corresponding to those points which are
closer to y than any other point on the variety. In this talk, we present the limiting behavior of Voronoi
diagrams of finite sets, where the finite sets are sampled from the variety and the sample size increases. In
this setting, we observe that many interesting features of the variety can be seen in a Voronoi Diagram,
including its medial axis, curvatures, normals, reach, and singularities.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.

This talk can be accessed via Zoom. The password is the number of lines on a cubic surface.