Richmond Geometry Meeting
Geometric Topology and Moduli
Virginia Commonwealth University
August 12 - 14, 2024
NOTE: VCU has now decommissioned Google Sites, and consequently this webpage will be updated only until June 2024. After that, please refer to the webpage https://math.vcu.edu/rgm/ for updates!
The Richmond Geometry Meeting will focus on emergent research topics while bringing together researchers in algebraic geometry, low-dimensional topology, and mathematical physics.
In summer 2024, we will highlight developments in Geometric Topology and Moduli.
Organizers
We would appreciate your feedback: Anonymous Feedback for RGM Organizers.
Speakers
Panelists
Andre Perunicic (Google)
Registration
Applications for funding are an optional part of the registration.
If you apply for funding, please register by July 9.
Logistics
Location. All lectures and the Career Panel will be held in Temple 1165 on VCU's Monroe Park Campus.
The Poster Session will be held in the STEM buildling on VCU's Monroe Park Campus (TBC).
Accommodation. Two otions:
1) A block of hotel rooms has been reserved at the Graduate Richmond. If you would like to take advantage of the discounted rate, please use this link for the booking before 7/10/2024.
2) A block of hotel rooms has been reserved at the Linden Row Inn. To take advantake of the discounted rate, either use this link or call their front desk at 804-783-7000 and ask for the Richmond Geometry Meeting Group Block.
Childcare. For participants wishing to arrange childcare in Richmond, VA, the Virginia Department of Social Services provides a child day care search tool here:
Please select the search criterion "Richmond City" or the nearby counties "Henrico" or "Chesterfield." A list of contact information for providers with some drop-in childcare options can also be found here. Other childcare options in Richmond include the YMCA, numerous area churches, and the Weinstein JCC. It may also be possible to locate home daycare providers or babysitters for hire through Care.com.
Poster Session
The meeting will feature a poster session with the aim of showcasing research by early-career participants.
Titles and abstracts of accepted posters will appear on the website at a later date.
Everyone is encouraged to apply to present their work at the poster session. The poster session application is an optional part of the registration.
Schedule
Displayed time is in EST
Day 1. Monday, August 12, 2024
12:45 PM – 01:00 PM Welcome message
01:00 PM – 02:00 PM
03:00 PM – 04:00 PM
05:00 PM – 06:00 PM
Day 2. Tuesday, August 13, 2024
09:00 AM – 10:00 AM
11:00 AM – 12:00 PM
02:00 PM – 03:30 PM Career Panel
04:00 PM – 05:00 PM
05:30 PM – 07:00 PM Poster Session
07:45 PM Social Event at Brambly Park
Day 3. Wednesday, August 14, 2024
09:00 AM – 10:00 AM
10:30 AM – 11:30 AM
12:00 PM – 01:00 PM
Lecture Abstracts
Ross Akhmechet
TBA
Scott Baldridge
TBA
Melissa Chiu-Chu Liu
TBA
Shashank Kanade
TBA
Caner Nazaroglu
Constructions and Applications of Mock Modularity at Depth Two
False and mock modular forms along with their higher depth generalizations make their appearance in mathematical physics and geometry in contexts such as Vafa-Witten invariants or Z-hat invariants of three manifolds. In this talk I will describe the interaction between various constructions of these objects and their Fourier coefficients by focusing on a particular example involving rank 2 Vafa-Witten invariants. In particular, I will demonstrate a Hardy-Ramanujan-Rademacher type exact formula for these Vafa-Witten invariants along with a twofold Eisenstein series construction for the pure component of the generating function. In particular, the latter construction leads to nontrivial identities for the Fourier coefficients of the aforementioned depth two mock modular forms, which have expressions as indefinite theta series derived from the wall-crossing formula. This is based on earlier as well as ongoing work with K. Bringmann.
Danielle O’Donnol
TBA
Nicola Pagani
Classification of compactified Jacobians over nodal curves
If X is a smooth proper curve, then the Jacobian of X is a classical and well-studied object in algebraic geometry. When X is singular, the moduli space of degree 0 line bundles is rarely compact, and over the last century many efforts have been made to study the modular compactifications of this space, which we call "compactified Jacobians of X". In this talk we focus on the case when X has at worst nodal singularities. Some compactified Jacobians cannot arise as limits of Jacobians of smooth curves - we regard them as exotic objects. We will see that, if one excludes these exotic cases, then one can give a simple and complete combinatorial classification of all compactified Jacobians. This is based on work of myself with Tommasi, on a paper by Viviani, and on work in progress with Fava and Viviani.
Sunghyuk Park
TBA
Burt Totaro
Algebraic varieties at the extremes
In trying to classify algebraic varieties, there is a particular fascination in trying to construct varieties with extreme behavior. For example, try to find Calabi-Yau varieties with large Betti numbers, or varieties of general type with many vanishing plurigenera. We construct varieties with doubly exponential behavior for several such problems. Some of these examples are conjecturally optimal. (Joint with Louis Esser and Chengxi Wang.)
Poster Abstracts
TBA