In spring 2020, I am starting a virtual seminar on open conjectures in number theory and arithmetic geometry. The seminar will provide 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 learn about 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.
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More information about this seminar is on this webpage: https://sites.google.com/view/vantageseminar
If you would like to join the e-mail list for this seminar, please go to this google group and apply for membership: https://groups.google.com/forum/#!forum/vantageseminar
This seminar will be run through blue jeans technology and can support 100 connections. Please consider reserving a room with a projector or a video conferencing room if there are several people at your institution who are interested in watching. The talks will typically occur on the first and third Tuesdays at 1 pm ET = 12 CT = 11 MT = 10 am PT.
The first topic of the seminar is CLASS GROUPS OF NUMBER FIELDS. The first talks of the seminar will focus on this survey paper.
On a conjecture for ?-torsion in class groups of number fields: from the perspective of moments - https://arxiv.org/abs/1902.02008
Jan 21: Lillian Pierce. On some questions in number theory, from the perspective of moments
Feb 4: Melanie Matchett-Wood. Conjectures for number field counting
Feb18: Caroline Turnage-Butterbaugh. Moments of zeta and the vertical distribution of its zeros
March 3: David Zureick-Brown. Moduli spaces and arithmetic statistics
If you have any suggestions or advice about this seminar, please send me an email.
Abstract: The cohomology (with complex coefficients) of a compact kahler manifold M admits an action of the algebra sl(2,C), and this action plays an essential role in the analysis of the cohomology. In the case that M is a hyperkahler manifold Verbitsky and Looijenga—Lunts showed there is a family of such sl(2,C)’s generating an algebra isomorphic to so(4,b_2-2), and this algebra similarly can tell us quite a bit about the cohomology of the hyperkahler. I will describe some results of this nature for both the Hodge numbers and Nagai’s conjecture on the nilpotent logarithm of monodromy arising from a degeneration. This is joint work with Mark Green, Radu Laza and Yoonjoo Kim.
In this talk, I will give a brief introduction to the subject of string topology discovered by Chas and Sullivan, and explain the connections to Hochschild homology and cohomology. If time permits, I will try to interpret string topology operations from the point of view of "derived noncommutative geometry" and briefly mention some joint works with Yuri Berest and Ajay Ramadoss.