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Repulsion : a how-to guide

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Rydin Myerson, Simon L. (2021) Repulsion : a how-to guide. [Online]. (https://hcm.uni-bonn.de/thecirclemethod2021/). Hausdorff Centre for Mathematics website and Youtube channel: Hausdorff Centre for Mathematics.

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Official URL: https://hcm.uni-bonn.de/thecirclemethod2021/

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Abstract

Consider the integral zeroes of one or more, not necessarily diagonal, integral polynomials in many variables with the same degree. The basic principles for applying the circle method here were laid out by Birch. One way to improve on his work is repulsion: showing that the exponential sum over the polynomials can be large only on small, well separated regions. Unusually for improvements on Birch’s work this idea has been successfully applied to systems which are not particularly singular and which contain many polynomials. To begin I will ask: what about Birch’s work suggests that repulsion could be an improvement? I will then discuss the quadratic and higher degree case in detail, and an application to systems of forms with real coefficients.

Item Type: Digital Scholarly Resource
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Publisher: Hausdorff Centre for Mathematics
Place of Publication: Hausdorff Centre for Mathematics website and Youtube channel
Official Date: 14 May 2021
Dates:
DateEvent
14 May 2021Available
Publication Status: Published
Media of Output (format): Video lectures, PDF slides
Access rights to Published version: Open Access (Creative Commons)
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDLeverhulme TrustUNSPECIFIED
UNSPECIFIEDHausdorff Centre for MathematicsUNSPECIFIED
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