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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/
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 | |||||||||
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| 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 | |||||||||
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| Publication Status: | Published | |||||||||
| Media of Output (format): | Video lectures, PDF slides | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
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