Colloquia/Fall 2024: Difference between revisions
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|Sept 6 | |Sept 6 | ||
| Dan Romik (UC Davis) | | Dan Romik (UC Davis) | ||
| | |Sphere packing in dimension 8, Viazovska's solution, and a new human proof of her modular form inequalities | ||
| Gurevitch | | Gurevitch | ||
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Revision as of 21:27, 14 August 2024
Organizers: Dallas Albritton and Michael Kemeny
UW-Madison Mathematics Colloquium is on Fridays at 4:00 pm in Van Vleck B239 unless otherwise noted.
mathcolloquium@g-groups.wisc.edu is the mailing list. Everyone in the math department is subscribed.
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| Sept 6 | Dan Romik (UC Davis) | Sphere packing in dimension 8, Viazovska's solution, and a new human proof of her modular form inequalities | Gurevitch | |
| Sept 13 | TBA | |||
| Sept 20 | Alireza Golsefidy (UCSD) | TBA | Marshall | |
| Sept 25 | Qing Nie (UC Irvine) | TBA | Craciun | |
| Oct 4 | Su Gao (Nankai University) | TBA | Lempp | |
| Oct 11 | Mikaela Iacobelli (ETH Zurich) | TBA | Li | |
| Oct 18 | Guillaume Bal (U Chicago) | TBA | Li, Stechmann | |
| Oct 25 | TBA | |||
| Nov 1 | Dima Arinkin (UW-Madison) | TBA | ||
| Nov 4-8 | Distinguished Lectures by Maksym Radziwill (Northwestern) | TBA | ||
| Nov 15 | Reserved by HC | TBA | Stechmann | |
| Nov 22 | Reserved by HC | TBA | Stechmann | |
| Nov 29 | Thanksgiving holiday break | |||
| Dec 6 | Reserved by HC | TBA | Stechmann | |
| Dec 13 | Reserved by HC | TBA | Stechmann |
Abstracts
September 6: Dan Romik (UC Davis)
Title: Sphere packing in dimension 8, Viazovska's solution, and a new human proof of her modular form inequalities
Abstract: Maryna Viazovska in 2016 found a remarkable application of complex analysis and the theory of modular forms to a fundamental problem in geometry, obtaining a solution to the sphere packing problem in dimension 8 through an explicit construction of a so-called "magic function" that she defined in terms of classical special functions. The same method also led shortly afterwards to the solution of the sphere packing problem in dimension 24 by her and several collaborators. One component of Viazovska's proof consisted of proving a pair of inequalities satisfied by the modular forms she constructed. Viazovska gave a proof of these inequalities that relied in an essential way on computer calculations. In this talk I will describe the background leading up to Viazovska's groundbreaking proof, and present a new proof of her inequalities that uses only elementary arguments that can be easily checked by a human.