On amoebas of random plane curves

Date

2022-05-30

Author

Kişisel, Ali Ulaş Özgür
Bayraktar, Turgay

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Due to a theorem of Passare and Rullgard, the area of the amoeba of a degreed" role="presentation" style="display: inline-block; line-height: 0; font-size: 16.16px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: "Times New Roman"; position: relative;">ddalgebraic curve in the complex projective plane is bounded above by&#x03C0;2d2/2" role="presentation" style="display: inline-block; line-height: 0; font-size: 16.16px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: "Times New Roman"; position: relative;">π2d2/2π2d2/2and the curves attaining the bound - special Harnack curves - have been characterized by Mikhalkin. In this talk, reporting on joint work with Turgay Bayraktar, I will argue that the expected area of a randomly chosen complex algebraic curve, with respect to the Kostlan distribution, is bounded above by a constant timesd" role="presentation" style="display: inline-block; line-height: 0; font-size: 16.16px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; font-family: "Times New Roman"; position: relative;">dd. This result also generalizes in a natural way to half dimensional complete intersections in toric varieties with an arbitrary Newton polytope.

URI

http://www.gokovagt.org/2022/index.html
https://hdl.handle.net/11511/100231

Conference Name

27th Gökova Geometry-Topology Conference

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Department of Mathematics, Conference / Seminar

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Citation Formats

A. U. Ö. Kişisel and T. Bayraktar, “On amoebas of random plane curves,” presented at the 27th Gökova Geometry-Topology Conference, Muğla, Türkiye, 2022, Accessed: 00, 2022. [Online]. Available: http://www.gokovagt.org/2022/index.html.