On amoebas of random plane curves

Date

2022-05-30

Author

Kişisel, Ali Ulaş Özgür
Bayraktar, Turgay

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

217
views

0
downloads

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

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

On entire rational maps of real surfaces Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01) In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
On some classes of semi-discrete darboux integrable equations Bilen, Ergün; Zheltukhın, Kostyantyn; Department of Mathematics (2017) In this thesis we consider Darboux integrable semi-discrete hyperbolic equations of the form $t_{1x} = f(t,t_{1}, t_{x}), \frac{\partial f}{\partial t_{x}} \neq 0.$ We use the notion of characteristic Lie ring for a classification problem based on dimensions of characteristic $x$- and $n$-rings. Let $A = (a_{ij})_{N\times N}$ be a $N\times N$ matrix. We also consider semi-discrete hyperbolic equations of exponential type $u_{1,x}^{i} - u_{x}^{i} = e^{\sum a_{ij}^{+}u_{1}^{j} + \sum a_{ij}^{-}u^{j}}, i,j = 1...
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
On the deformation chirality of real cubic fourfolds Finashin, Sergey (Wiley, 2009-09-01) According to our previous results, the conjugacy class of the involution induced by the complex conjugation in the homology of a real non-singular cubic fourfold determines the fourfold tip to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and obtain a pure deformation classification, that is, how to respond to the chirality problem: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of...
On endomorphisms of surface mapping class groups Korkmaz, Mustafa (Elsevier BV, 2001-05-01) In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

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.