Gökova Geometry Topology Institute

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**Date:** October 19-22, 2021

**Speakers:** Grigory Mikhalkin (University of Geneva) and Ilia Itenberg (Sorbonne University)

**Title:** Area considerations in Real Algebraic Geometry

**Abstract:** These lectures are devoted to real algebraic curves in real algebraic surfaces and to areas delimited by these curves.
We will start with several basic notions and facts in topology of real algebraic curves and surfaces
paying a particular attention to algebraic curves in the real plane.
The discussion around amoebas and areas of these curves will naturally lead us to the notion of simple Harnack curves.
After the study of various properties of simple Harnack curves, we will present analogs of these curves in the framework of K3-surfaces
and will finish the lectures by introducing areas of connected components of the real point set of a real K3-surface (using a holomorphic symplectic form of the surface)
and establishing certain inequalities for these areas.

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**Lecture 1.** Tuesday, October 19 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Logarithmic images of algebraic curves in the real plane by **Grigory Mikhalkin**.

  * [[http://www.youtube.com/watch?v=W8myggXeioY|Lecture video]]

**Zoom Meeting ID** 952 4893 3373

**Password** Initials of the speaker's name (use capitals)

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**Lecture 2.** Wednesday, October 20 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)
 
Topology of real algebraic curves and surfaces by **Ilia Itenberg**.

  * [[http://www.youtube.com/watch?v=09wyic86WCg|Lecture video]]

**Zoom Meeting ID** 949 1884 3438

**Password** Initials of the speaker's name (use capitals)

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**Lecture 3.** Thursday, October 21 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

 Amoebas, coamoebas and simple Harnack curves by **Grigory Mikhalkin**.

  * [[http://www.youtube.com/watch?v=nENQF6IoH14|Lecture video]]

**Zoom Meeting ID** 952 4893 3373

**Password** Initials of the speaker's name (use capitals)

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**Lecture 4.** Friday, October 22 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Areas in K3-surfaces by **Ilia Itenberg**.

  * [[https://www.youtube.com/watch?v=1OjRLzIJuto|Lecture video]]

**Zoom Meeting ID** 949 1884 3438

**Password** Initials of the speaker's name (use capitals)

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The topics of the lectures are tentative. We encourage the audience to participate actively by interrupting the lecturers and asking questions. 
The actual content of the lectures will depend on these interactions.
Gökova Geometry Topology Institute

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