[Turkmath:7421] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-581

[Ali Sinan Sertöz]

*Welcome to the 2026 Spring talks of ODTÜ-Bilkent Algebraic Geometry 
Seminars**
*
/since 2000/
**=================================================================**

This week the ODTÜ-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/~sertoz/agseminar.htm>  is *online*

/This talk will begin at _*15:40*__ (GMT+3)_/
Please check your time difference between Ankara and your city here 
<https://www.timeanddate.com/worldclock/fixedtime.html?msg=ODT%C3%9C-Bilkent+Algebraic+Geometry+Seminar&iso=20260313T1540&p1=19&ah=1>
*=================================================================

*

/Ben Viegers (1886-1947)
/
/
/
/
/
**Speaker: Michele Ancona <https://math.univ-cotedazur.fr/%7Emancona/>**
******Affiliation: /Université Côte d'Azur

/**
**Title:  Harnack manifolds
**
**Abstract:**  Abstract: In 1876, Axel Harnack proved in a foundational 
article that

1) every real algebraic curve of degree d in RP^2 has at most 
(d-1)(d-2)/2 + 1 connected components;
2) for every d there exists a curve of degree d with exactly this number 
of connected components.

Over the past 150 years, these results have played a central role in the 
study of the topology of real algebraic varieties. The first part of 
Harnack’s theorem generalizes to the so-called Smith–Floyd inequality 
for arbitrary real algebraic varieties: the sum of the Betti numbers of 
the real part is at most the corresponding sum for the complex part. 
Despite spectacular advances, the generalization of the second part of 
Harnack’s theorem remains open in the case of projective hypersurfaces.

For these, however, Ilia Itenberg and Oleg Viro showed that the 
Smith–Floyd inequality is asymptotically optimal by using the 
combinatorial patchworking technique. In joint work with Erwan Brugallé 
and Jean-Yves Welschinger, we show that an elementary generalization of 
Harnack’s original construction method in dimension 2 yields this 
asymptotic optimality for any ample line bundle on a real algebraic 
variety. Beyond Betti numbers, we also describe the diffeomorphism type 
of an open subset of these topologically rich varieties.

*Date: 13 March 2026, Friday*
*Time: 15:40 /(GMT+3)/*
*Place: **Zoom*

    /*Participants who have registered will receive the Zoom link via
    email one day before the seminar.*/

    /*If you registered for a previous talk in this series, there's no
    need to register again—you'll automatically receive the link for
    this session.*/

    /*If you haven't registered yet, please contact
    sertoz at bilkent.edu.tr to be added to the mailing list.*/

You are most cordially invited to attend.

Ali Sinan Sertöz

*/*/This seminar series is organized by a joint team from ODTÜ and Bilkent

Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
/*/*


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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
e-mail:sertoz at bilkent.edu.tr <mailto:sertoz at bilkent.edu.tr> 
Web:sertoz.bilkent.edu.tr <http://sertoz.bilkent.edu.tr> 
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