Welcome to the 2026
Spring talks of ODTÜ-Bilkent Algebraic Geometry
Seminars
since 2000
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This week the ODTÜ-Bilkent Algebraic Geometry Seminar is online
This talk will begin at 15:40 (GMT+3)
Please check your time difference between Ankara and your city here
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This week the ODTÜ-Bilkent Algebraic Geometry Seminar is online
This talk will begin at 15:40 (GMT+3)
Please check your time difference between Ankara and your city here
=================================================================
Ben Viegers (1886-1947)
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.
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
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@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)
Alexander Degtyarev (Bilkent)
Ali Sinan Sertöz (Bilkent) contact person
Ali Ulaş Özgür Kişisel (ODTÜ)
Yıldıray Ozan (ODTÜ)
---------------------------------------------------------------------------- Ali Sinan Sertöz Bilkent University, Department of Mathematics, 06800 Ankara, Türkiye Office: (90)-(312) - 290 1490 Department: (90)-(312) - 266 4377 e-mail: sertoz@bilkent.edu.tr Web: sertoz.bilkent.edu.tr ----------------------------------------------------------------------------