[Turkmath:7335] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-575

[Ali Sinan Sertöz]

*Welcome to the 2025 Fall talks of ODTÜ-Bilkent Algebraic Geometry 
Seminars**
*
/since 2000/
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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=20251128T1540&p1=19&ah=1>
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*

/Gustave Boulanger (1824-1888)
/
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**Speaker: Syed Waqar Ali Shah <https://sites.google.com/view/swshah/home>**
******Affiliation: /Bilkent

/**
**Title: Euler systems for exterior square motives**
**
**
**Abstract: **The Birch–Swinnerton-Dyer conjecture relates the behavior 
of the L-function of an elliptic curve at its central point to the rank 
of its group of rational points. The Bloch–Kato conjecture generalizes 
this principle to a broad family of motivic Galois representations, 
predicting a precise relationship between the order of vanishing of 
motivic L-functions at integer values and the structure of the 
associated Selmer groups. Since the foundational work of Kolyvagin in 
the nineties, Euler systems have played a central role in approaching 
these conjectures, and in recent years their scope has expanded 
significantly within the automorphic setting of Shimura varieties.

In this talk, I will focus on unitary Shimura varieties GU(2,2), whose 
middle-degree cohomology realizes the exterior square of the 
four-dimensional Galois representations attached to certain automorphic 
representations of GL_4. The period integral formula of Pollack–Shah for 
exterior square L-functions has a natural motivic interpretation, 
suggesting the feasibility of constructing a nontrivial Euler system. A 
key obstacle to this construction is the failure of a suitable 
multiplicity-one property, which has long prevented the verification of 
the certain norm relations required for Euler system methods. I will 
present a new approach that overcomes this difficulty. The resulting 
Euler system in the middle-degree cohomology of GU(2,2) provides the 
first nontrivial evidence toward the Bloch–Kato conjecture for exterior 
square motives and opens several promising avenues for further 
arithmetic applications. This is joint work with Andrew Graham and 
Antonio Cauchi.

*Date: 28 November 2025, 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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