[Turkmath:5185] ODTU-Bilkent Algebraic Geometry Seminar-Zoom-491

[Ali Sinan Sertöz]

*
*
*Welcome to the 2021 Fall talks of ODTU-Bilkent Algebraic Geometry 
Seminars**
*****
**
/since 2000/
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This week the ODTU-Bilkent Algebraic Geometry Seminar 
<http://www.bilkent.edu.tr/%7Esertoz/agseminar.htm>  is *Online.*

/This talk will begin at _*15:40*__(GMT+3)_/

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**//
/Paul Gauguin (1848-1903)
/

**Speaker:Oğuzhan Yürük**
**Affiliation: TU-Berlin
Title:Nonnegativity of the polynomials supported on circuits

**
**Abstract:**A real multivariate polynomial is called nonnegative if its 
evaluation at any given point in R^n is nonnegative. Checking the 
nonnegativity of a real polynomial is a not only a mathematically 
challenging task, but also is an effective tool both for mathematics and 
for sciences. Often one uses nonnegativity certificates in order to 
tackle this problem, i.e., easily verifiable conditions that imply the 
nonnegativity for a large class of polynomials. The typical 
nonnegativity certificates usually make use of the fact that a 
polynomial is nonnegative if it is a sum of squares of polynomials (SOS 
polynomial), however not every nonnegative polynomial is of this form. 
In the first part this talk, we focus on a relatively new nonnegativity 
certificate based on the arithmetic and geometric means (AM-GM) 
inequality, and we elaborate on the fact that this class of polynomials 
neither contains nor is contained in the class of SOS polynomials. 
Unlike the SOS certificates, one is only interested in the exponents 
that show up in the support while working with AM-GM certificates. In 
particular, this gives us a framework to write sufficient symbolic 
conditions for the nonnegativity of a given sparse polynomial in terms 
of its coefficients. We utilize the aforementioned AM-GM framework in 
the second part of the talk, and present an application to a particular 
problem from the chemical reaction networks theory.

*Date:15 October 2021*, Friday
*Time: 15:40*
*Place: **Zoom
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    **One day before the seminar, an announcement with the Zoom meeting
    link will be sent to those who registered with Sertöz.
    **

    **If you have registered before for one of the previous talks, there
    is no need to register again; you will automatically receive a link
    for this talk too.
    **

    **If you have not registered before, please contact him at
    sertoz at bilkent.edu.tr
    <mailto:sertoz at bilkent.edu.tr?subject=Zoom%20Seminar%20Address%20Request>.**

**


Please bring your own tea and cookies and self-serve at the convenience 
of your own home! 😁

You are most cordially invited to attend.

Ali Sinan Sertöz
**

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Ali Sinan Sertöz
Bilkent University, Department of Mathematics, 06800 Ankara, Turkey
Office: (90)-(312) - 290 1490
Department: (90)-(312) - 266 4377
Fax: (90)-(312) - 290 1797
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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