ODTÜ-BİLKENT Algebraic Geometry Seminar

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ordered according to speaker or date)

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**** 2024 Spring Talks ****

 

This semester we plan to have most of our seminars online,
except the last one!


  1.   Zoom, 23 February 2024, Friday, 15:40

    Pınar Mete-[Balıkesir] - On some invariants of the tangent cones of numerical semigroup rings

    Abstract: The minimal free resolution is a very useful tool for extracting information about modules. Many important numerical invariants of a module such as Hilbert function and Betti numbers can be deduced from its minimal free resolution. Stamate gave a broad survey on these topics when the modules are the semigroup ring or its tangent cone for a numerical semigroup S. He also stated the problem of describing the Betti numbers and the minimal free resolution for the tangent cone when S is 4-generated semigroup which is symmetric. In this talk, I will first give some of our results, based on a joint work with E.E. Zengin on the problem. Then, I will talk about our ongoing study which is an application of the Apery table of the numerical semigroup to determine some properties of its tangent cone.

    DI. STAMATE, Betti numbers for numerical semigroup rings. Multigraded Algebra and Applications,
    238, 133-157, Springer Proceedings in Mathematics and Statistics, Springer, Cham 2018.

     
      
  2. Zoom, 1 March 2024, Friday, 15:40

    Turgay Bayraktar-[Sabancı] - Equidistribution for Zeros of Random Polynomial Systems

    Abstract: A classical result of Erdös and Turan asserts that for a univariate complex polynomial whose middle coefficients are comparable to the extremal ones, the zeros accumulate near the unit circle. We prove  the analogues result for random polynomial mappings with Bernoulli coefficients. The talk is based on the joint work with Çiğdem Çelik.

        

  3. Zoom, 15 March 2024 Friday, 15:40
      
    Kaan Bilgin-[Amsterdam] - The Langlands – Kottwitz method for GSpin Shimura varieties and eigenvarieties

    Abstract:   Given a connected reductive algebraic group G over a number field F, the global Langlands (reciprocity) conjecture roughly predicts that, there should be a correspondence between (automorphic side) the isomorphism classes of  (cuspidal, cohomological) automorphic representations of G and (Galois side) the isomorphism classes of (irreducible, locally de-Rham) Galois representations for Gal(\bar{F} / F) taking values in the Langlands dual group of G.

    In the first part of this talk, I will sketch the main argument of our expected theorem/proof for (automorphic to Galois) direction of this conjecture, for G = GSpin(n,2), n odd and F to be totally real, under 3 technical assumptions (for time being), namely we assume that automorphic representations are additionally “non-CM” and “non-endoscopic” and “std-regular”.

    In the second part, mainly following works of Loeffler and Chenevier on overconvergent p-adic automorphic forms,  I will present an idea to remove the std-regular assumption on the theorem via the theory of eigenvarieties.

      
      
  4. Zoom, 22 March 2024, Friday, 15:40
      
    Haydar Göral-[İYTE] - Arithmetic Progressions in Finite Fields

    Abstract:  In 1927, van der Waerden proved a theorem regarding the existence of arithmetic progressions in any partition of the positive integers with finitely many classes. In 1936, a strengthening of van der Waerden's theorem was conjectured by Erdös and Turan, which states that any subset of positive integers with a positive upper density contains arbitrarily long arithmetic progressions. In 1975, Szemeredi developed his combinatorial method to resolve this conjecture, and the affirmative answer to Erdös and Turan's conjecture is now known as Szemeredi's theorem. As well as in the integers, Szemeredi-type problems have been extensively studied in subsets of finite fields. While much work has been done on the problem of whether subsets of finite fields contain arithmetic progressions, in this talk we concentrate on how many arithmetic progressions we have in certain subsets of finite fields. The technique is based on certain types of Weil estimates. We obtain an asymptotic for the number of k-term arithmetic progressions in squares with a better error term. Moreover our error term is sharp and best possible when k is small, owing to the Sato-Tate conjecture. This work is supported by the Scientific and Technological Research Council of Turkey with the project number 122F027.

         

  5. Zoom, 29 March 2024, Friday, 15:40
      
    Büşra Karadeniz Şen-[GTU] -Boundaries of the dual Newton polyhedron may describe the singularity

    Abstract:  We are dealing with a hypersurface $X\subset \mathbb{C}^3$ having non-isolated singularities.We construct an embedded toric resolution of $X$ using some specific vectors in its dual Newton polyhedron. To do this, we first define the profile of a full dimensional cone and we establish a relation between the jet vectors and the integer points in the profile.

    This is a part of the joint work with C. Plénal and M. Tosun.

    References
    [1] A. Altintaş Sharland, C. O. Oğuz, M. Tosun and Z.aferiakopoulos, An algorithm to find nonisolated forms of rational singularities, In preparation.
    [2] C. Bouvier and G. Gonzalez-Sprinberg, Systéme générateur minimal, diviseurs essentiels et G-désingularisations de variétés torique, Tohoku Math. J., 47, 125-149,
    1995.
    [3] B. Karadeniz Şen, C. Plénat and M. Tosun, Minimality of a toric embedded resolution of singularities after Bouvier-Gonzalez-Sprinberg, Kodai Math J., accepted, 2024.

      
      

  6. Zoom, 5 April 2024, Friday, 15:40
      
    Enis Kaya-[KU Leuven] - TBA

    Abstract: 

         

  7. Zoom, 19 April 2024, Friday, 15:40
      
    Ichiro Shimada-[Hiroshima] - Real line arrangements and vanishing cycles

    Abstract:

     
      
  8. Zoom, 26 April 2024, Friday, 15:40
      
    Yaacov Kopeliovich -[Connecticut] - TBA

    Abstract:

       
     
  9. Zoom, 3 May 2024, Friday, 15:40
      
    Meirav Amram-[Shamoon] - TBA

    Abstract: 



  10. Bilkent, 10 May 2024, Friday, 15:40
      
    Alexander Degtyarev-[Bilkent] - TBA

    Abstract:






ODTÜ talks are either at Hüseyin Demir Seminar room or at Gündüz İkeda seminar room at the Mathematics building of ODTÜ.
Bilkent talks are
at room 141 of Faculty of Science A-building at Bilkent.
Zoom talks are online.


 


  Talks of previous years

Year

Year

1
2000 Fall Talks  (1-15) 2001 Spring Talks  (16-28) 2
2001 Fall Talks  (29-42) 2002 Spring Talks  (43-54)
3
2002 Fall Talks  (55-66) 2003 Spring Talks  (67-79) 4
2003 Fall Talks  (80-90) 2004 Spring Talks (91-99)
5
2004 Fall Talks (100-111) 2005 Spring Talks (112-121) 6
2005 Fall Talks (122-133) 2006 Spring Talks (134-145)
7
2006 Fall Talks (146-157) 2007 Spring Talks (158-168) 8
2007 Fall Talks (169-178) 2008 Spring Talks (179-189)
9
2008 Fall Talks (190-204) 2009 Spring Talks (205-217) 10
2009 Fall Talks (218-226) 2010 Spring Talks (227-238)
11
2010 Fall Talks (239-248) 2011 Spring Talks (249-260) 12
2011 Fall Talks (261-272) 2012 Spring Talks (273-283)
13
2012 Fall Talks (284-296) 2013 Spring Talks (297-308) 14
2013 Fall Talks (309-319) 2014 Spring Talks (320-334)
15
2014 Fall Talks (335-348) 2015 Spring Talks (349-360) 16
2015 Fall Talks (361-371) 2016 Spring Talks (372-379)
17
2016 Fall Talks (380-389) 2017 Spring Talks (390-401) 18
2017 Fall Talks (402-413) 2018 Spring Talks (414-425)
19
2018 Fall Talks (426-434) 2019 Spring Talks (435-445) 20
2019 Fall Talks (446-456) 2020 Spring Talks (457-465)
21
2020 Fall Talks (467-476)
2021 Spring Talks (477-488)
22
2021 Fall Talks (478-500)
2022 Spring Talks (501-511)
23
2022 Fall Talks (512-520)
2023 Spring Talks (520-530)
24
2023 Fall Talks (531-540)
2024 Spring Talks (541-550)
























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