ODTÜ-BİLKENT Algebraic Geometry Seminar
(See all past talks ordered according to speaker and date)

**** 2018 Fall Talks ****

426. Bilkent, 12 October 2018, Friday, 15:40

     Ali Sinan Sertöz-[Bilkent] - K3 covers of Enriques surfaces
         
     

     Abstract: I last talked on this subject on 2001 when I talked about Keum's 1990 work on the problem. There has been some activity on the subject since then which I want to talk about. I will explain the problem and summarize what has been done so far and prepare the audience for the next two talks where the speakers will explain their most recent contributions to the subject.

          
     
     
     
427. ODTÜ, 19 October 2018, Friday, 15:40
     
     

     Serkan Sonel-[Bilkent ] - K3 covers of Enriques surfaces with Picard rank 18 and 19
         
     

     Abstract: In this talk, we partially determine the necessary and sufficient conditions on the entries of the intersection matrix of the transcendental lattice of algebraic K3 surface with Picard number 18 ≤ ρ(X) ≤ 19 for the surface to doubly cover an Enriques surface.

          
     
     
428. Bilkent, 26 October 2018, Friday, 15:40
     

     Oğuzhan Yörük-[Bilkent] - Parity arguments on K3 covers of Enrique surfaces with Picard rank 19
         
     

     Abstract: Last two talks of the seminar were mostly on the theoretical parts of the subject. This time, we introduce some computational arguments by using equivalence of parities of the transcendental lattice of K3 surfaces, right after a brief reminding of what was talked on previous two talks to warm up. Then, we will apply this idea to reduce the number of cases and time spent on showing which K3 surfaces of Picard number 18 &19 cover an Enriques surface.

          
     
     
429. ODTÜ, 2 November 2018, Friday, 15:40
     

     Alexander Degtyarev-[Bilkent] - A few further remarks on Enriques surfaces
         
     

     Abstract: I will continue the subject of the previous talks, viz. a characterization of the K3-surfaces covering an Enriques surface. I will: (1) explain that the existence of a fixed point free involution depends on the *genus* of the transcendental lattice only; (2) give the answer for *most* genera, leaving just a few of them open; (3) outline the difficulties that may arise in the case of those few open genera. (Following Nikulin, we describe the genus of an even lattice by means of its signature and discriminant form; for small ranks, the relevant data, viz. length and parity of the 2-primary part, can be restated in terms of the parity of the coefficients of the Gram matrix.)

          
     
     
     
430. Bilkent, 9 November 2018, Friday, 15:40
     

     Emre Coşkun-[ODTÜ] - Serre's GAGA (Géometrie Algébrique et Géométrie Analytique)
         
     

     Abstract: Serre's famous theorem known as "GAGA" (Géometrie Algébrique et Géométrie Analytique - Algebraic Geometry and Analytic Geometry) is a fundamental result in algebraic geometry. It basically says that the theory of complex analytic subvarieties of projective space and the theory of algebraic subvarieties of projective space coincide. In this series of lectures, we shall start with the fundamentals of complex analytic geometry and then move toward the proof of GAGA.

          
     
     
     
431. ODTU, 16 November 2018, Friday, 15:40
     

     Emre Coşkun-[ODTÜ] - Serre's GAGA-II
         
     

     Abstract: Serre's famous theorem known as "GAGA" (Géometrie Algébrique et Géométrie Analytique - Algebraic Geometry and Analytic Geometry) is a fundamental result in algebraic geometry. It basically says that the theory of complex analytic subvarieties of projective space and the theory of algebraic subvarieties of projective space coincide. In this series of lectures, we shall start with the fundamentals of complex analytic geometry and then move toward the proof of GAGA.

          
     
     
     
432. Bilkent, 23 November  2018, Friday, 15:40
     
     

     Emre Coşkun-[ODTÜ] - Serre's GAGA-III
         
     

     Abstract: Serre's famous theorem known as "GAGA" (Géometrie Algébrique et Géométrie Analytique - Algebraic Geometry and Analytic Geometry) is a fundamental result in algebraic geometry. It basically says that the theory of complex analytic subvarieties of projective space and the theory of algebraic subvarieties of projective space coincide. In this series of lectures, we shall start with the fundamentals of complex analytic geometry and then move toward the proof of GAGA.

          
     
     ******** 30 November 2018 talk is cancelled due to some personal circumstances of the speaker *****
     
     
     
433. ODTÜ, 7 December 2018, Friday, 15:40
     

     Yıldıray Ozan-[ODTÜ] - Manifolds Admitting No Real Projective Structure
         
     

     Abstract: In this talk first, we will define and give basic results about real projective structures on smooth manifolds.  Then we will discuss such structures on two and three manifolds. Next we will mention the 2015 result by D. Cooper and W. Goldman that the smooth manifold ${\mathbb RP}^3\sharp {\mathbb RP}^3$ does not admit any real projective structure (the first known example in dimension three), and we will generalize this result to all higher dimensions.  If time permits, we will mention different type of examples of smooth manifolds with no real projective structure.

          
     
      
     
434. Bilkent, 14 December 2018, Friday, 15:40
     

     Nil Şahin-[Bilkent] - One dimensional Gorenstein Local Rings with decreasing Hilbert Function
         
     

     Abstract: In this talk, starting from Rossi's conjecture stating "Hilbert function of a one dimensional Gorenstein Local Ring is non-decreasing", I will give a little history of the recent works in this subject and talk about Oneto, Strazzanti and Tamone's work that constructs infinitely many one-dimensional Gorenstein Local rings that decreases at some level.

          
     
     
     

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.