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

2014 Spring Talks

 The first half of this semester is devoted to toric varieties. The speaker will be mostly MESUT SAHIN. The basic source will be the book: Toric Varieties, Cox, Little and Schenck, Graduate studies in mathematics vol 124, American Mathematical Society,  2011. The second half of this semester will be devoted to deformation theory. The speaker for this topic will be exclusively EMRE COSKUN. He will follow the book: Deformations of Algebraic Schemes, Edoardo Sernesi, Springer-Verlag, 2006. (Grundlehren der mathematischen Wissenschaften, no. 334)

1. Bilkent, 28 February 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Toric Varieties I

 Abstract:    After recalling briefly basics of sheaf of a divisor on a normal variety, we will concentrate on the toric case. In particular, we give an explicit description of global sections of the sheaf of a torus invariant divisor.

2. ODTU, 7 March 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Toric Varieties II

 Abstract: We will continue with divisors and sheaves on toric varieties. Reference is chapter 4 of Cox, Little and Schenck.

3. Bilkent, 14 March 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Toric Varieties III

 Abstract:  We will talk about quasicoherent sheaves on the normal toric variety which come from multigraded modules over its Cox ring.

4. ODTU, 21 March 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Toric Varieties IV

 Abstract:  We will talk about The Toric Ideal-Variety Correspondence from Cox-Little-Schenck's book Toric Varieties,  see in particular page 220.

5. Býlkent, 28 March 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Toric ideal-subscheme correspondence

 Abstract:  .We will talk about the correspondence between closed subschemes in a normal toric variety and B-saturated homogeneous ideals in its Cox ring.

6. ODTU, 4 April 2014 Friday, 15:40

Mesut Þahin-[Karatekin] - Multigraded Hilbert functions and toric complete intersection codes 1

 Abstract: We will talk about how multigraded Hilbert functions can be used to compute dimensions of toric codes and list some basic properties of multigraded Hilbert functions. This is a joint work with Ivan Soprunov of Cleveland State University.

7. Bilkent, 11 April 2014, Friday, 15:40

Mesut Þahin-[Karatekin] - Multigraded Hilbert functions and toric complete intersection codes 2

 Abstract: We will give a nice formula for the dimension of toric complete intersection codes. We also give a bound on the multigraded regularity of a zero dimensional complete intersection subscheme of a projective simplicial toric variety. The latter is important to eliminate trivial codes. This is a joint work with Ivan Soprunov of Cleveland State University.

8. ODTU, 18 April 2014, Friday, 15:40

Emre Coskun-[ODTÜ] - Deformation Theory 1

 Abstract:  In this series of lectures, we will develop deformation theory of functors of Artin rings. After discussing extensions of algebras over a fixed base ring, we will develop the theory of functors of Artin rings. These occur as 'local' versions of various moduli problems, and can give information about the local structure (e.g. smoothness, dimension) of moduli spaces near a point. We apply the theory to concrete examples of moduli problems, such as invertible sheaves on a variety, Hilbert schemes and Quot schemes.

9. Bilkent, 25 April 2014, Friday, 15:40

Emre Coskun-[ODTÜ] - Deformation Theory 2

 Abstract:   Last week we defined the $R$-module $Ex_A(R,I)$. This week we will continue from there and talk about the extensions of schemes.

10. ODTU, 9 May 2014, Friday, 15:40

Emre Coskun-[ODTÜ] - Deformation Theory 3

 Abstract:  This week we will start formal deformation theory. This will be the content of chapter 2 in Sernesi's book.

11. Bilkent, 16 May 2014, Friday, 15:40

Emre Coskun-[ODTÜ] - Deformation Theory 4

 Abstract:  Last time we discussed briefly Schlessinger's theorem. We will continue from there.

12. Bilkent, 21 May 2014, Wednesday, 15:40

Caner Koca-[Vanderbild] - The Monge-Ampere Equations and Yau's Proof of the Calabi Conjecture

 Abstract:  The resolution of Calabi's Conjecture by S.-T. Yau in 1977 is considered to be one of the crowning achievements in mathematics in 20th century. Although the statement of the conjecture is very geometric, Yau's proof involves solving a non-linear second order elliptic PDE known as the complex Monge-Ampere equation. An immediate consequence of the conjecture is the existence of Kähler-Einstein metrics on compact Kähler manifolds with vanishing first Chern class (better known as Calabi-Yau Manifolds). In this expository talk, I will start with the basic definitions and facts from geometry to understand the statement of the conjecture, then I will show how to turn it into a PDE problem, and finally I will highlight the important steps in Yau's proof.

13. ODTU, 23 May 2014, Friday, 15:40

Emre Coskun-[ODTÜ] - Deformation Theory 5

 Abstract:  We will discuss the closing remarks of deformation theory for this semester.

14. Bilkent, 27 May 2014, Tuesday, 15:40

Caner Koca-[Vanderbilt] - Einstein's Equations on Compact Complex Surfaces

 Abstract:  After a brief review of Einstein's Equations in General Relativity and Riemannian Geometry, I will talk about one of my results: The only positively curved Hermitian solution to Einstein's Equations (in vacuo) is the Fubini-Study metric on the complex projective plane.

15. Bilkent, 3 June 2014, Tuesday, 15:40

Caner Koca-[Vanderbilt] - Extremal Kähler Metrics and Bach-Maxwell Equations

 Abstract:  Extremal Kähler metrics are introduced by Calabi in 1982 as part of the quest for finding "canonical" Riemannian metrics on compact complex manifolds. Examples of such metrics include the Kähler-Einstein metrics, or more generally, Kähler metrics with constant scalar curvature. In this talk, I will start with an expository discussion on extremal metrics. Then I will show that, in dimension 4, these metrics satisfy a conformally-invariant version of the classical Einstein-Maxwell equations, known as the Bach-Maxwell equations, and thereby are related to physics (conformal gravity) in a surprising and mysterious way.

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

 2000-2001 Talks  (1-28) 2001 Fall Talks  (29-42) 2002 Spring Talks  (43-54) 2002 Fall Talks  (55-66) 2003 Spring Talks  (67-79) 2003 Fall Talks  (80-90) 2004 Spring Talks (91-99) 2004 Fall Talks (100-111) 2005 Spring Talks (112-121) 2005 Fall Talks (122-133) 2006 Spring Talks (134-145) 2006 Fall Talks (146-157) 2007 Spring Talks (158-168) 2007 Fall Talks (169-178) 2008 Spring Talks (179-189) 2008 Fall Talks (190-204) 2009 Spring Talks (205-217) 2009 Fall Talks (218-226) 2010 Spring Talks (227-238) 2010 Fall Talks (239-248) 2011 Spring Talks (249-260) 2011 Fall Talks (261-272) 2012 Spring Talks (273-283) 2012 Fall Talks (284-296) 2013 Spring Talks (297-308) 2013 Fall Talks (309-319)