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

**** 2018 Spring Talks ****

 Learning seminar on threefolds and lots more Organized by: Ali Ulaþ Özgür Kiþisel The main theme of the series of talks in this semester will be the classification of higher dimensional algebraic varieties, and in particular the minimal model program. The central ideas of the minimal model program and some recent developments will be discussed.

1. ODTU, 16 February 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU] - Introduction to minimal model program. MMP for surfaces

 Abstract: In this talk, the general strategy of the minimal model program will be outlined. Some well-known results about the classification of surfaces will be rephrased in this setting.

2. Bilkent,  23 February 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU] - Cone and contraction theorems for surfaces

 Abstract:  We will first review notions of ample and nef divisors and several numerical criteria. Afterwards, we will discuss the cone and contraction theorems for the case of surfaces.

3. ODTÜ, 2 March 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU] The Logarithmic Category

 Abstract:  The minimal model program in higher dimensions necessarily involves singular varieties since a minimal model for a smooth variety doesn't have to be smooth. Iitaka's philosophy is that considering logarithmic pairs, each containing a variety $X$ together with a normal crossing boundary divisor $D$, is essential when dealing with problems involving such singular varieties. The goal of this talk will be to explain this generalization.

4. Bilkent, 9 March 2018, Friday, 15:40

Tolga Karayayla-[ODTU- Singularities

 Abstract:   In this talk I will give the descriptions and characterizations of the types of singularities which arise in Minimal Model Program, namely terminal singularities, canonical singularities, log terminal singularities and log canonical singularities.

5. ODTU, 16 March 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU] - Vanishing theorems

 Abstract:  We will discuss Kodaira Vanishing Theorem and its various generalizations.

6. Bilkent, 23 March 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU- Cone and Contraction Theorems in Higher Dimensions

 Abstract:  We will state the cone and contraction theorems for dimensions greater than or equal to three and discuss their proofs.

7. ODTU, 30 March 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU-Flips

 Abstract:  We will discuss the definition of flips and some examples, together with results and conjectures about their existence and termination.

8. Bilkent, 6 April 2018, Friday, 15:40

Ali Ulaþ Özgür Kiþisel-[ODTU- Existence and termination of flips

 Abstract:   We will discuss results and conjectures about the existence and termination of flips. Some of these developments are relatively recent.

*******
******* 13 April 2018 Friday seminar is cancelled due to the
*******AGNT seminar in Ýstanbul the next day
******

9. Bilkent, 20 April 2018, Friday, 15:40

Alexander Degtyarev-[Bilkent] - Can a smooth sextic have more than 72 tritangents?

 Abstract:  After a brief introduction to the history of the subject, I will motivate the conjecture that a smooth plane sextic curve cannot have more than 72 tritangents, i.e., lines intersecting the curve with even multiplicity at each point. (A stronger conjecture is that the number of tritangents is 72 or at most 68, with all values taken.) I will also put the problem into a larger context and discuss the known results and a few steps towards the proof of this conjecture.

10. ODTU, 27 April 2017, Friday, 15:40

Melih Üçer-[Bilkent] - Miyaoka-Yau inequality in higher dimensions

 Abstract:  Miyaoka-Yau inequality is a classical inequality that concerns the Chern numbers of a minimal algebraic surface of general type, together with a rigid geometric characterization of the case of equality. Namely, an algebraic surface satisfies equality if and only if it is a quotient of the unit ball. Corresponding result for higher-dimensional smooth varieties with ample canonical class also dates back to Yau. In this talk, I will present a recent paper by (Greb, Kebekus, Peternell, Taji) in which the authors prove the Miyaoka-Yau inequality for all minimal varieties of general type and generalize the ball quotient characterization to this context.

11. ODTU, 4 May 2018, Friday, 15:40

Rabia Gülþah Uysal-[ODTU] - Brauer-Manin obstruction

 Abstract:  In this talk, we will discuss the paper  "Insufficiency of The Brauer-Manin Obstruction Applied to Etale Covers"  by Bjorn Poonen. Firstly, we will explain Hasse principle and Brauer groups. Then, we will construct a nice (smooth, projective and geometrically integral) 3-fold  and we will show that  Brauer-Manin obstruction doesn't explain failure of Hasse principle in this case.

12.   Bilkent, 11 May 2018, Friday, 15:40

Turgay Akyar-[ODTU] - The fundamental group of a rationally connected variety

 Abstract:  In the minimal model program it is known that there exist many examples of rationally connected varieties, such as smooth Fano varieties. In this talk I will present a paper by Janos Kollar, mainly concerned with the  etale fundamental groups of separably rationally connected varieties.

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) 2014 Spring Talks (320-334) 2014 Fall Talks (335-348) 2015 Spring Talks (349-360) 2015 Fall Talks (361-371) 2016 Spring Talks (372-379) 2016 Fall Talks (380-389) 2017 Spring Talks (390-401) 2017 Fall Talks (402-413)