ODTÜ-BİLKENT Algebraic Geometry Seminar
(See all past talks
ordered according to speaker and
date)
2011 Fall Talks
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Abstract: (joint
with Nermin Salepci, Université de Lyon) Trivial as it seems, this simplest case has a number of geometric applications. As a first one, we prove that any maximal real elliptic Lefschetz fibration over the sphere is algebraic. Other applications include the semi-simplicity statement for real trigonal M-curves in Hirzebruch surfaces. (One may try to speculate that products of two Dehn twists are still `tame' precisely because they are related to maximal geometric objects.) The principal tool is a description of subgroups of the modular group in terms of a certain class of Grothendieck's dessins d'enfants, followed by high school geometry. |
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Abstract: The purpose of this expository talk is to lay a basis for Sinan's forthcoming account of our joint project. Recall that a quartic surface in P3 is merely a K3-surface equipped with a polarization of degree 4. Thus, I will give a gentle introduction to theory of K3-surfaces: the period space, the global Torelli theorem and surjectivity of the period map, and the implications of the Riemann--Roch theorem. I will explain how the problem of counting lines on a quartic can be reduced to a purely arithmetical question and, should time permit, give a brief account of the results obtained so far, viz. a more or less explicit description of the Picard group of the champion quartic. |
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Abstract: Let G be a reductive group. A GxG-variety X is called an embedding of G if X is normal, projective, and contains G as an open dense orbit. Regular compactifications and standard embeddings are the main source of examples. In the former case, they are smooth varieties, and their equivariant cohomology has been explicitely described by Brion using GKM theory. His description relies on the associated torus embedding and the structure of the GxG-orbits. In contrast, standard embeddings constitute a much larger class of embeddings than the smooth ones, and their equivariant cohomology was, just until recently, only understood in some cases. Based on results of Renner, standard embeddings were known to come equipped with a canonical cell decomposition, given in terms of underlying monoid data. The purpose of this talk is three-fold. First, I will give an overview of the theory of group embeddings, putting more emphasis on Renner's approach, and describe the structure of the so called rational cells. Secondly, I will explain how such cellular decompositions lead to a further application of GKM theory to the study of standard embeddings. Finally, I provide a complete description of the equivariant cohomology of any rationally smooth standard embedding. The major results of this talk are part of the speaker's PhD thesis. References: PS: The speaker is supported under TUBITAK ISBAP Grant 107T897 -Matematik İşbirliği Ağı: Cebir ve Uygulamaları. |
The afternoon of 28 October is a National Holiday.
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Abstract: I will wrap up my recent investigations on lines on surfaces with a view towards settling some problems jointly with Degtyarev. |
There is no talk on 11 November 2011 due to Kurban
Bayramı.
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Abstract: The surgery method of classifying manifolds seeks to answer the following question: Given a homotopy equivalence of m-dimensional manifolds f: M --> N, is f homotopic to a diffeomorphism ? The surgery theory developed by Browder, Novikov, Sullivan and Wall in the 1960’s provides a systematic solution to this problem. My talk will aim to be a friendly introduction to the basic concepts of the surgery theory. |
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Abstract: Splines or piecewise polynomial functions are used most commonly to approximate functions, especially by numerical analysts for approximating solutions to differential equation. Most recently, splines have also played an important role in computer graphics. That’s why it is of interest to study spline spaces. In this talk, we will discuss analyzing the piecewise functions with a specified degree of smoothness on polyhedral subdivision of region on Rn and their dimension. |
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Abstract: In this talk, we review the genus zero Gromov-Witten invariants by first defining them in a brief way and then applying them in examples of dimension four and six. We also prove that the use of genus zero Gromov-Witten invariants to distinguish the symplectic structures on a smooth 6-manifold is restricted in a certain sense. |
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Abstract: We give a survey of Geometric Invariant Theory for Toric Varieties, and present an application to the Einstein-Weyl Geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP_(1,1,2). We also find and classify all possible quotients. |
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Abstract: We
study the fibre products of a finite number of Kummer covers of the
projective line over finite fields. We determine the number of rational
points of the fibre product under certain conditions. We also |
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Abstract: Toric codes are some evaluation codes obtained by projective toric varieties corresponding to convex lattice polytopes. We will explain how their basic parameters are related to the torus and the number of lattice points of the polytope and introduce certain generalizations. We will also review some recent results about the minimum distance. |
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Abstract: In the talk I will discuss the structure of toric variety XG equal to closure of a generic orbit of a maximal torus of a simple group G in its flag variety FG, the respective restriction map H*(FG)-->H*(XG) together with some applications. |
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Abstract: How should greengrocers most efficiently stack their oranges? How about pennies on a tabletop or atoms of a single element in a crystal? More than 400 years ago Kepler conjectured that the most efficient way is the face-centered cubic packing which is well known for greengrocers nowadays. Just recently a "proof" (referees are 99% are certain) for Kepler's conjecture is given. In this talk we will give a brief history of the conjecture and related problems. By considering the problem in higher dimensions we will illustrate some special cases and their applications to different areas of mathematics. In particular, the connection between lattices and theta functions will be discussed. |
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.
| 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) |