ODTÜBİLKENT
Algebraic Geometry Seminar
(See all past talks
ordered according to speaker
and date)
**** 2017 Spring Talks ****

Ali Sinan Sertöz[Bilkent]
 On the moduli of K3 surfaces
Abstract:
We will discuss the main line of
ideas involved in the proofs of the Torelli
theorems for K3 surfaces as outlined by Huybrechts
in his recent book "Lectures on K3 Surfaces." 
Ali Sinan Sertöz[Bilkent]
 On the moduli of K3 surfacesII
Abstract: This is going to be a continuation of last week's talk. In particular we will talk about the ideas involved around proving the Global Torelli Theorem for K3 surfaces. Most proofs will be referred to the literature but we will try to relate the concepts involved. 
Ali Ulaş Özgür Kişisel[ODTU]
 Tropical curves
Abstract: In this talk, we will discuss several approaches to defining tropical curves and the theory of linear systems on tropical curves. 
Ali Ulaş Özgür Kişisel[ODTU]
 Tropical curvesII
Abstract: In this talk, we will continue our discussion of several approaches to defining tropical curves and the theory of linear systems on tropical curves. 
Emre Coşkun[ODTU]  The Beilinson spectral sequence
Abstract: We overview
the Beilinson spectral sequence and its
applications in the construction of sheaves and
vector bundles. 
Abstract: I will explain
the proof of my conjectures (reported earlier in
this seminar) on the maximal number of straight
lines in sextic surfaces in $\mathbb{P}^4$, (42
lines) and octic surfaces/triquadrics in
$\mathbb{P}^5$, (36 lines). I will also try to
make it clear that the complexity of the problem
decreases when the polarization grows. The
asymptotic bound for K3surfaces in large
projective spaces is 24 lines, all constituting
fiber components of an elliptic pencil. 
Mesut Şahin[Hacettepe]
 Lattice ideals and toric codes
Abstract: I
will briefly recall basics of toric varieties over
finite fields and evaluation codes on them. Then, we
will see that some vanishing ideals of subvarieties
are lattice ideals. Using this, we characterize
whether they are complete intersections or not. In the
former case; dimension, length and regularity of the
code will be understood easily. 
Nil Şahin[Bilkent]
 On Pseudo Symmetric Monomial Curves
Abstract:
After giving basic definitions and
concepts about symmetric and pseudo symmetric
numerical semigroups, we will focus on 4generated
pseudo symmetric numerical semigroups/monomial
curves. Determining the indispensable binomials of
the defining ideal, we will give characterizations
under which the tangent cone is CohenMacaulay. If
time permits, determining minimal graded free
resolutions of the tangent cones, we’ll show that
“If the 4 generated pseudo symmetric numerical
semigroup S is homogeneous and the corresponding
tangent cone is Cohen Macaulay, then S is also
Homogeneous type. 
Alexander Klyachko[Bilkent]
 Transformation of cyclic words into
Lie elements
Abstract:
Let $V$ be a complex vector space
and $T(V)=\sum_{n=0}^\infty V^{\otimes n}$ be its
tensor algebra. We are primarily concerned
with Lie subalgebra $L(V)\subset T(V)$
generated by commutators of elements in $V$ and
graded by degrees of the tensor components. 
Özgün Ünlü[Bilkent]
 Semicharacteristic classes
Abstract:
In this talk, I will first give
basic definitions and theorems about
semicharacteristic classes. Secondly, I will
discuss some applications of semicharacteristic
classes. 
Çisem Güneş Aktaş[Bilkent]
 An Introduction to Nikulin's Theory
of Discriminant FormsI
Abstract:
In this talk I will first recall
some basic definitions and notions about lattices.
Then I will introduce fundamentals of Nikulins's
theory of discriminant forms. Finally, I will
discuss some principal applications of this theory
and give an example in the particular case of
K3lattice. 
Çisem Güneş Aktaş[Bilkent]
 An Introduction to Nikulin's Theory
of Discriminant FormsII
Abstract: This is the
continuation of last week's talk. 
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
Abuilding at Bilkent.
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