ODTÜ-BİLKENT
Algebraic Geometry Seminar
(See all past talks
ordered according to speaker
and date)
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**** 2020 Spring Talks ****
Emre Coşkun-[ODTÜ] -
Quiver Representations I
|
Abstract: In this
series of talks, we shall introduce quivers and
their representations and discuss their basic
properties. We shall also discuss and prove (if
time permits) Gabriel's theorem, which gives a
complete classification of quivers of finite
type. |
Emre Coşkun-[ODTÜ] -
Quiver Representations II
|
Abstract: In this series
of talks, we shall introduce quivers and their
representations and discuss their basic
properties. We shall also discuss and prove (if
time permits) Gabriel's theorem, which gives a
complete classification of quivers of finite type.
|
Davide Cesare Veniani-[Stuttgart]
- Free involutions on ihs manifolds
|
Abstract: Irreducible
holomorphic symplectic manifolds are one of the
building blocks of kähler manifolds with vanishing
first Chern class. In dimension 2 they are called
K3 surfaces. Free involutions on K3 surfaces are
quite interesting because they connect this class
of surfaces with another class, namely Enriques
surfaces. I will talk about a formula for the
number of free involutions on a K3 surface (joint
work with I. Shimada), the classification of K3
surfaces without any free involution (joint work
with S. Brandhorst and S. Sonel) and the
generalization to higher dimensions (joint work
with S. Boissière). |
|
Abstract: In this talk,
we shall introduce quivers and their
representations and discuss their basic
properties. We shall also discuss and prove (if
time permits) Gabriel's theorem, which gives a
complete classification of quivers of finite type. |
Ayşegül Öztürkalan-[AGÜ]
- Ayşegül Öztürkalan
|
Abstract: The space of
real algebraic plane projective curves of a fixed
degree has a natural stratification. The strata of
top dimension consists of non-singular curves and
are known up to curves of degree 6. Topology and,
in particular, fundamental groups of individual
strata have not been studied systematically. We
study the stratum formed by non-singular sextics
with the real part consisting of 9 ovals which lie
outside each other and divide the set of complex
points. Apparently this stratum has one of the
most complicated fundamental groups. In the talk I
will study its subgroups which originate from
spaces of linear equivalent real divisors on a
real cubic curve and tell the connections. |
Kadri İlker Berktav-[ODTÜ]
- Symplectic Structures on Derived
Schemes
|
Abstract: This is an
overview on the basic aspects of so-called $
\textit{shifted symplectic geometry}$ on (affine)
derived $\mathbb{K}$-schemes with $\mathbb{K}$
being a field of characteristic 0. In this talk,
we always study objects with higher structures in
a functorial perspective, and we shall focus on
local models for those structures. To this end, in
the first part of the talk, the basics of
commutative differential graded
$\mathbb{K}$-algebras (cdgas) and their cotangent
complexes will be introduced. Using particular
cdgas as local models, we shall introduce the
notion of a (closed) p-form of degree k on
an affine derived $\mathbb{K}$-scheme with the
concept of a non-degeneracy. As a
particular case, we shall eventually define
$\textit{a k-shifted symplectic structure}$
$\omega$ on an affine derived $\mathbb{K}$-scheme,
and outline the construction of a Darboux-like
local model for $\omega$ together with some
examples. These will be the main topics of
interest in the second part of the talk. |
Alexander Degtyarev-[Bilkent]
- The global Torelli theorem for cubic
4-folds and its applications
|
Abstract: Undoubtedly,
in theory of K3-surfaces the principal tool of
study making the theory tractable is the global
Torelli theorem (essentially stating that the
isomorphism class of a surface is determined by
that of its Hodge structure), together with the
surjectivity of the period map (a description of
the realizable Hodge structures). There are a few
other classes of analytic varieties (most notably
curves, from which the name originates, or Abelian
surfaces) for which similar statements hold. I
will try to discuss the version of the global
Torelli theorem/surjectivity of the period map for
cubic 4-folds in $\mathbb{P}^5$ (mostly due to
Clair Voisin). Then, I will discuss a recent
application of these statements to the
classification of large configurations of 2-planes
in cubic 4-folds. |
Muhammed Uludağ-[Galatasaray]
- Mapping class groupoids and
Thompson's groups
|
Abstract: (Joint work
with Ayberk Zeytin) |
James D. Lewis-[Alberta]
- The Hodge Conjecture
|
Abstract: We introduce
the classical Hodge conjecture and formulate a
birational version. We then show how this
birational version is used to formulate the Hodge
conjecture for higher K-groups of smooth
quasiprojective varieties. |
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.
