ODTÜ-BİLKENT Algebraic
Geometry Seminar
(See all past talks ordered according
to speaker or date)
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**** 2024 Fall Talks ****
This
semester we plan to have all of our seminars online
Emre Can Sertöz - [Leiden] - Computing transcendence and linear relations of 1-periods
| Abstract:
I
will sketch a modestly practical algorithm to
compute all linear relations with algebraic
coefficients between any given finite set of
1-periods. As a special case, we can algorithmically
decide transcendence of 1-periods. This is based on
the "qualitative description" of these relations by
Huber and Wüstholz. We combine their result with the
recent work on computing the endomorphism ring of
abelian varieties. This is a work in progress with
Jöel Ouaknine (MPI SWS) and James
Worrell (Oxford). |
Davide
Veniani -[Stuttgart] - Entropy and
non-degeneracy of Enriques surfaces
|
Abstract: The entropy
of an algebraic surface serves as an invariant
that quantifies the complexity of its automorphism
group. Recently, K3 surfaces with zero entropy
have been classified by Brandhorst-Mezzedimi and
Yu. In this talk, I will discuss joint work
with Martin (Bonn) and Mezzedimi (Bonn) concerning
the classification of Enriques surfaces with zero
entropy. To conclude, I will propose a conjecture
on the connection between zero entropy and the
non-degeneracy invariant. |
|
Abstract: We
have obtained the complete deformation
classification of singular real plane sextic
curves with smooth real part, i.e., those without
real singular points. This was made possible due
to the fact that, under the assumption, contrary
to the general case, the equivariant equisingular
deformation type is determined by the so-called
real homological type in its most naïve sense,
i.e., the homological information about the
polarization, singularities, and real structure;
one does not need to compute the fundamental
polyhedron of the group generated by reflections
and identify the classes of ovals therein. Should
time permit, I will outline our proof of this
theorem. |
|
Abstract: In this
talk, we explore the connection between the
enumerative geometry of rational curves on del
Pezzo surfaces over a field k and the arithmetic
properties of k. In particular, we classify the
number of k-rational lines and conic families that
can occur on del Pezzo surfaces of degrees 3
through 9 in terms of the Galois theory of k, and
we give partial results in degrees 1 and 2. Our
results generalize well-known theorems in the
setting of smooth cubic surfaces. This is joint
work in progress with Stephen McKean, Sam Streeter
and Harkaran Uppal. |
|
Abstract: A
smooth hypersurface $X\subset \mathbb{RP}^{n+1}$
of degree $d$ is called reversible if its defining
homogeneous polynomial $f$ can be continuously
deformed to $-f$ without creating singularities
during the deformation. The question of
reversibility was discussed in the paper titled
``On the deformation chirality of real cubic
fourfolds'' by Finashin and Kharlamov. For $n=1$,
the case of plane curves, and $d\leq 5$ odd, it is
known that all smooth curves of degree $d$ are
reversible. Our goal in this talk is to present an
obstruction for reversibility of odd degree curves
and use it in particular to demonstrate that there
exist irreversible curves in $\mathbb{RP}^2$ for
all odd degrees $d\geq 7$. This talk is based on
joint work in progress with Ferit Öztürk. |
|
Abstract: In
1950, Nash published a very influential two-page
paper proving the existence of Nash equilibria for
any finite game. The proof uses an elegant
application of the Kakutani fixed-point theorem
from the field of topology. This opened a new
horizon not only in game theory, but also in areas
such as economics, computer science, evolutionary
biology, and social sciences. It has, however,
been noted that in some cases the Nash equilibrium
fails to predict the most beneficial outcome for
all players. To address this, generalizations of
Nash equilibria such as correlated and dependency
equilibria were introduced. In this talk, I
elaborate on how nonlinear algebra is
indispensable for studying undiscovered facets of
these concepts of equilibria in game theory. |
|
Abstract: In the last decade most questions concerning line configurations on degree-four surfaces in three-dimensional projective space have been answered. In contrast, far less is known in the case of degree-d surfaces for $d>4$ even in complex case. In my talk I will discuss the best known bound for number of lines on degree-$d$ surfaces in three-dimensional projective space (based on joint work with Thomas Bauer and Matthias Schuett). |
|
Abstract:
In moduli problems, one usually
needs to impose some sort of "stability" on the
objects being classified in order to have
well-behaved moduli spaces. Generalizing this
concept, in 2007, Bridgeland defined "stability
conditions" on a triangulated category and proved
that, under some mild conditions, the set of
stability conditions can be given the structure of
a complex manifold. In this three-part series, we
shall explore this construction. We shall also
give examples of stability conditions when the
underlying triangulated category is the derived
category of coherent sheaves on a smooth,
projective variety. |
|
Abstract: In moduli
problems, one usually needs to impose some sort of
"stability" on the objects being classified in
order to have well-behaved moduli spaces.
Generalizing this concept, in 2007, Bridgeland
defined "stability conditions" on a triangulated
category and proved that, under some mild
conditions, the set of stability conditions can be
given the structure of a complex manifold. In this
three-part series, we shall explore this
construction. We shall also give examples of
stability conditions when the underlying
triangulated category is the derived category of
coherent sheaves on a smooth, projective variety.
|
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.
Zoom talks are online.
Talks of previous
years
