ODTÜ-BİLKENT Algebraic
Geometry Seminar
(See all past talks ordered according
to speaker or date)
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**** 2022 Spring Talks ****
This
semester we plan to have most of our seminars online
tentatively we now list all talks as
online
check for last minute changes
Deniz Kutluay-[Indiana]
- Winding homology of knotoids
Abstract: Knotoids
were introduced by Turaev as open-ended knot-type
diagrams that generalize knots. Turaev defined a
two-variable polynomial invariant of knotoids
generalizing the Jones knot polynomial to
knotoids. We will give a construction of a
triply-graded homological invariant of knotoids
categorifying the Turaev polynomial, called the
winding homology. Forgetting one of the three
gradings gives a generalization of the Khovanov
knot homology to knotoids. We will briefly review
the basics of the theory of knotoids and also
explain the notion of categorification which plays
an important role in contemporary knot theory --
no prior knowledge will be assumed. |
Turgay Bayraktar-[Sabancı]
- Universality results for zeros of
random holomorphic sections
Abstract: In this
talk, I will present some recent results on the
asymptotic expansion of the Bergman kernel
associated with sequences of singular Hermitian
holomorphic line bundles $(L_p,h_p)$ over compact
Kähler manifolds. As an application, I
will also present several universality results
regarding the equidistribution of zeros of random
holomorphic sections in this geometric setup. |
Ilia Itenberg-[imj-prg]
- Real enumerative invariants and their
refinement
Abstract: The talk is
devoted to several real and tropical enumerative
problems. We suggest new invariants of the
projective plane (and, more generally, of toric
surfaces) that arise as results of an appropriate
enumeration of real elliptic curves. |
Alexander Degtyarev-[Bilkent]
- Towards 800 conics on a smooth
quartic surfaces
Abstract: This will be a technical talk where I will discuss a few computational aspects of my work in progress towards the following conjecture. Conjecture: A smooth
quartic surface in $\mathbb{P}^3$ may contain at
most $800$ conics. |
Matthias Schütt-[Hannover] - Finite symplectic automorphism groups of supersingular K3 surfaces
Abstract: Automorphism
groups form a classical object of study in
algebraic geometry. In recent years, a special
focus has been put on automorphisms of K3 surface,
the most famous example being Mukai’s
classification of finite symplectic automorphism
groups on complex K3 surfaces. Building on work of
Dolgachev-Keum, I will discuss a joint project
with Hisanori Ohashi (Tokyo) extending Mukai’s
results to fields positive characteristic.
Notably, we will retain the close connection to
the Mathieu group $M_{23}$ while realizing many
larger groups compared to the complex setting. |
Emre Can Sertöz-[Hannover] - Heights, periods, and arithmetic on curves
Abstract: The
size of an explicit representation of a given
rational point on an algebraic curve is captured
by its canonical height. However, the canonical
height is defined through the dynamics on the
Jacobian and is not particularly accessible to
computation. In 1984, Faltings related the
canonical height to the transcendental
"self-intersection" number of the point, which was
recently used by van Bommel-- Holmes--Müller
(2020) to give a general algorithm to compute
heights. The corresponding notion for heights in
higher dimensions is inaccessible to computation.
We present a new method for computing heights that
promises to generalize well to higher dimensions.
This is joint work with Spencer Bloch and Robin de
Jong. |
Halil İbrahim Karakaş-[Başkent]
- Arf Partitions of Integers
Abstract: The
colection of partitions of positive integers, the
collection of Young diagrams and the collection of
numerical sets are in one to one correspondance
with each other. Therefore any concept in one of
these collections has its counterpart in the other
collections. For example the concept of Arf
numerical semigroup in the collection of numerical
sets, gives rise to the concept of Arf partition
of a positive integer in the collection of
partitions. Several characterizations of Arf
partitions have been given in recent works. In
this talk we wil characterize Arf partitions of
maximal length of positive integers. |
Yıldıray Ozan-[ODTÜ] -
Picard Groups of the Moduli Spaces of
Riemann Surfaces with Certain Finite Abelian Symmetry
Groups
Abstract: In 2021, H.
Chen determined all finite abelian regular
branched covers of the 2-sphere with the property
that all homeomorphisms of the base preserving the
branch set lift to the cover, extending the
previous works of Ghaswala-Winarski and
Atalan-Medettoğulları-Ozan. In this talk, we will
present a consequence of this classification to
the computation of Picard groups of moduli spaces
of complex projective curves with certain
symmetries. Indeed, we will use the work by K.
Kordek already used by him for similar
computations. During the talk we will try to
explain the necessary concepts and tools following
Kordek's work. |
Ali Ulaş Özgür Kişisel-[ODTÜ]
- An upper bound on the expected areas
of amoebas of plane algebraic curves
Abstract:The amoeba of
a complex plane algebraic curve has an area
bounded above by $\pi^2 d^2/2$. This is a
deterministic upper bound due to Passare and
Rullgard. In this talk I will argue that if the
plane curve is chosen randomly with respect to the
Kostlan distribution, then the expected area
cannot be more than $\mathcal{O}(d)$. The results
in the talk will be based on our joint work in
progress with Turgay Bayraktar. |
Muhammed
Uludağ-[Galatasaray] - Heyula
Abstract: This talk is
about the construction of a space H and its
boundary on which the group PGL(2,Q) acts. The
ultimate aim is to recover the action of PSL(2,Z)
on the hyperbolic plane as a kind of boundary
action. |
Melih Üçer-[Yıldırım Beyazıt] - Burau Monodromy Groups of Trigonal Curves
Abstract:
For a trigonal curve on a
Hirzebruch surface, there are several notions of
monodromy ranging from a very coarse one in S_3 to
a very fine one in a certain subgroup of Aut(F_3),
and one group in this range is PSL(2,Z).
Except for the special case of isotrivial curves,
the monodromy group (the subgroup generated by all
monodromy actions) in PSL(2,Z) is a subgroup of
genus-zero and conversely any genus-zero subgroup
is the monodromy group of a trigonal curve (This
is a result of Degtyarev). |
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.