BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Ilia Itenberg (imj-prg)
DTSTART:20220304T124000Z
DTEND:20220304T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/1
DESCRIPTION:Title: Real enumerative invariants and their refinement\nby Ilia Itenber
g (imj-prg) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nThe 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 o
f real elliptic curves.\nThese invariants admit a refinement (according to
the quantum index) similar to the one introduced by Grigory Mikhalkin in
the rational case. We discuss tropical counterparts of the elliptic invari
ants under consideration and establish a tropical algorithm allowing one t
o compute them.\nThis is a joint work with Eugenii Shustin.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20220311T124000Z
DTEND:20220311T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/2
DESCRIPTION:Title: Towards 800 conics on a smooth quartic surfaces\nby Alexander Deg
tyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nThis will be a technical talk where I will discuss a few computa
tional aspects of my work in progress towards the following conjecture.\n\
nConjecture: A smooth quartic surface in P3 may contain at most 800 conics
.\n\nI will suggest and compare several arithmetical reductions of the pro
blem. Then\, for the chosen one\, I will discuss a few preliminary combina
torial bounds and some techniques used to handle the few cases where those
bounds are not sufficient.\n\nAt the moment\, I am quite confident that t
he conjecture holds. However\, I am trying to find all smooth quartics con
taining 720 or more conics\, in the hope to find the real quartic maximizi
ng the number of real lines and to settle yet another conjecture (recall
that we count all conics\, both irreducible and reducible).\n\nConjecture:
If a smooth quartic X⊂P3 contains more than 720 conics\, then X has no
lines\; in particular\, all conics are irreducible.\n\nCurrently\, similar
bounds are known only for sextic K3-surfaces in P4.\n\nAs a by-product\,
I have found a few examples of large configurations of conics that are not
Barth--Bauer\, i.e.\, do not contain\na 16-tuple of pairwise disjoint con
ics or\, equivalently\, are not Kummer surfaces with all 16 Kummer divisor
s conics.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Schütt (Hannover)
DTSTART:20220318T124000Z
DTEND:20220318T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/3
DESCRIPTION:Title: Finite symplectic automorphism groups of supersingular K3 surfaces\nby Matthias Schütt (Hannover) as part of ODTU-Bilkent Algebraic Geomet
ry Seminars\n\n\nAbstract\nAutomorphism groups form a classical object of
study in algebraic geometry. In recent years\, a special focus has been pu
t on automorphisms of K3 surface\, the most famous example being Mukai’s
classification of finite symplectic automorphism groups on complex K3 sur
faces. Building on work of Dolgachev-Keum\, I will discuss a joint project
with Hisanori Ohashi (Tokyo) extending Mukai’s results to fields positi
ve characteristic. Notably\, we will retain the close connection to the Ma
thieu group M23 while realizing many larger groups compared to the complex
setting.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Can Sertöz (Hannover)
DTSTART:20220325T124000Z
DTEND:20220325T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/4
DESCRIPTION:Title: Heights\, periods\, and arithmetic on curves\nby Emre Can Sertöz
(Hannover) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nThe size of an explicit representation of a given rational point on a
n algebraic curve is captured by its canonical height. However\, the canon
ical height is defined through the dynamics on the Jacobian and is not par
ticularly accessible to computation. In 1984\, Faltings related the canoni
cal 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 met
hod for computing heights that promises to generalize well to higher dimen
sions. This is joint work with Spencer Bloch and Robin de Jong.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Halil İbrahim Karakaş (Başkent)
DTSTART:20220401T124000Z
DTEND:20220401T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/5
DESCRIPTION:Title: Arf Partitions of Integers\nby Halil İbrahim Karakaş (Başkent)
as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe co
lection of partitions of positive integers\, the collection of Young diagr
ams 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 nume
rical semigroup in the collection of numerical sets\, gives rise to the co
ncept of Arf partition of a positive integer in the collection of partitio
ns. Several characterizations of Arf partitions have been given in recent
works. In this talk we wil characterize Arf partitions of maximal length o
f positive integers.\nThis is a joint work with Nesrin Tutaş and Nihal G
ümüşbaş from Akdeniz University.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yıldıray Ozan (ODTÜ)
DTSTART:20220408T124000Z
DTEND:20220408T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/6
DESCRIPTION:Title: Picard Groups of the Moduli Spaces of Riemann Surfaces with Certain F
inite Abelian Symmetry Groups\nby Yıldıray Ozan (ODTÜ) as part of O
DTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn 2021\, H. Chen d
etermined 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 consequenc
e of this classification to the computation of Picard groups of moduli spa
ces of complex projective curves with certain symmetries. Indeed\, we will
use the work by K. Kordek already used by him for similar computations. D
uring the talk we will try to explain the necessary concepts and tools fol
lowing Kordek's work.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Ulaş Özgür Kişisel (ODTÜ)
DTSTART:20220415T124000Z
DTEND:20220415T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/7
DESCRIPTION:Title: An upper bound on the expected areas of amoebas of plane algebraic cu
rves\nby Ali Ulaş Özgür Kişisel (ODTÜ) as part of ODTU-Bilkent Al
gebraic Geometry Seminars\n\n\nAbstract\nThe amoeba of a complex plane alg
ebraic curve has an area bounded above by $\\pi^2 d^2/2$. This is a determ
inistic 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 di
stribution\, 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.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammed Uludağ (Galatasaray)
DTSTART:20220422T124000Z
DTEND:20220422T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/8
DESCRIPTION:Title: Heyula\nby Muhammed Uludağ (Galatasaray) as part of ODTU-Bilkent
Algebraic Geometry Seminars\n\n\nAbstract\nThis talk is about the constru
ction 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 plan
e as a kind of boundary action.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melih Üçer (Yıldırım Beyazıt)
DTSTART:20220429T124000Z
DTEND:20220429T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/9
DESCRIPTION:Title: Burau Monodromy Groups of Trigonal Curves\nby Melih Üçer (Yıld
ırım Beyazıt) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nFor 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 PS
L(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 monod
romy group of a trigonal curve (This is a result of Degtyarev).\n\nA sligh
tly finer notion in the same range is the monodromy in the Burau group Bu_
3. The aforementioned result of Degtyarev imposes obvious restrictions on
the monodromy group in this case but without a converse result. Here we sh
ow that there are additional non-obvious restrictions as well and\, with t
hese restrictions\, we show the converse as well.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Sutherland (MIT)
DTSTART:20221014T124000Z
DTEND:20221014T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/10
DESCRIPTION:Title: Sato-Tate groups of abelian varieties\nby Andrew Sutherland (MIT
) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in O
DTÜ Mathematics department Room M-203.\n\nAbstract\nLet A be an abelian v
ariety of dimension g defined over a number field K. As defined by Serre\
, the Sato-Tate group ST(A) is a compact subgroup of the unitary symplecti
c group USp(2g) equipped with a map that sends each Frobenius element of t
he absolute Galois group of K at primes p of good reduction for A to a con
jugacy class of ST(A) whose characteristic polynomial is determined by the
zeta function of the reduction of A at p. Under a set of axioms proposed
by Serre that are known to hold for g <= 3\, up to conjugacy in Usp(2g) t
here is a finite list of possible Sato-Tate groups that can arise for abel
ian varieties of dimension g over number fields. Under the Sato-Tate conj
ecture (which is known for g=1 when K has degree 1 or 2)\, the asymptotic
distribution of normalized Frobenius elements is controlled by the Haar me
asure of the Sato-Tate group.\n\nIn this talk I will present a complete cl
assification of the Sato-Tate groups that can and do arise for g <= 3.\n\n
This is joint work with Francesc Fite and Kiran Kedlaya.\n\nThis is a hybr
id talk. To request Zoom link please write to sertoz@bilkent.edu.tr\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART:20221021T124000Z
DTEND:20221021T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/11
DESCRIPTION:Title: McKay correspondence I\nby Emre Coşkun (METU) as part of ODTU-B
ilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics de
partment Room M-203.\n\nAbstract\nJohn McKay observed\, in 1980\, that the
re is a one-to-one correspondence between the nontrivial finite subgroups
of SU(2) (up to conjugation) and connected Euclidean graphs (other than th
e Jordan graph) up to isomorphism. In these talk\, we shall first examine
the finite subgroups of SU(2) and then establish this one-to-one correspon
dence\, using the representation theory of finite groups.\n\nThis is a hyb
rid talk. To request a Zoom link please write to sertoz@bilkent.edu.tr\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART:20221104T124000Z
DTEND:20221104T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/12
DESCRIPTION:Title: McKay correspondence II\nby Emre Coşkun (METU) as part of ODTU-
Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics D
epartment Room M-203.\n\nAbstract\nLet $G \\subset SU(2)$ be a finite subg
roup containing $-I$\, and let \n$Q$ be the corresponding Euclidean graph.
Given an orientation on $Q$\, \none can define the (bounded) derived cate
gory of the representations \nof the resulting quiver. Let $\\bar{G} = G /
{\\pm I}$. Then one can \nalso define the category $Coh_{\\bar{G}}(\\math
bb{P}^1)$ of \n$\\bar{G}$-equivariant coherent sheaves on the projective l
ine\; this \nabelian category also has a (bounded) derived category. In th
e second \nof these talks dedicated to the McKay correspondence\, we estab
lish an \nequivalence between the two derived categories mentioned above.\
n\nThis is a hybrid talk. To request Zoom link please write to sertoz@bilk
ent.edu.tr.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Can Sertöz (Hannover)
DTSTART:20221111T124000Z
DTEND:20221111T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/13
DESCRIPTION:Title: Computing limit mixed Hodge structures\nby Emre Can Sertöz (Han
nover) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\n
Consider a smooth family of varieties over a punctured disk that is extend
ed to a flat family over the whole disk\, e.g.\, consider a 1-parameter fa
mily of hypersurfaces with a central singular fiber. The Hodge structures
(i.e. periods) of smooth fibers exhibit a divergent behavior as you approa
ch the singular fiber. However\, Schmid's nilpotent orbit theorem states t
hat this divergence can be "regularized" to construct a limit mixed Hodge
structure. This limit mixed Hodge structure contains detailed information
about the geometry and arithmetic of the singular fiber. I will explain ho
w one can compute such limit mixed Hodge structures in practice and give a
demonstration of my code.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Müfit Sezer (Bilkent)
DTSTART:20221118T124000Z
DTEND:20221118T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/14
DESCRIPTION:Title: Vector invariants of a permutation group over characteristic zero\nby Müfit Sezer (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Se
minars\n\n\nAbstract\nWe consider a finite permutation group acting natura
lly on a vector space V over a field k. A well known theorem o
f Göbel asserts that the corresponding ring of invariants k[V]^G is
generated by invariants of degree at most dim V choose 2. We point
out that if the characteristic of k is zero then the top degree of
the vector coinvariants k[mV]_G is also bounded above by n choose 2
implying that Göbel's bound almost holds for vector invariants as
well in characteristic zero.\nThis work is joint with F. Reimers.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Cesare Veniani (Stuttgart)
DTSTART:20221125T124000Z
DTEND:20221125T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/15
DESCRIPTION:Title: Non-degeneracy of Enriques surfaces\nby Davide Cesare Veniani (S
tuttgart) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nEnriques' original construction of Enriques surfaces involves a 10-dime
nsional family of sextic surfaces in the projective space which are non-no
rmal along the edges of a tetrahedron. The question whether all Enriques s
urfaces arise through Enriques' construction has remained open for more th
an a century.\n\nIn two joint works with G. Martin (Bonn) and G. Mezzedimi
(Hannover)\, we have now settled this question in all characteristics by
studying particular configurations of genus one fibrations\, and two invar
iants called maximal and minimal non-degeneracy. The proof involves so-cal
led `triangle graphs' and the distinction between special and non-special
3-sequences of half-fibers.\n\nIn this talk\, I will present the problem a
nd explain its solution\, illustrating further possible developments and a
pplications.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Karaoğlu (Gebze Teknik)
DTSTART:20221202T124000Z
DTEND:20221202T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/16
DESCRIPTION:Title: Smooth cubic surfaces with 15 lines\nby Fatma Karaoğlu (Gebze T
eknik) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\n
It is well-known that a smooth cubic surface has 27 lines over an algebrai
cally closed field. If the field is not closed\, however\, fewer lines are
possible. The next possible case is that of smooth cubic surfaces with 15
lines. This work is a contribution to the problem of classifying smooth c
ubic surfaces with 15 lines over fields of positive characteristic. We pre
sent an algorithm to classify such surfaces over small finite fields. Our
classification algorithm is based on a new normal form of the equation of
a cubic surface with 15 lines and less than 10 Eckardt points. The case of
cubic surfaces with more than 10 Eckardt points is dealt with separately.
Classification results for fields of order at most 13 are presented and a
verification using an enumerative formula of Das is performed. Our work i
s based on a generalization of the old result due to Cayley and Salmon tha
t there are 27 lines if the field is algebraically closed.\n\n Smooth cubi
c surfaces with 15 lines\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meral Tosun (Galatasaray)
DTSTART:20221209T124000Z
DTEND:20221209T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/17
DESCRIPTION:Title: Jets schemes and toric embedded resolution of rational triple points
\nby Meral Tosun (Galatasaray) as part of ODTU-Bilkent Algebraic Geome
try Seminars\n\n\nAbstract\nOne of the aims of J.Nash in an article on the
arcs spaces (1968) was to understand resolutions of singularities via the
arcs living on the singular variety. He conjectured that there is a one-
to-one relation between a family of the irreducible components of the jet
schemes of an hypersurface centered at the singular point and the essentia
l divisors on every resolution. J.Fernandez de Bobadilla and M.Pe Pereira
(2011) have shown his conjecture\, but the proof is not constructive to ge
t the resolution from the arc space. We will construct an embedded toric r
esolution of singularities of type rtp from the irreducible components of
the jet schemes.\n\nThis is a joint work with B.Karadeniz\, H. Mourtada an
d C.Plenat.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özhan Genç (Jagiellonian)
DTSTART:20221216T124000Z
DTEND:20221216T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/18
DESCRIPTION:Title: Finite Length Koszul Modules and Vector Bundles\nby Özhan Genç
(Jagiellonian) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nA
bstract\nLet $V$ be a complex vector space of dimension $n\\ge 2$ and $K$
be a subset of $\\bigwedge^2V$ of dimension $m$. Denote the Koszul module
by $W(V\,K)$ and its corresponding resonance variety by $\\mathcal R(V\,K
)$. Papadima and Suciu showed that there exists a uniform bound $q(n\,m)$
such that the graded component of the Koszul module $W_q(V\,K)=0$ for all
$q\\ge q(n\,m)$ and for all $(V\,K)$ satisfying $\\mathcal R(V\,K)=\\{0\\}
$. In this talk\, we will determine this bound $q(n\,m)$ precisely\, and f
ind an upper bound for the Hilbert series of these Koszul modules. Then we
will consider a class of Koszul modules associated to vector bundles.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Floccari (Hannover)
DTSTART:20230303T124000Z
DTEND:20230303T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/19
DESCRIPTION:Title: Sixfolds of generalized Kummer type and K3 surfaces\nby Salvator
e Floccari (Hannover) as part of ODTU-Bilkent Algebraic Geometry Seminars\
n\n\nAbstract\nThe classical Kummer construction associates a K3 surface t
o any 2-dimensional complex torus. In my talk I will present an analogue o
f this construction\, which involves the two most well-studied deformation
types of hyper-Kähler manifolds in dimension 6. Namely\, starting from a
ny hyper-Kähler sixfold K of generalized Kummer type\, I am able to const
ruct geometrically a hyper-Kähler manifold of K3^[3]-type. When K is proj
ective\, the associated variety is birational to a moduli space of sheaves
on a uniquely determined K3 surface. As application of this construction
I will show that the Kuga-Satake correspondence is algebraic for many K3 s
urfaces of Picard rank 16.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominico Valloni (Hannover)
DTSTART:20230310T124000Z
DTEND:20230310T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/20
DESCRIPTION:Title: Rational points on the Noether-Lefschetz locus of K3 moduli spaces\nby Dominico Valloni (Hannover) as part of ODTU-Bilkent Algebraic Geome
try Seminars\n\n\nAbstract\nLet L be an even hyperbolic lattice and denote
by $\\mathcal{F}_L$ the moduli space of L-polarized K3 surfaces. This par
ametrizes K3 surfaces $X$ together with a primitive embedding of lattices
$L \\hookrightarrow \\mathrm{NS}(X)$ and\, when $L = \\langle 2d \\rangle
$\, one recovers the classical moduli spaces of 2d-polarized K3 surfaces.
In this talk\, I will introduce a simple criterion to decide whether a giv
en $\\overline{ \\mathbb{Q}}$-point of $\\mathcal{F}_L$ has generic Néro
n-Severi lattice (that is\, $\\mathrm{NS}(X) \\cong L$). The criterion is
of arithmetic nature and only uses properties of covering maps between Shi
mura varieties.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Rams (Jagiellonian)
DTSTART:20230317T124000Z
DTEND:20230317T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/21
DESCRIPTION:Title: On maximal number of rational curves of bounded degree on certain s
urfaces\nby Slawomir Rams (Jagiellonian) as part of ODTU-Bilkent Algeb
raic Geometry Seminars\n\n\nAbstract\nI will discuss bounds on the number
of rational curves of fixed degree on surfaces of various types with speci
al emphasis on polarized Enriques surfaces. In particular\, I will sketch
the proof of the bound of at most 12 rational curves of degree at most d
on high-degree Enriques surfaces (based mostly on joint work with Prof. M
. Schuett (Hannover)).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Türkü Özlüm Çelik (Boğaziçi)
DTSTART:20230324T124000Z
DTEND:20230324T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/22
DESCRIPTION:Title: Singular curves and their theta functions\nby Türkü Özlüm Ç
elik (Boğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\
nAbstract\nRiemann's theta function becomes polynomial when the underlying
curve degenerates to a singular curve. We will give a classification of s
uch curves accompanied by historical remarks on the topic. We will touch o
n relations of such theta functions with solutions of the Kadomtsev-Petvia
shvili hierarchy if time permits.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tolga Karayayla (ODTÜ)
DTSTART:20230331T124000Z
DTEND:20230331T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/23
DESCRIPTION:Title: On a class of non-simply connected Calabi-Yau 3-folds with positive
Euler characteristic-Part 1\nby Tolga Karayayla (ODTÜ) as part of ODT
U-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will p
resent a class of non-simply connected Calabi-Yau 3-folds with positive Eu
ler characteristic which are the quotient spaces of fixed-point-free group
actions on desingularizations of singular Schoen 3-folds. A Schoen 3-fold
is the fiber product of two rational elliptic surfaces with section. Smoo
th Schoen 3-folds are simply connected CY 3-folds. Desingularizations of c
ertain singular Schoen 3-folds by small resolutions have the same property
. If a finite group G acts freely on such a 3-fold\, the quotient is again
a CY 3-fold. I will present how to classify such group actions using the
automorphism groups of rational elliptic surfaces with section. The smooth
Schoen 3-fold case gives 0 Euler characteristic whereas the singular case
results in positive Euler characteristic for the quotient CY threefolds.\
n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tolga Karayayla (ODTÜ)
DTSTART:20230407T124000Z
DTEND:20230407T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/24
DESCRIPTION:Title: On a class of non-simply connected Calabi-Yau 3-folds with positive
Euler characteristic-Part 2\nby Tolga Karayayla (ODTÜ) as part of ODT
U-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will p
resent a class of non-simply connected Calabi-Yau 3-folds with positive Eu
ler characteristic which are the quotient spaces of fixed-point-free group
actions on desingularizations of singular Schoen 3-folds. A Schoen 3-fold
is the fiber product of two rational elliptic surfaces with section. Smoo
th Schoen 3-folds are simply connected CY 3-folds. Desingularizations of c
ertain singular Schoen 3-folds by small resolutions have the same property
. If a finite group G acts freely on such a 3-fold\, the quotient is again
a CY 3-fold. I will present how to classify such group actions using the
automorphism groups of rational elliptic surfaces with section. The smooth
Schoen 3-fold case gives 0 Euler characteristic whereas the singular case
results in positive Euler characteristic for the quotient CY threefolds.\
n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig van Coevering (Boğaziçi)
DTSTART:20230414T124000Z
DTEND:20230414T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/25
DESCRIPTION:Title: Extremal Kähler metrics and the moment map\nby Craig van Coever
ing (Boğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nAn extremal Kähler metric is a canonical Kähler metric\, intro
duced by E.\nCalabi\, which is somewhat more general than a constant scala
r curvature Kähler metric. The existence of such a metric is an ongoing r
esearch subject and expected to be equivalent to some form of geometric st
ability of the underlying polarized complex manifold $(M\, J\, [\\omega])$
–the Yau-Tian-Donaldson Conjecture. Thus it is no surprise that there
is a moment map\, the scalar curvature (A. Fujiki\, S. Donaldson)\, and th
e problem can be described as an infinite dimensional version of the famil
iar finite dimensional G.I.T.\n\nI will describe how the moment map can be
used to describe the local space of extremal metrics on a symplectic mani
fold. Essentially\, the local picture can be reduced to finite dimensional
G.I.T. In particular\, we can construct a course moduli space of extremal
Kähler metrics with a fixed polarization $[\\omega] \\in H^2(M\, \\math
bb{R})$\, which is an Hausdorff complex analytic space\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mesut Şahin (Hacettepe)
DTSTART:20230428T120000Z
DTEND:20230428T130000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/26
DESCRIPTION:Title: Vanishing ideals and codes on toric varieties\nby Mesut Şahin (
Hacettepe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstra
ct\nMotivated by applications to the theory of error-correcting codes\, we
give an algorithmic method for computing a generating set for the ideal g
enerated by $\\beta$-graded polynomials vanishing on a subset of a simplic
ial complete toric variety $X$ over a finite field $\\mathbb{F}_q$\, param
eterized by rational functions\, where $\\beta$ is a $d\\times r$ matrix w
hose columns generate a subsemigroup $\\mathbb{N}\\beta$ of $\\mathbb{N}^d
$. We also give a method for computing the vanishing ideal of the set of $
\\mathbb{F}_q$-rational points of $X$. We talk about some of its algebraic
invariants related to basic parameters of the corresponding evaluation co
de. When $\\beta=[w_1 \\cdots w_r]$ is a row matrix corresponding to a num
erical semigroup $\\mathbb{N}\\beta=\\langle w_1\,\\dots\,w_r \\rangle$\,
$X$ is a weighted projective space and generators of its vanishing ideal i
s related to the generators of the defining (toric) ideals of some numeric
al semigroup rings corresponding to semigroups generated by subsets of $\\
{w_1\,\\dots\,w_r\\}$.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ekin Ozman (Boğaziçi)
DTSTART:20230505T124000Z
DTEND:20230505T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/27
DESCRIPTION:Title: The p ranks of Prym varieties\nby Ekin Ozman (Boğaziçi) as par
t of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk
we will start with basics of moduli space of curves\, coverings of curves\
, p-ranks and mention the differences in characteristics 0 and positive ch
aracteristics.Then we'll define Prym variety which is a central object of
study in arithmetic geometry like Jacobian variety. The goal of the talk
is to understand various existence results about Prym varieties of given g
enus\, p-rank and characteristics of the base field. This is joint work wi
th Rachel Pries.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20230512T124000Z
DTEND:20230512T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/28
DESCRIPTION:Title: Counting lines on polarized K3-surfaces\nby Alexander Degtyarev
(Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nCounting or estimating the number of lines or\, more generally\, low de
gree\nrational curves on a polarized algebraic surface is a classical prob
lem going\nback almost 1.5 centuries. After a brief historical excurse\, I
will try to\ngive an account of the considerable progress made in the sub
ject in the last\ndecade or so\, mainly related to various (quasi-)polariz
ations of\n$K3$-surfaces: \n\n$\\bullet$\nlines on $K3$-surfaces with any
polarization\,\n\n$\\bullet$\nlines on low degree $K3$-surfaces with singu
larities\,\n\n$\\bullet$\nconics on low degree $K3$-surfaces.\n\nIf time p
ermits\, I will briefly discuss other surfaces/varieties as well.\n\nSome
parts of this work are joint projects\n(some still in progress) with Ilia
Itenberg\, Slavomir Rams\, Ali\nSinan Sertöz.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20231013T124000Z
DTEND:20231013T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/30
DESCRIPTION:Title: Singular real plane sextic curves without real points\nby Alexan
der Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminar
s\n\n\nAbstract\n(joint with Ilia Itenberg)\nIt is a common understanding
that any reasonable geometric question about K3\n-surfaces can be restated
and solved in purely arithmetical terms\, by means of an appropriately de
fined homological type. For example\, this works well in the study of sing
ular complex sextic curves in P2 or quartic surfaces in P3 (see [1\,2])\
, as well as in that of smooth real ones (see [4\,6]). However\, when the
two are combined (both singular and real curves or surfaces)\, the approac
h fails as the `"obvious'' concept of homological type does not fully refl
ect the geometry (cf.\, e.g.\, [3] or [5]).\n\nWe show that the situation
can be repaired if the curves in question have empty real part or\, more g
enerally\, have no real singular points\; then\, one can indeed confine on
eself to the homological types consisting of the exceptional divisors\, po
larization\, and real structure.\n\nStill\, the resulting arithmetical pro
blem is not quite straightforward\, but we manage to solve it and obtain a
satisfactory classification in the case of empty real part\; it matches a
ll known results obtained by an alternative purely geometric approach. In
the general case of smooth real part\, we also have a formal classificatio
n\; however\, establishing a correspondence between arithmetic and geometr
ic invariants (most notably\, the distribution of ovals among the componen
ts of a reducible curve) still needs a certain amount of work.\n\nThis pro
ject was conceived and partially completed during our joint stay at the Ma
x-Planck-Institut für Mathematik\, Bonn. The speaker is partially support
ed by TÜBİTAK project 123F111.\n\nREFERENCES\n\n[1]. Ayşegül Akyol and
Alex Degtyarev\, Geography of irreducible plane sextics\, Proc. Lond. Mat
h. Soc. (3) 111 (2015)\, no. 6\, 13071337. MR 3447795\n\n[2]. Çisem Gün
eş Aktaş\, Classi\ncation of simple quartics up to equisingular deformat
ion\, Hiroshima Math. J. 47 (2017)\, no. 1\, 87112. MR 3634263\n\n[3]. I.
V. Itenberg\, Curves of degree 6 with one nondegenerate double point and
groups of monodromy of nonsingular curves\, Real algebraic geometry (Renne
s\, 1991)\, Lecture Notes in Math.\, vol. 1524\, Springer\, Berlin\, 1992\
, pp. 267288. MR 1226259\n\n[4]. V. M. Kharlamov\, On the classi\ncation
of nonsingular surfaces of degree 4 in RP3\n with respect to rigid isotopi
es\, Funktsional. Anal. i Prilozhen. 18 (1984)\, no. 1\, 4956. MR 739089\
n\n[5]. Sébastien Moriceau\, Surfaces de degré 4 avec un point double no
n dégénéré dans l'espace projectif réel de dimension 3\, Ph.D. thesis
\, 2004.\n\n[6]. V. V. Nikulin\, Integer symmetric bilinear forms and some
of their geometric applications\, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979
)\, no. 1\, 111177\, 238\, English translation: Math USSR-Izv. 14 (1979)\
, no. 1\, 103167 (1980). MR 525944 (80j:10031)\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Turgay Akyar (METU)
DTSTART:20231020T124000Z
DTEND:20231020T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/31
DESCRIPTION:Title: Special linear series on real trigonal curves\nby Turgay Akyar (
METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nF
or a given trigonal curve $C$\, geometric features of the Brill-Noether v
ariety $W_d^r(C)$ parametrizing complete linear series of degree $d$ and d
imension at least $r$ are well known. If the curve $C$ is real\, then $W_d
^r(C)$ is also defined over $\\mathbb{R}$. In this talk we will see the ba
sic properties of real linear series and discuss the topology of the real
locus $W_d^r(C)(\\mathbb{R})$ for some specific cases.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:İzzet Coşkun (UIC)
DTSTART:20231027T124000Z
DTEND:20231027T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/32
DESCRIPTION:Title: Dense orbits of the PGL(n)-action on products of flag varieties\
nby İzzet Coşkun (UIC) as part of ODTU-Bilkent Algebraic Geometry Semina
rs\n\n\nAbstract\nIt is a classical and very useful fact that any n+2 line
arly general points in P^n are projectively equivalent. In this talk\, I w
ill consider generalizations of this statement to higher dimensional linea
r spaces. The group PGL(n) acts on products of Grassmannians or more gener
ally flag varieties. I will discuss cases when this action has a dense orb
it. This talk is based on joint work with Demir Eken\, Abuzer Gündüz\, M
ajid Hadian\, Chris Yun and Dmitry Zakharov.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Çisem Güneş Aktaş (Abdullah Gül)
DTSTART:20231103T124000Z
DTEND:20231103T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/33
DESCRIPTION:Title: Geometry of equisingular strata of quartic surfaces with simple sing
ularities\nby Çisem Güneş Aktaş (Abdullah Gül) as part of ODTU-Bi
lkent Algebraic Geometry Seminars\n\n\nAbstract\nThe geometry of the equis
ingular strata of curves\, surfaces\, etc. is one of the central problems
of K3-surfaces. Thanks to the global Torelli theorem and surjectivity of
the period map\, the equisingular deformation classification of singular p
rojective models of K3-surfaces with any given polarization becomes a mere
computation. The most popular models studied intensively in the literatur
e are plane sextic curves and spatial quartic surfaces. Using the arithmet
ical reduction\, Akyol and Degtyarev [1] completed the problem of equising
ular deformation classification of simple plane sextics. Simple quartic su
rfaces which play the same role in the realm of spatial surfaces as sextic
s do for curves\, are a relatively new subject\, promising interesting dis
coveries.\n\nIn this talk\, we discuss the problem of classifying quartic
surfaces with simple singularities up to equisingular deformations by redu
cing the problem to an arithmetical problem about lattices. This research
[3] originates from our previous study [2] where the classification was
given only for nonspecial quartics\, in the spirit of Akyol ve Degtyarev
[1]. Our principal result is extending the classification to the whole spa
ce of simple quartics and\, thus\, completing the equisingular deformation
classification of simple quartic surfaces.\n\n [1] Akyol\, A.
ve Degtyarev\, A.\, 2015. Geography of irreducible plane sex- tics. Proc.
Lond. Math. Soc. (3)\, 111(6)\, 13071337. ISSN 0024-6115. doi:10.1112/plms
/pdv053.\n [2] Güneş Aktaş\, Ç\, 2017. Classification of si
mple quartics up to equisin- gular deformation. Hiroshima Math. J.\, 47(1)
\, 87112. ISSN 0018-2079. doi:10.32917/hmj/1492048849.\n\n [3]
Güneş Aktaş\, Ç\, to appear in Deformation classification of quartic s
urfaces with simple singularities. Rev. Mat. Iberoam. doi:10.4171/RMI/1431
\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nurömür Hülya Argüz (Georgia)
DTSTART:20231110T124000Z
DTEND:20231110T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/34
DESCRIPTION:Title: Quivers and curves in higher dimensions\nby Nurömür Hülya Arg
üz (Georgia) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbs
tract\nQuiver Donaldson-Thomas invariants are integers determined by the g
eometry of moduli spaces of quiver representations. I will describe a corr
espondence between quiver Donaldson-Thomas invariants and Gromov-Witten co
unts of rational curves in toric and cluster varieties. This is joint work
with Pierrick Bousseau (arXiv:2302.02068 and arXiv:arXiv:2308.07270).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Genlik (OSU)
DTSTART:20231117T124000Z
DTEND:20231117T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/35
DESCRIPTION:Title: Holomorphic anomaly equations for $\\mathbb{C}^n/\\mathbb{Z}_n$\
nby Deniz Genlik (OSU) as part of ODTU-Bilkent Algebraic Geometry Seminars
\n\n\nAbstract\nIn this talk\, we present certain results regarding the hi
gher genus Gromov-Witten theory of $\\mathbb{C}^n/\\mathbb{Z}_n$ obtained
by studying its cohomological field theory structure in detail. Holomorphi
c anomaly equations are certain recursive partial differential equations p
redicted by physicists for the Gromov-Witten potential of a Calabi-Yau thr
eefold. We prove holomorphic anomaly equations for $\\mathbb{C}^n/\\mathbb
{Z}_n$ for any $n\\geq 3$. In other words\, we present a phenomenon of hol
omorphic anomaly equations in arbitrary dimension\, a result beyond the co
nsideration of physicists. The proof of this fact relies on showing that t
he Gromov-Witten potential of $\\mathbb{C}^n/\\mathbb{Z}_n$ lies in a cert
ain polynomial ring. This talk is based on the joint work arXiv:2301.08389
with Hsian-Hua Tseng.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Ulaş Özgür Kişisel (METU)
DTSTART:20231124T124000Z
DTEND:20231124T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/36
DESCRIPTION:Title: Random Algebraic Geometry and Random Amoebas\nby Ali Ulaş Özg
ür Kişisel (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\
n\nAbstract\nRandom algebraic geometry studies variable properties of typi
cal algebraic varieties as opposed to invariant properties or extremal pro
perties. For instance\, a complex algebraic projective plane curve is alwa
ys topologically connected\, which is an invariant property\; a real alge
braic projective plane curve of degree $d$ has\, by a classical theorem of
Harnack\, at most $\\displaystyle{g+1=(d-1)(d-2)/2+1}$ connected componen
ts where $g$ denotes genus\, which is an extremal property\; whereas a ran
dom real algebraic projective degree $d$ plane curve in a suitable precise
sense (to be explained in the talk) has an expected number of connected c
omponents of order $d$. In this talk\, I will first present the setup and
some of the main known results of the field of random algebraic geometry.
I will then proceed to discuss some of our results on the expected propert
ies of amoebas of random complex algebraic varieties\, based on a joint wo
rk with Turgay Bayraktar\, and another joint work with Jean-Yves Welsching
er.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nil Şahin (Bilkent)
DTSTART:20231201T124000Z
DTEND:20231201T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/37
DESCRIPTION:Title: Monotonicity of the Hilbert Functions of some monomial curves\nb
y Nil Şahin (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars
\n\n\nAbstract\nLet $S$ be a 4-generated pseudo-symmetric semigroup genera
ted by the positive integers $\\{n_1\, n_2\, n_3\, n_4\\}$ where $\\gcd(n_
1\, n_2\, n_3\, n_4) = 1$. $k$ being a field\, let $k[S]$ be the correspon
ding semigroup ring and\n$I_S$ be the defining ideal of $S$. $f_*$ being t
he homogeneous summand of $f$\, tangent cone of $S$ is $k[S]/{I_S}_*$ wher
e ${I_S}_* =< f_*|f \\in I_S >$. We will show that the "Hilbert function
of the local ring (which is isomorphic to the tangent cone) for a 4 genera
ted pseudo-symmetric numerical semigroup $$ is always
non-decreasing when $n_1Kapranov's higher-dimensional Langlands reciprocity principle for GL
(n)\nby Kazım İlhan İkeda (Boğaziçi) as part of ODTU-Bilkent Alge
braic Geometry Seminars\n\n\nAbstract\nAbelian class field theory\, which
describes (including the arithmetic of) all abelian extensions of local an
d global fields using algebraic and analytic objects related to the ground
field via Artin reciprocity laws has undergone two generalizations. The f
irst one\, which is still largely conjectural\, is the non-abelian class f
ield theory of Langlands\, is an extreme generalization of the abelian cla
ss field theory\, describes the whole absolute Galois groups of local and
global fields using automorphic objects related to the ground field via th
e celebrated Langlands reciprocity principles\, (and more generally via fu
nctoriality principles). The second generalization is the higher-dimension
al class field theory of Kato and Parshin\, which describes (including the
arithmetic of) all abelian extensions of higher-dimensional local fields
and higher-dimensional global fields (function fields of schemes of finite
type over ℤ) using this time K-groups of objects related to the ground
field via Kato-Parshin reciprocity laws.\nSo it is a very natural question
to ask the possibility to construct higher-dimensional Langlands reciproc
ity principle. In this direction\, as an answer to this question\, Kaprano
v proposed a conjectural framework for higher-dimensional Langlands recipr
ocity principle for GL(n). In this talk\, we plan to sketch this conjectur
al framework of Kapranov (where we plan to focus on the local case only).\
n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20231215T124000Z
DTEND:20231215T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/39
DESCRIPTION:Title: Lines on singular quartic surfaces via Vinberg\nby Alexander Deg
tyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nLarge configurations of lines (or\, more generally\, rational cu
rves of low degree) on algebraic surfaces appear in various contexts\, bu
t only in the case of cubic surfaces the picture is complete. Our principa
l goal is the classification of large configurations of lines on quasi-pol
arized K3-surfaces in the presence of singularities. To the best of our kn
owledge\, no attempt has been made to attack this problem from the lattice
-theoretical\, based on the global Torelli theorem\, point of view\; some
partial results were obtained by various authors using ``classical'' alge
braic geometry\, but very little is known. The difficulty is that\, given
a polarized N\\'eron--Severi lattice\, computing the classes of smooth rat
ional curves depends on the choice of a Weyl chamber of a certain root lat
tice\, which is not unique.\n\nWe show that this ambiguity disappears and
the algorithm becomes deterministic provided that sufficiently many classe
s of lines are fixed. Based on this fact\, Vinberg's algorithm\, and a com
binatorial version of elliptic pencils\, we develop an algorithm that\, in
principle\, would list all extended Fano graphs. After testing it on octi
c K3-surfaces\, we turn to the most classical case of simple quartics wher
e\, prior to our work\, only an upper bound of 64 lines (Veniani\, same as
in the smooth case) and an example of 52 lines (the speaker) were known.
We show that\, in the presence of singularities\, the sharp upper bound is
indeed 52\, substantiating the long standing conjecture (by the speaker)
that the upper bound is reduced by the presence of smooth rational curves
of lower degree.\n\nWe also extend the classification (I. Itenberg\, A.S.
Sertöz\, and the speaker) of large configurations of lines on smooth quar
tics down to 49 lines. Remarkably\, most of these configurations were know
n before.\n\nThis project was conceived and partially completed during our
joint stay at the Max-Planck-Institut f\\ür Mathematik\, Bonn. The speak
er is partially supported by TÜBİTAK project 123F111.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pınar Mete (Balıkesir)
DTSTART:20240223T124000Z
DTEND:20240223T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/40
DESCRIPTION:Title: On some invariants of the tangent cones of numerical semigroup rings
\nby Pınar Mete (Balıkesir) as part of ODTU-Bilkent Algebraic Geomet
ry Seminars\n\n\nAbstract\nThe minimal free resolution is a very useful to
ol for extracting information about modules. Many important numerical inva
riants of a module such as Hilbert function and Betti numbers can be deduc
ed from its minimal free resolution. Stamate gave a broad survey on these
topics when the modules are the semigroup ring or its tangent cone for a n
umerical semigroup S. He also stated the problem of describing the Betti n
umbers and the minimal free resolution for the tangent cone when S is 4-ge
nerated semigroup which is symmetric. In this talk\, I will first give som
e of our results\, based on a joint work with E.E. Zengin on the problem.
Then\, I will talk about our ongoing study which is an application\nof the
Apery table of the numerical semigroup to determine some properties of it
s tangent cone.\n\nDI. STAMATE\, Betti numbers for numerical semigroup rin
gs. Multigraded Algebra and Applications\,\n238\, 133-157\, Springer Proce
edings in Mathematics and Statistics\, Springer\, Cham 2018.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Turgay Bayraktar (Sabancı)
DTSTART:20240301T124000Z
DTEND:20240301T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/41
DESCRIPTION:Title: Equidistribution for Zeros of Random Polynomial Systems\nby Turg
ay Bayraktar (Sabancı) as part of ODTU-Bilkent Algebraic Geometry Seminar
s\n\n\nAbstract\nA classical result of Erdös and Turan asserts that for a
univariate complex polynomial whose middle coefficients are comparable to
the extremal ones\, the zeros accumulate near the unit circle. We prove
the analogues result for random polynomial mappings with Bernoulli coeffic
ients. The talk is based on the joint work with Çiğdem Çelik.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaan Bilgin (Amsterdam)
DTSTART:20240315T124000Z
DTEND:20240315T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/42
DESCRIPTION:Title: The Langlands – Kottwitz method for GSpin Shimura varieties and ei
genvarieties\nby Kaan Bilgin (Amsterdam) as part of ODTU-Bilkent Algeb
raic Geometry Seminars\n\n\nAbstract\nGiven a connected reductive algebrai
c group G over a number field F\, the global Langlands (reciprocity) conje
cture roughly predicts that\, there should be a correspondence between (au
tomorphic side) the isomorphism classes of (cuspidal\, cohomological) aut
omorphic representations of G and (Galois side) the isomorphism classes of
(irreducible\, locally de-Rham) Galois representations for Gal(\\bar{F} /
F) taking values in the Langlands dual group of G.\n\nIn the first part o
f this talk\, I will sketch the main argument of our expected theorem/proo
f for (automorphic to Galois) direction of this conjecture\, for G = GSpin
(n\,2)\, n odd and F to be totally real\, under 3 technical assumptions (f
or time being)\, namely we assume that automorphic representations are add
itionally “non-CM” and “non-endoscopic” and “std-regular”.\n\n
In the second part\, mainly following works of Loeffler and Chenevier on o
verconvergent p-adic automorphic forms\, I will present an idea to remove
the std-regular assumption on the theorem via the theory of eigenvarietie
s.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haydar Göral (İYTE)
DTSTART:20240322T124000Z
DTEND:20240322T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/43
DESCRIPTION:Title: Arithmetic Progressions in Finite Fields\nby Haydar Göral (İYT
E) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn 1
927\, van der Waerden proved a theorem regarding the existence of arithmet
ic progressions in any partition of the positive integers with finitely ma
ny classes. In 1936\, a strengthening of van der Waerden's theorem was con
jectured by Erdös and Turan\, which states that any subset of positive in
tegers with a positive upper density contains arbitrarily long arithmetic
progressions. In 1975\, Szemeredi developed his combinatorial method to re
solve this conjecture\, and the affirmative answer to Erdös and Turan's c
onjecture is now known as Szemeredi's theorem. As well as in the integers\
, Szemeredi-type problems have been extensively studied in subsets of fini
te fields. While much work has been done on the problem of whether subsets
of finite fields contain arithmetic progressions\, in this talk we concen
trate on how many arithmetic progressions we have in certain subsets of fi
nite fields. The technique is based on certain types of Weil estimates. We
obtain an asymptotic for the number of k-term arithmetic progressions in
squares with a better error term. Moreover our error term is sharp and bes
t possible when k is small\, owing to the Sato-Tate conjecture. This work
is supported by the Scientific and Technological Research Council of Turke
y with the project number 122F027.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Büşra Karadeniz Şen (Gebze Technical University)
DTSTART:20240329T124000Z
DTEND:20240329T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/44
DESCRIPTION:Title: Boundaries of the dual Newton polyhedron may describe the singularit
y\nby Büşra Karadeniz Şen (Gebze Technical University) as part of O
DTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nWe are dealing with
a hypersurface $X\\subset\\mathbb{C}^3$\n having non-isolated singulariti
es.We construct an embedded toric resolution of $X$\n using some specific
vectors in its dual Newton polyhedron. To do this\, we first define the pr
ofile of a full dimensional cone and we establish a relation between the j
et vectors and the integer points in the profile.\n\nThis is a part of the
joint work with C. Plénat and M. Tosun.\n\nReferences
\n[1] A. Altin
taş Sharland\, C. O. Oğuz\, M. Tosun and Z.aferiakopoulos\, An algori
thm to find nonisolated forms of rational singularities\, In preparati
on.
\n[2] C. Bouvier and G. Gonzalez-Sprinberg\, Systéme générat
eur minimal\, diviseurs essentiels et G-désingularisations de variétés
torique\, Tohoku Math. J.\, 47\, 1995.
\n[3] B. Karadeniz Şen\, C
. Plénat and M. Tosun\, Minimality of a toric embedded resolution of s
ingularities after Bouvier-Gonzalez-Sprinberg\, Kodai Math J.\, accept
ed\, 2024.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enis Kaya (KU Leuven)
DTSTART:20240405T124000Z
DTEND:20240405T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/45
DESCRIPTION:Title: p-adic Integration Theories on Curves\nby Enis Kaya (KU Leuven)
as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nFor cur
ves over the field of p-adic numbers\, there are two notions of p-adic int
egration: Berkovich-Coleman integrals which can be performed locally\, and
Vologodsky integrals with desirable number-theoretic properties. These in
tegrals have the advantage of being insensitive to the reduction type at p
\, but are known to coincide with Coleman integrals in the case of good re
duction. Moreover\, there are practical algorithms available to compute Co
leman integrals.\n\nBerkovich-Coleman and Vologodsky integrals\, however\,
differ in general. In this talk\, we give a formula for passing between t
hem. To do so\, we use combinatorial ideas informed by tropical geometry.
We also introduce algorithms for computing Berkovich-Coleman and Vologodsk
y integrals on hyperelliptic curves of bad reduction. By covering such a c
urve by certain open spaces\, we reduce the computation of Berkovich-Colem
an integrals to the known algorithms on hyperelliptic curves of good reduc
tion. We then convert the Berkovich-Coleman integrals into Vologodsky inte
grals using our formula. We illustrate our algorithm with a numerical exam
ple.\n\nThis talk is partly based on joint work with Eric Katz from the Oh
io State University.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ichiro Shimada (Hiroshima)
DTSTART:20240419T124000Z
DTEND:20240419T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/46
DESCRIPTION:Title: Real line arrangements and vanishing cycles\nby Ichiro Shimada (
Hiroshima) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstra
ct\nWe investigate the topology of a double cover of a complex affine plan
e branching along a nodal real line arrangement.We define certain topologi
cal 2-cycles in the double plane using the real structure of the arrangeme
nt.These cycles resemble vanishing cycles of Lefschetz.We then calculate
their intersection numbers.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaacov Kopeliovich (Connecticut)
DTSTART:20240426T124000Z
DTEND:20240426T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/47
DESCRIPTION:Title: The fundamental group of compact algebraic curve above complex numbe
rs\nby Yaacov Kopeliovich (Connecticut) as part of ODTU-Bilkent Algebr
aic Geometry Seminars\n\n\nAbstract\nIt is well known that fundamental cur
ves above complex numbers have 2g generators where g is the genus of the
curve with one non trivial relation that is the commutation relation. Surp
risingly I haven’t found a proof of this well known fact in the literatu
re.\nIn this talk I will attempt to fill in the gap and show how this can
be shown in a straightforward matter.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meirav Amram (SCE)
DTSTART:20240503T124000Z
DTEND:20240503T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/48
DESCRIPTION:Title: Interesting methods to classify algebraic curves and surfaces\nb
y Meirav Amram (SCE) as part of ODTU-Bilkent Algebraic Geometry Seminars\n
\n\nAbstract\nWe present a few algebraic\, geometric and topological metho
ds that we use in the classification of algebraic curves and surfaces. We
speak about a few invariants of the classification as well. We discuss de
generation of algebraic surfaces\, the calculation of fundamental groups a
nd some computational methods that help with these calculations.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20240510T124000Z
DTEND:20240510T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/49
DESCRIPTION:Title: Singular real plane sextic curves with smooth real part\nby Alex
ander Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Semin
ars\n\n\nAbstract\nFor a change\, I will give a detailed proof of one of o
ur joint results announced in an earlier talk\, viz. the fact that the equ
isingular equivariant deformation type of a real plane sextic curve with s
mooth real part is determined by its real homological type (in the most na
ïve meaning of the term)\; this theorem has been used to obtain a complet
e classification of such curves. The principal goal is introducing the new
er generation into the fascinating theory of K3-surfaces\, real aspects th
ereof\, and algebra/number theory involved.\n\nThis is a joint work in pro
gress with Ilia Itenberg.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Can Sertöz (Leiden)
DTSTART:20241011T124000Z
DTEND:20241011T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/50
DESCRIPTION:Title: Computing transcendence and linear relations of 1-periods\nby Em
re Can Sertöz (Leiden) as part of ODTU-Bilkent Algebraic Geometry Seminar
s\n\n\nAbstract\nI will sketch a modestly practical algorithm to compute a
ll linear relations with algebraic coefficients between any given finite s
et of 1-periods. As a special case\, we can algorithmically decide transce
ndence of 1-periods. This is based on the "qualitative description" of the
se relations by Huber and Wüstholz. We combine their result with the rece
nt work on computing the endomorphism ring of abelian varieties. This is a
work in progress with Jöel Ouaknine (MPI SWS) and James Worrell (Oxford)
.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Veniani (Stuttgart)
DTSTART:20241018T124000Z
DTEND:20241018T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/51
DESCRIPTION:Title: Entropy and non-degeneracy of Enriques surfaces\nby Davide Venia
ni (Stuttgart) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAb
stract\nThe entropy of an algebraic surface serves as an invariant that qu
antifies 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) an
d 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.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20241025T124000Z
DTEND:20241025T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/52
DESCRIPTION:Title: Real plane sextic curves with smooth real part\nby Alexander Deg
tyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nWe have obtained the complete deformation classification of sing
ular 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 equisingu
lar deformation type is determined by the so-called real homological type
in its most naïve sense\, i.e.\, the homological information about the po
larization\, singularities\, and real structure\; one does not need to com
pute 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.\n\nAs usual\, this classification leads us to
a number of observations\, some of which we have already managed to genera
lize. Thus\, we have an Arnol’d-Gudkov-Rokhlin type congruence for close
to maximal surfaces (and\, hence\, even degree curves) with certain singu
larities. Another observation (which has not been quite understood yet and
may turn out K3-specific) is that the contraction of any empty oval of a
type I real scheme results in a bijection of the sets of deformation class
es.\n(joined work with Ilia Itenberg)\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enis Kaya (KU Leuven)
DTSTART:20241101T124000Z
DTEND:20241101T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/53
DESCRIPTION:Title: Rational curves on del Pezzo surfaces\nby Enis Kaya (KU Leuven)
as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this
talk\, we explore the connection between the enumerative geometry of rati
onal curves on del Pezzo surfaces over a field k and the arithmetic proper
ties 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 degre
es 1 and 2. Our results generalize well-known theorems in the setting of s
mooth cubic surfaces. This is joint work in progress with Stephen McKean\,
Sam Streeter and Harkaran Uppal.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Ulaş Özgür Kişisel (METU)
DTSTART:20241108T124000Z
DTEND:20241108T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/54
DESCRIPTION:Title: Irreversible odd degree curves in $\\mathbb{RP}^2$\nby Ali Ulaş
Özgür Kişisel (METU) as part of ODTU-Bilkent Algebraic Geometry Semina
rs\n\n\nAbstract\nA 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 durin
g the deformation. The question of reversibility was discussed in the pape
r titled ``On the deformation chirality of real cubic fourfolds'' by Finas
hin and Kharlamov. For $n=1$\, the case of plane curves\, and $d\\leq 5$ o
dd\, 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 de
gree curves and use it in particular to demonstrate that there exist irrev
ersible curves in $\\mathbb{RP}^2$ for all odd degrees $d\\geq 7$. This ta
lk is based on joint work in progress with Ferit Öztürk.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:İrem Portakal (Max Planck at Leipzig)
DTSTART:20241115T124000Z
DTEND:20241115T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/55
DESCRIPTION:Title: Nonlinear algebra in game theory\nby İrem Portakal (Max Planck
at Leipzig) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nn 1950\, Nash published a very influential two-page paper proving the
existence of Nash equilibria for any finite game. The proof uses an elega
nt application of the Kakutani fixed-point theorem from the field of topol
ogy. 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 equili
brium fails to predict the most beneficial outcome for all players. To add
ress this\, generalizations of Nash equilibria such as correlated and depe
ndency equilibria were introduced. In this talk\, I elaborate on how nonli
near algebra is indispensable for studying undiscovered facets of these co
ncepts of equilibria in game theory.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Rams (Jagiellonian])
DTSTART:20241122T124000Z
DTEND:20241122T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/56
DESCRIPTION:Title: Counting lines on projective surfaces\nby Slawomir Rams (Jagiell
onian]) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\
nIn the last decade most questions concerning line configurations on degre
e-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\n
even in complex case. In my talk I will discuss the best known bound for
number of lines on degree-d\n surfaces in three-dimensional projective s
pace (based on joint work with Thomas Bauer and Matthias Schuett).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART:20241129T124000Z
DTEND:20241129T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/57
DESCRIPTION:Title: Stability Conditions I\nby Emre Coşkun (METU) as part of ODTU-B
ilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn moduli problems\, one
usually needs to impose some sort of "stability" on the objects being cla
ssified in order to have well-behaved moduli spaces. Generalizing this con
cept\, in 2007\, Bridgeland defined "stability conditions" on a triangulat
ed category and proved that\, under some mild conditions\, the set of stab
ility conditions can be given the structure of a complex manifold. In this
three-part series\, we shall explore this construction. We shall also giv
e examples of stability conditions when the underlying triangulated catego
ry is the derived category of coherent sheaves on a smooth\, projective va
riety.\n\nReference: Bridgeland\, Tom. Stability conditions on triangulate
d categories. Ann. of Math. (2) 166 (2007)\, no.2\, 317–345.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART:20241206T124000Z
DTEND:20241206T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/58
DESCRIPTION:Title: Stability Conditions II\nby Emre Coşkun (METU) as part of ODTU-
Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn moduli problems\, on
e usually needs to impose some sort of "stability" on the objects being cl
assified in order to have well-behaved moduli spaces. Generalizing this co
ncept\, in 2007\, Bridgeland defined "stability conditions" on a triangula
ted category and proved that\, under some mild conditions\, the set of sta
bility conditions can be given the structure of a complex manifold. In thi
s three-part series\, we shall explore this construction. We shall also gi
ve examples of stability conditions when the underlying triangulated categ
ory is the derived category of coherent sheaves on a smooth\, projective v
ariety.\n\nReference: Bridgeland\, Tom. Stability conditions on triangulat
ed categories. Ann. of Math. (2) 166 (2007)\, no.2\, 317–345.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20250228T124000Z
DTEND:20250228T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/59
DESCRIPTION:Title: Split hyperplane sections on polarized K3-surfaces\nby Alexander
Degtyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n
\n\nAbstract\nI will discuss a new result which is an unexpected outcome\,
following a question by Igor Dolgachev\, of a long saga about smooth rati
onal curves on (quasi-)polarized $K3$-surfaces. The best known example of
a $K3$-surface is a quartic surface in space. A simple dimension count sho
ws that a typical quartic contains no lines. Obviously\, some of them do a
nd\, according to B.~Segre\, the maximal number is $64$ (an example is to
be worked out). The key r\\^ole in Segre's proof (as well as those by othe
r authors) is played by plane sections that split completely into four lin
es\, constituting the dual adjacency graph $K(4)$. A similar\, though less
used\, phenomenon happens for sextic $K3$-surfaces in~$\\mathbb{P}^4$ (co
mplete intersections of a quadric and a cubic): a split hyperplane section
consists of six lines\, three from each of the two rulings\, on a hyperbo
loid (the section of the quadric)\, thus constituting a $K(3\,3)$.\n\nGoin
g further\, in degrees $8$ and $10$ one's sense of beauty suggests that th
e graphs should be the $1$-skeleton of a $3$-cube and Petersen graph\, re
spectfully. However\, further advances to higher degrees required a system
atic study of such $3$-regular graphs and\, to my great surprise\, I disco
vered that typically there is more than one! Even for sextics one can also
imagine the $3$-prism (occurring when the hyperboloid itself splits into
two planes).\n\nThe ultimate outcome of this work is the complete classifi
cation of the graphs that occur as split hyperplane sections (a few dozens
) and that of the configurations of split sections within a single surface
(manageable starting from degree $10$). In particular\, answering Igor's
original question\, the maximal number of split sections on a quartic is $
72$\, whereas on a sextic in $\\mathbb{P}^4$ it is $40$ or $76$\, dependin
g on the question asked. The ultimate champion is the Kummer surface of de
gree~$12$: it has $90$ split hyperplane sections.\n\nThe tools used (proba
bly\, not to be mentioned) are a fusion of graph theory and number theory\
, sewn together by the geometric insight.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (Oslo)
DTSTART:20250307T124000Z
DTEND:20250307T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/60
DESCRIPTION:Title: Fano varieties with torsion in the third cohomology group\nby Jo
hn Christian Ottem (Oslo) as part of ODTU-Bilkent Algebraic Geometry Semin
ars\n\n\nAbstract\nI will explain a construction of Fano varieties with to
rsion in their third cohomology group. The examples are constructed as dou
ble covers of linear sections of rank loci of symmetric matrices\, and can
be seen as higher-dimensional analogues of the Artin– Mumford threefold
. As an application\, we will answer a question of Voisin on the coniveau
and strong coniveau filtrations of rationally connected varieties.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART:20250314T124000Z
DTEND:20250314T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/61
DESCRIPTION:Title: Stability conditions on K3 surfaces\nby Emre Coşkun (METU) as p
art of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nStability c
onditions have been a topic of intense research in recent years. The prese
nt talk will review briefly their definition and basic properties as well
as the existence of stability conditions on curves\, and outline the const
ruction of stability conditions on a K3 surface.\n\n(MR2373143\, MR2376815
\, MR4093206\, MR2998828\, MR3729077)\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selma Altınok Bhupal (Hacettepe)
DTSTART:20250321T124000Z
DTEND:20250321T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/62
DESCRIPTION:Title: The Algebra of Generalised Splines\nby Selma Altınok Bhupal (Ha
cettepe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract
\nClasical splines are piecewise polynomial functions over polyhedral comp
lexes with a certain degree of smoothness at the intersections of adjacent
faces. They are widely used in applications of different areas\, ranging
from approximation theory to geometric modelling. Alternativaly\, splines
can be interpreted as a collection of polynomial labeling the vertices of
a (compinatorial) graph\, with adjacent vertex-labels differing by the po
wer of an affine line form attacthed to the edge. The concept of splines c
an be generalized to define on graphs with edge labels over arbitrary ring
s. Such splines are called generalized splines.\n\nIn this talk\, we give
a brief description of what generalized splines are on arbitrary garphs an
d their properties. We explain algebraic geometric and combinatorial moti
vations behind studying generalized splines. In the rest of the talk\, we
mainly focus on the module structure of generalized splines and discuss th
eir basis.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahir Bilen Can (Tulane)
DTSTART:20250328T124000Z
DTEND:20250328T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/63
DESCRIPTION:Title: Two new families of spherical varieties\nby Mahir Bilen Can (Tul
ane) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nMa
ny familiar varieties\, such as Grassmannians\, toric varieties\, symmetri
c spaces\, and algebraic monoids\, arise naturally as representation-theor
etic objects. Understanding their geometric and representation-theoretic d
istinctions and similarities often reveals deeper underlying structures an
d results. In this talk\, we introduce two new families of spherical varie
ties: nearly toric and doubly spherical. We will discuss their intriguing
connections to combinatorics and representation theory\, with a focus on t
heir manifestations among Schubert varieties. This presentation is based o
n joint work with Nestor Diaz Morera (Fitchburg State University\, USA)\,
Pinaki Saha (IIT Delhi\, India)\, and Senthamarai Kannan (Chennai Mathemat
ical Institute\, India).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sema Salur (Rochester/Bilkent)
DTSTART:20250411T124000Z
DTEND:20250411T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/65
DESCRIPTION:Title: Manifolds with Special Holonomy and Applications\nby Sema Salur
(Rochester/Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\
n\nAbstract\nThe talk will focus on manifolds with special holonomy\, a cl
ass of spaces whose infinitesimal symmetries play a crucial role in M-theo
ry compactifications. M-theory\, often referred to as the "theory of every
thing\," has emerged in recent decades as a leading candidate for unifying
the four fundamental forces of nature: electromagnetism\, gravity\, and t
he weak and strong nuclear forces.\n\nWe will begin with a brief introduct
ion to Calabi-Yau and G₂ manifolds\, followed by an overview of my recen
t research on the connections between symplectic\, contact\, and calibrate
d structures in these manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Yves Welschinger (Institut Camille Jordan Université Lyon 1)
DTSTART:20250418T124000Z
DTEND:20250418T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/66
DESCRIPTION:Title: Amoeba measures of random complex plane curves\nby Jean-Yves Wel
schinger (Institut Camille Jordan Université Lyon 1) as part of ODTU-Bilk
ent Algebraic Geometry Seminars\n\n\nAbstract\nI will estimate the asympto
tic behavior of the expected measure of the amoeba of complex plane curves
. Given a collection of complex bidisks of size inverse to the square root
of the degree\, it involves a lower estimate of the probability that one
of these bidisk be a submanifold chart of a complex plane curve. This is a
joint work with Ali Ulaş Özgür Kişisel.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hasan Suluyer (METU)
DTSTART:20250425T124000Z
DTEND:20250425T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/67
DESCRIPTION:Title: Pencils of Conic-Line Curves\nby Hasan Suluyer (METU) as part of
ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nA pencil is a lin
e in the projective space of complex homogeneous polynomials of some degre
e d > 2. The number m of curves whose irreducible components are only line
s in some pencils of degree d curves plays an important role for the exist
ence of special line arrangements\, which are called (m\,d)-nets. It was p
roved that the number m\, independent of d\, cannot exceed 4 for an (m\,d)
-net. When the degree of each irreducible component of a curve is at most
2\, this curve is called a conic-line curve and it is a union of lines or
irreducible conics in the complex projective plane. Our main goal is to fi
nd an upper bound on the number m of such curves in pencils in CP^2 with t
he number of concurrent lines in these pencils.\n\nIn this talk\, we study
the restrictions on the number m of conic-line curves in special pencils.
The most general result we obtain is the relation between upper bounds on
m and the number of concurrent lines in these pencils. We construct a one
-parameter family of pencils such that each pencil in the family contains
exactly 4 conic-line curves.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ratko Darda (Sabancı)
DTSTART:20250509T124000Z
DTEND:20250509T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/68
DESCRIPTION:Title: Manin's Conjecture and stacks\nby Ratko Darda (Sabancı) as part
of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nGiven a system
of polynomial equations\, one may ask how many solutions it has in the ra
tional numbers. If there are infinitely many\, we further ask about the nu
mber of solutions of bounded "size." The answer depends heavily on the geo
metry of the variety defined by the system. When the variety is Fano—mea
ning that the top wedge power of the tangent bundle is ample—the "correc
t" mathematical framework is provided by Manin's conjecture\, which predic
ts the asymptotic number of rational points of bounded height.\n\nAnother
important conjecture in a similar spirit is Malle's conjecture\, which pre
dicts the number of Galois extensions of the rational numbers with bounded
discriminant.\n\nWe explain how both conjectures can be viewed as special
cases of a single conjecture concerning the number of rational points of
bounded height on stacks. We then discuss some recent advances\, including
the positive characteristic. This talk is based on joint work with Takehi
ko Yasuda.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bayram Tekin (Bilkent)
DTSTART:20251017T124000Z
DTEND:20251017T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/69
DESCRIPTION:Title: A rank-4 tensor Riemann would have loved plus spinor-techniques in d
ifferential geometry\nby Bayram Tekin (Bilkent) as part of ODTU-Bilken
t Algebraic Geometry Seminars\n\n\nAbstract\nI would like to discuss two t
opics that have proved very useful in the parts of differential geometry u
sed in General Relativity and other theories of gravity. The first one is
the introduction of a divergence-free rank 4 tensor which was hiding in pl
ain sight up until our paper ( Phys. Rev. D 99 (2019) 4\, 044026). The sec
ond topic will include formulating differential geometry in terms of Weyl
spinors which are fundamental representations of SL(2\,C).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Türkü Özlüm Çelik (Max Planck Institute of Molecular Cell Bio
logy and Genetics)
DTSTART:20251024T124000Z
DTEND:20251024T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/70
DESCRIPTION:Title: Interaction Networks via Grassmannians\nby Türkü Özlüm Çeli
k (Max Planck Institute of Molecular Cell Biology and Genetics) as part of
ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nWhen can a networ
k of mutually reinforcing N components remain stable? To approach such que
stions\, we describe the interactions through generalized Lotka–Volterra
equations—a broad class of dynamical systems modeling how components in
fluence one another over time. This formulation leads to a family of semi-
algebraic sets determined by the sign pattern of the parameters. These set
s encode positivity conditions defining regions of potential coexistence\,
with polynomial degrees growing exponentially in N. Embedding the paramet
er space into the real Grassmannian Gr(N\,2N) transforms these conditions
into sign relations governed by the Grassmann–Plücker equations and ori
ented matroids. This geometric reformulation yields a realization problem
through which we detect impossible interaction networks and study the alge
braic structure underlying stability. If time permits\, we will also touch
on how these structures connect to algebraic curves. This talk is based o
n our recent work arXiv:2509.00165.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farbod Shokrieh (Washington)
DTSTART:20251031T134000Z
DTEND:20251031T144000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/71
DESCRIPTION:Title: Graphs in algebraic and arithmetic geometry\nby Farbod Shokrieh
(Washington) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbst
ract\nGraphs can be viewed as (non-archimedean) analogs of Riemann surface
s. For example\, there is a notion of Jacobians for graphs. More classical
ly\, graphs can be viewed as electrical networks. I will explain the inter
play between these points of view and some applications in arithmetic geom
etry.\n\nNotice that this talk starts at 16:40 Türkiye time (+3GMT)\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Halil İbrahim Karakaş (Başkent)
DTSTART:20251107T124000Z
DTEND:20251107T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/72
DESCRIPTION:Title: On the enumeration of Arf numerical semigroups with given multiplici
ty and conductor\nby Halil İbrahim Karakaş (Başkent) as part of ODT
U-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe number of numeric
al semigroups with given Frobenious number (or conductor\, or genus) is on
e of the topics that is studied by many researchers. In our previous works
\, we have given parametrizations of Arf numerical semigroups of small mul
tiplicity and obtained formulas for the number of Arf numerical semigroups
with multiplicity less than 14 and arbitrary conductor. I presented part
of these results in ODTÜ-Bikent AG seminars 6 years ago. We noticed that
the number of Arf numerical semigroups with multiplicity $m$ and conducto
r $c$ is (eventually) constant for some $m$ (especially for prime $m$) wh
en restricted to some congruence classes of $c$ modulo $m$. In a recent wo
rk with N. Tutaş\, we have characterized those multiplicities $m$ and con
gruence classes of $c$ modulo $m$ for which the above property holds. This
talk will be based on [Karakaş H İ and Tutaş N\, (2025)\, On the enume
ration of Arf numerical semigroups with given multiplicity and conductor\,
Semigroup Forum 110\, 308-316.] where the above characterization is given
.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Rams (Jagiellonian)
DTSTART:20251114T124000Z
DTEND:20251114T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/73
DESCRIPTION:Title: Maximal configurations of rational curves on K3-surfaces of high de
grees\nby Slawomir Rams (Jagiellonian) as part of ODTU-Bilkent Algebra
ic Geometry Seminars\n\n\nAbstract\nOne of unexpected consequences of the
orbibundle Miyaoka-Yau-Sakai inequality is a bound on the maximal number
of rational degree-d curves on smooth complex K3-surfaces of given degre
e obtained by Miyaoka in 2009. After recalling the necessary notions\, in
my talk I will present various results concerning the question whether t
he above bound is sharp for rational (resp. smooth rational) curves on K
3-surfaces of high degree. \n\nBased on joint work with M. Schuett (Hanno
ver) and A. Degtyarev (Ankara).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohammed Sadek (Sabancı)
DTSTART:20251121T124000Z
DTEND:20251121T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/74
DESCRIPTION:Title: Torsion Subgroups of Hyperelliptic Jacobian Varieties\nby Mohamm
ed Sadek (Sabancı) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\
n\nAbstract\nIn this talk\, we explore some number theoretic aspects of hy
perelliptic curves. It is known that the number of isomorphism classes of
hyperelliptic curves with the same discriminant over a fixed number field
is finite. A more challenging task is to count\, if not list\, all such is
omorphism classes. We also present explicit constructions of hyperelliptic
Jacobian varieties with rational torsion points of prescribed order.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Syed Waqar Ali Shah (Bilkent)
DTSTART:20251128T124000Z
DTEND:20251128T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/75
DESCRIPTION:Title: Euler systems for exterior square motives\nby Syed Waqar Ali Sha
h (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nThe Birch–Swinnerton-Dyer conjecture relates the behavior of the L-
function of an elliptic curve at its central point to the rank of its grou
p of rational points. The Bloch–Kato conjecture generalizes this princip
le to a broad family of motivic Galois representations\, predicting a prec
ise relationship between the order of vanishing of motivic L-functions at
integer values and the structure of the associated Selmer groups. Since th
e foundational work of Kolyvagin in the nineties\, Euler systems have play
ed a central role in approaching these conjectures\, and in recent years t
heir scope has expanded significantly within the automorphic setting of Sh
imura varieties.\n\nIn this talk\, I will focus on unitary Shimura varieti
es GU(2\,2)\, whose middle-degree cohomology realizes the exterior square
of the four-dimensional Galois representations attached to certain automor
phic representations of GL_4. The period integral formula of Pollack–Sha
h for exterior square L-functions has a natural motivic interpretation\, s
uggesting the feasibility of constructing a nontrivial Euler system. A key
obstacle to this construction is the failure of a suitable multiplicity-o
ne property\, which has long prevented the verification of the certain nor
m relations required for Euler system methods. I will present a new approa
ch that overcomes this difficulty. The resulting Euler system in the middl
e-degree cohomology of GU(2\,2) provides the first nontrivial evidence tow
ard the Bloch–Kato conjecture for exterior square motives and opens seve
ral promising avenues for further arithmetic applications. This is joint w
ork with Andrew Graham and Antonio Cauchi.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nil Şahin (Bilkent)
DTSTART:20251205T124000Z
DTEND:20251205T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/76
DESCRIPTION:Title: Numerical semigroups with multiplicity one more than its width\n
by Nil Şahin (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminar
s\n\n\nAbstract\nA numerical semigroup S is called Sally type if its multi
plicity is one more than its width. In this talk\, we will analyze the pro
perties of numerical semigroups of Sally type with embedding dimension $e-
1$ and $e-2$ where $e$ denotes the multiplicity. We compute the minimal
number of generators of the defining ideal using Hochster's Formula then w
e determine the minimal generators.\n\nJoint work with Dubey\, Goel\, Sing
h and Srinivasan\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20251212T124000Z
DTEND:20251212T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/77
DESCRIPTION:Title: Automorphisms of sextic $K3$-surfaces\nby Alexander Degtyarev (B
ilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\
n$K3$-surfaces play the role of elliptic curves in the realm of algebraic
surfaces. They are sophisticated enough to produce interesting and meaning
ful results that may hint possible generalizations\, yet simple enough to
make their study feasible. One remarkable feature of $K3$-surfaces is that
\, among all complete intersections of dimension at least two\, they are t
he only ones whose group of projective automorphisms may (and typically is
) much smaller than their group of birational automorphisms.\n\nI will dis
cuss a particular example of sextic $K3$-surfaces and a particular constru
ction of non-projective automorphisms\, related to lines. In particular\,
it will be shown that\, whenever a sextic has at least two lines\, its gro
up of birational automorphisms is infinite.\n\nThis is a joint work with I
gor Dolgachev\, Shigeyuki Kondo\, and Slawomir Rams.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Öznur Turhan (Galatasaray & Polish Academy)
DTSTART:20260220T124000Z
DTEND:20260220T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/78
DESCRIPTION:Title: Newton-nondegenerate line singularities\, Lê numbers and Bekka (c)-
regularity\nby Öznur Turhan (Galatasaray & Polish Academy) as part of
ODTU-Bilkent Algebraic Geometry Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meral Tosun (Galatasaray)
DTSTART:20260227T124000Z
DTEND:20260227T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/79
DESCRIPTION:Title: McKay quivers Beyond ADE\nby Meral Tosun (Galatasaray) as part o
f ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe classical Mc
Kay correspondence relates finite subgroups of SL(2\,C) to affine ADE Dynk
in diagrams and Du Val surface singularities. In this talk\, we extend thi
s perspective to small finite subgroups of GL(2\,C) whose quotients produc
e isolated surface singularities. Using character theory and a product for
mula for McKay quivers\, we give an explicit description of the quivers as
sociated with the natural two-dimensional representation.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierrick Bousseau (Oxford)
DTSTART:20260306T124000Z
DTEND:20260306T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/80
DESCRIPTION:Title: BPS polynomials and Welschinger invariants\nby Pierrick Bousseau
(Oxford) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nUsing tropical geometry\, Block-Göttsche defined polynomials with the
remarkable property to interpolate between Gromov-Witten counts of complex
curves and Welschinger counts of real curves in toric del Pezzo surfaces.
I will describe a generalization of Block-Göttsche polynomials to arbitr
ary\, not-necessarily toric\, rational surfaces and propose a conjectural
relation with refined Donaldson-Thomas invariants. This is joint work with
Hulya Arguz.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Ancona (Côte d'Azur)
DTSTART:20260313T124000Z
DTEND:20260313T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/81
DESCRIPTION:Title: Harnack manifolds\nby Michele Ancona (Côte d'Azur) as part of O
DTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn 1876\, Axel Harn
ack proved in a foundational article that\n\n1) every real algebraic curve
of degree d in RP^2 has at most (d-1)(d-2)/2 + 1 connected components\;\n
\n2) for every d there exists a curve of degree d with exactly this number
of connected components.\n\n\nOver the past 150 years\, these results hav
e played a central role in the study of the topology of real algebraic var
ieties. The first part of Harnack’s theorem generalizes to the so-called
Smith–Floyd inequality for arbitrary real algebraic varieties: the sum
of the Betti numbers of the real part is at most the corresponding sum for
the complex part. Despite spectacular advances\, the generalization of th
e second part of Harnack’s theorem remains open in the case of projectiv
e hypersurfaces.\n\nFor these\, however\, Ilia Itenberg and Oleg Viro show
ed that the Smith–Floyd inequality is asymptotically optimal by using th
e combinatorial patchworking technique. In joint work with Erwan Brugallé
and Jean-Yves Welschinger\, we show that an elementary generalization of
Harnack’s original construction method in dimension 2 yields this asympt
otic optimality for any ample line bundle on a real algebraic variety. Bey
ond Betti numbers\, we also describe the diffeomorphism type of an open su
bset of these topologically rich varieties.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mesut Şahin (Hacettepe)
DTSTART:20260327T124000Z
DTEND:20260327T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/82
DESCRIPTION:Title: Grobner Bases and Linear Codes on Weighted Projective Planes\nby
Mesut Şahin (Hacettepe) as part of ODTU-Bilkent Algebraic Geometry Semin
ars\n\n\nAbstract\nLet $F$ be the finite field with $q$ elements and $K$ b
e its algebraic closure. The ring $S=F[x_0\,x_1\,x_2]$ is graded via $\\de
g(x_i)=w_i$\, for $i=0\,1\,2$\, where $w_0\, w_1$ and $w_2$ generate a num
erical semigroup! We study some linear codes obtained from the weighted pr
ojective plane $P(w_0\,w_1\,w_2)$ over $K$.\n\nWe get a linear code by eva
luating homogeneous polynomials of degree $d$ at the subset $Y\\{ P_1\,..
.\,P_N\\}$ of $F$-rational points\, which defines the evaluation map: $f \
\mapsto (f(P_1)\,...f(P_N))$. The image is a subspace of $F^N$\, which is
called a weighted projective Reed-Muller (WPRM) code. Its length is $|Y|=N
=q^2+q+1$. In the present talk\, we discuss how Grobner theory is used for
studying the other two parameters: the dimension and the minimum distance
extending and generalizing the results scattered throughout the literatur
e. We also determine the regularity set which helps eliminating the trivia
l codes as well as giving a lower bound for the minimum distance.\n\nThis
is a joint work with Yağmur Çakıroğlu (Hacettepe University) and Jade
Nardi (Université de Rennes 1).\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Villaflor Loyola (Universidad Técnica Federico Santa Mar
ía)
DTSTART:20260403T124000Z
DTEND:20260403T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/83
DESCRIPTION:Title: On the linear cycles conjecture\nby Roberto Villaflor Loyola (Un
iversidad Técnica Federico Santa María) as part of ODTU-Bilkent Algebrai
c Geometry Seminars\n\n\nAbstract\nThe classical Noether-Lefschetz theorem
claims that a very general degree $d>3$ surface in $\\mathbb{P}^3$ has Pi
card number one. The locus of surfaces with higher Picard rank is known as
the Noether-Lefschetz locus\, which is known to have a countable number o
f irreducible components. For $d>4$\, it is classical result due independe
ntly to Green and Voisin\, that the unique component of highest codimensio
n corresponds to the locus of surfaces which contain lines. \n\nThe natura
l generalization of this question to higher dimensional hypersurfaces of t
he projective space is known as the "linear cycles conjecture"\,
and remains open even for fourfolds. For surfaces\, the proof is based in
the fact that locally (analytically) one can parametrize each component by
a Hodge locus\, and then use the Infinitesimal Variation of Hodge Structu
re to compute (and bound) the dimension of its Zariski tangent space. \n\n
A natural stronger version of the linear cycles conjecture is that the Hod
ge loci with maximal tangent space are those corresponding to linear cycle
s. \n\nIn this talk I will report on recent results disproving this conjec
ture for all degrees and dimensions. \n\nThis is a joint work with Jorge D
uque Franco.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART:20260417T124000Z
DTEND:20260417T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/84
DESCRIPTION:by Alexander Degtyarev (Bilkent) as part of ODTU-Bilkent Algeb
raic Geometry Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Leopold Knutsen (Bergen)
DTSTART:20260424T124000Z
DTEND:20260424T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/85
DESCRIPTION:by Andreas Leopold Knutsen (Bergen) as part of ODTU-Bilkent Al
gebraic Geometry Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Chitayat (Padova)
DTSTART:20260410T124000Z
DTEND:20260410T134000Z
DTSTAMP:20260404T110828Z
UID:OBAGS/86
DESCRIPTION:Title: Borel subgroups of $\\rm{Aut}(\\mathbb{A}^n)$\nby Michael Chitay
at (Padova) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nLet $X$ be an affine variety. It was recently proved that a connected
solvable $G\\subseteq \\rm{Aut}(X)$ can be decomposed as a semi-direct pr
oduct $G=T\\ltimes U$ where $T$ is an algebraic torus and $U$ is a nested
unipotent subgroup. A $\\textit{Borel Subgroup of}$ $\\rm{Aut}(X)$ is a ma
ximal element of the set of connected solvable subgroups of $\\rm{Aut}(X)$
. In this talk I will discuss Borel subgroups of $\\rm{Aut}(X)$ with a foc
us on the special case where $X=\\mathbb{A}^n$.\n\nThis is joint work with
Andriy Regeta and Daniel Daigle.\n
LOCATION:https://stable.researchseminars.org/talk/OBAGS/86/
END:VEVENT
END:VCALENDAR