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BEGIN:VEVENT
SUMMARY:Ilia Itenberg (imj-prg)
DTSTART;VALUE=DATE-TIME:20220304T124000Z
DTEND;VALUE=DATE-TIME:20220304T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/1
DESCRIPTION:Title: Re
al enumerative invariants and their refinement\nby Ilia Itenberg (imj-
prg) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nTh
e talk is devoted to several real and tropical enumerative problems. We su
ggest new invariants of the projective plane (and\, more generally\, of to
ric surfaces) that arise as results of an appropriate enumeration of real
elliptic curves.\nThese invariants admit a refinement (according to the qu
antum index) similar to the one introduced by Grigory Mikhalkin in the rat
ional case. We discuss tropical counterparts of the elliptic invariants un
der consideration and establish a tropical algorithm allowing one to compu
te them.\nThis is a joint work with Eugenii Shustin.\n
LOCATION:https://researchseminars.org/talk/OBAGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART;VALUE=DATE-TIME:20220311T124000Z
DTEND;VALUE=DATE-TIME:20220311T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/2
DESCRIPTION:Title: To
wards 800 conics on a smooth quartic surfaces\nby Alexander Degtyarev
(Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nThis will be a technical talk where I will discuss a few computational
aspects of my work in progress towards the following conjecture.\n\nConjec
ture: A smooth quartic surface in P3 may contain at most 800 conics.\n\nI
will suggest and compare several arithmetical reductions of the problem. T
hen\, for the chosen one\, I will discuss a few preliminary combinatorial
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 the conj
ecture holds. However\, I am trying to find all smooth quartics containing
720 or more conics\, in the hope to find the real quartic maximizing 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 s
mooth 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 conics or\
, equivalently\, are not Kummer surfaces with all 16 Kummer divisors conic
s.\n
LOCATION:https://researchseminars.org/talk/OBAGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Schütt (Hannover)
DTSTART;VALUE=DATE-TIME:20220318T124000Z
DTEND;VALUE=DATE-TIME:20220318T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/3
DESCRIPTION:Title: Fi
nite symplectic automorphism groups of supersingular K3 surfaces\nby M
atthias Schütt (Hannover) as part of ODTU-Bilkent Algebraic Geometry Semi
nars\n\n\nAbstract\nAutomorphism groups form a classical object of study i
n algebraic geometry. In recent years\, a special focus has been put on au
tomorphisms of K3 surface\, the most famous example being Mukai’s classi
fication of finite symplectic automorphism groups on complex K3 surfaces.
Building on work of Dolgachev-Keum\, I will discuss a joint project with H
isanori Ohashi (Tokyo) extending Mukai’s results to fields positive char
acteristic. Notably\, we will retain the close connection to the Mathieu g
roup M23 while realizing many larger groups compared to the complex settin
g.\n
LOCATION:https://researchseminars.org/talk/OBAGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Can Sertöz (Hannover)
DTSTART;VALUE=DATE-TIME:20220325T124000Z
DTEND;VALUE=DATE-TIME:20220325T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/4
DESCRIPTION:Title: He
ights\, periods\, and arithmetic on curves\nby Emre Can Sertöz (Hanno
ver) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nTh
e size of an explicit representation of a given rational point on an algeb
raic curve is captured by its canonical height. However\, the canonical he
ight is defined through the dynamics on the Jacobian and is not particular
ly accessible to computation. In 1984\, Faltings related the canonical hei
ght 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 hig
her dimensions is inaccessible to computation. We present a new method for
computing heights that promises to generalize well to higher dimensions.
This is joint work with Spencer Bloch and Robin de Jong.\n
LOCATION:https://researchseminars.org/talk/OBAGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Halil İbrahim Karakaş (Başkent)
DTSTART;VALUE=DATE-TIME:20220401T124000Z
DTEND;VALUE=DATE-TIME:20220401T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/5
DESCRIPTION:Title: Ar
f Partitions of Integers\nby Halil İbrahim Karakaş (Başkent) as par
t of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nThe colection
of partitions of positive integers\, the collection of Young diagrams and
the collection of numerical sets are in one to one correspondance with ea
ch other. Therefore any concept in one of these collections has its counte
rpart in the other collections. For example the concept of Arf numerical s
emigroup in the collection of numerical sets\, gives rise to the concept o
f Arf partition of a positive integer in the collection of partitions. Sev
eral characterizations of Arf partitions have been given in recent works.
In this talk we wil characterize Arf partitions of maximal length of posit
ive integers.\nThis is a joint work with Nesrin Tutaş and Nihal Gümüşb
aş from Akdeniz University.\n
LOCATION:https://researchseminars.org/talk/OBAGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yıldıray Ozan (ODTÜ)
DTSTART;VALUE=DATE-TIME:20220408T124000Z
DTEND;VALUE=DATE-TIME:20220408T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/6
DESCRIPTION:Title: Pi
card Groups of the Moduli Spaces of Riemann Surfaces with Certain Finite A
belian Symmetry Groups\nby Yıldıray Ozan (ODTÜ) as part of ODTU-Bil
kent Algebraic Geometry Seminars\n\n\nAbstract\nIn 2021\, H. Chen determin
ed all finite abelian regular branched covers of the 2-sphere with the pro
perty that all homeomorphisms of the base preserving the branch set lift t
o the cover\, extending the previous works of Ghaswala-Winarski and Atalan
-Medettoğulları-Ozan. In this talk\, we will present a consequence of th
is classification to the computation of Picard groups of moduli spaces of
complex projective curves with certain symmetries. Indeed\, we will use th
e work by K. Kordek already used by him for similar computations. During t
he talk we will try to explain the necessary concepts and tools following
Kordek's work.\n
LOCATION:https://researchseminars.org/talk/OBAGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Ulaş Özgür Kişisel (ODTÜ)
DTSTART;VALUE=DATE-TIME:20220415T124000Z
DTEND;VALUE=DATE-TIME:20220415T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/7
DESCRIPTION:Title: An
upper bound on the expected areas of amoebas of plane algebraic curves\nby Ali Ulaş Özgür Kişisel (ODTÜ) as part of ODTU-Bilkent Algebraic
Geometry Seminars\n\n\nAbstract\nThe amoeba of a complex plane algebraic
curve has an area bounded above by $\\pi^2 d^2/2$. This is a deterministic
upper bound due to Passare and Rullgard. In this talk I will argue that i
f the plane curve is chosen randomly with respect to the Kostlan distribut
ion\, then the expected area cannot be more than $\\mathcal{O}(d)$. The re
sults in the talk will be based on our joint work in progress with Turgay
Bayraktar.\n
LOCATION:https://researchseminars.org/talk/OBAGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammed Uludağ (Galatasaray)
DTSTART;VALUE=DATE-TIME:20220422T124000Z
DTEND;VALUE=DATE-TIME:20220422T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/8
DESCRIPTION:Title: He
yula\nby Muhammed Uludağ (Galatasaray) as part of ODTU-Bilkent Algebr
aic Geometry Seminars\n\n\nAbstract\nThis talk is about the construction o
f a space H and its boundary on which the group PGL(2\,Q) acts. The ultima
te aim is to recover the action of PSL(2\,Z) on the hyperbolic plane as a
kind of boundary action.\n
LOCATION:https://researchseminars.org/talk/OBAGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melih Üçer (Yıldırım Beyazıt)
DTSTART;VALUE=DATE-TIME:20220429T124000Z
DTEND;VALUE=DATE-TIME:20220429T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/9
DESCRIPTION:Title: Bu
rau Monodromy Groups of Trigonal Curves\nby Melih Üçer (Yıldırım
Beyazıt) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nFor a trigonal curve on a Hirzebruch surface\, there are several notion
s of monodromy ranging from a very coarse one in S_3 to a very fine one in
a certain subgroup of Aut(F_3)\, and one group in this range is PSL(2\,Z)
. Except for the special case of isotrivial curves\, the monodromy group (
the subgroup generated by all monodromy actions) in PSL(2\,Z) is a subgrou
p of genus-zero and conversely any genus-zero subgroup is the monodromy gr
oup of a trigonal curve (This is a result of Degtyarev).\n\nA slightly fin
er notion in the same range is the monodromy in the Burau group Bu_3. The
aforementioned result of Degtyarev imposes obvious restrictions on the mon
odromy group in this case but without a converse result. Here we show that
there are additional non-obvious restrictions as well and\, with these re
strictions\, we show the converse as well.\n
LOCATION:https://researchseminars.org/talk/OBAGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Sutherland (MIT)
DTSTART;VALUE=DATE-TIME:20221014T124000Z
DTEND;VALUE=DATE-TIME:20221014T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/10
DESCRIPTION:Title: S
ato-Tate groups of abelian varieties\nby Andrew Sutherland (MIT) as pa
rt of ODTU-Bilkent Algebraic Geometry Seminars\n\nLecture held in ODTÜ Ma
thematics department Room M-203.\n\nAbstract\nLet A be an abelian variety
of dimension g defined over a number field K. As defined by Serre\, the S
ato-Tate group ST(A) is a compact subgroup of the unitary symplectic group
USp(2g) equipped with a map that sends each Frobenius element of the abso
lute Galois group of K at primes p of good reduction for A to a conjugacy
class of ST(A) whose characteristic polynomial is determined by the zeta f
unction of the reduction of A at p. Under a set of axioms proposed by Ser
re that are known to hold for g <= 3\, up to conjugacy in Usp(2g) there is
a finite list of possible Sato-Tate groups that can arise for abelian var
ieties of dimension g over number fields. Under the Sato-Tate conjecture
(which is known for g=1 when K has degree 1 or 2)\, the asymptotic distrib
ution of normalized Frobenius elements is controlled by the Haar measure o
f the Sato-Tate group.\n\nIn this talk I will present a complete classific
ation of the Sato-Tate groups that can and do arise for g <= 3.\n\nThis is
joint work with Francesc Fite and Kiran Kedlaya.\n\nThis is a hybrid talk
. To request Zoom link please write to sertoz@bilkent.edu.tr\n
LOCATION:https://researchseminars.org/talk/OBAGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART;VALUE=DATE-TIME:20221021T124000Z
DTEND;VALUE=DATE-TIME:20221021T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/11
DESCRIPTION:Title: M
cKay correspondence I\nby Emre Coşkun (METU) as part of ODTU-Bilkent
Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics departmen
t Room M-203.\n\nAbstract\nJohn McKay observed\, in 1980\, that there is a
one-to-one correspondence between the nontrivial finite subgroups of SU(2
) (up to conjugation) and connected Euclidean graphs (other than the Jorda
n graph) up to isomorphism. In these talk\, we shall first examine the fin
ite subgroups of SU(2) and then establish this one-to-one correspondence\,
using the representation theory of finite groups.\n\nThis is a hybrid tal
k. To request a Zoom link please write to sertoz@bilkent.edu.tr\n
LOCATION:https://researchseminars.org/talk/OBAGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Coşkun (METU)
DTSTART;VALUE=DATE-TIME:20221104T124000Z
DTEND;VALUE=DATE-TIME:20221104T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/12
DESCRIPTION:Title: M
cKay correspondence II\nby Emre Coşkun (METU) as part of ODTU-Bilkent
Algebraic Geometry Seminars\n\nLecture held in ODTÜ Mathematics Departme
nt Room M-203.\n\nAbstract\nLet $G \\subset SU(2)$ be a finite subgroup co
ntaining $-I$\, and let \n$Q$ be the corresponding Euclidean graph. Given
an orientation on $Q$\, \none can define the (bounded) derived category of
the representations \nof the resulting quiver. Let $\\bar{G} = G / {\\pm
I}$. Then one can \nalso define the category $Coh_{\\bar{G}}(\\mathbb{P}^1
)$ of \n$\\bar{G}$-equivariant coherent sheaves on the projective line\; t
his \nabelian category also has a (bounded) derived category. In the secon
d \nof these talks dedicated to the McKay correspondence\, we establish an
\nequivalence between the two derived categories mentioned above.\n\nThis
is a hybrid talk. To request Zoom link please write to sertoz@bilkent.edu
.tr.\n
LOCATION:https://researchseminars.org/talk/OBAGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emre Can Sertöz (Hannover)
DTSTART;VALUE=DATE-TIME:20221111T124000Z
DTEND;VALUE=DATE-TIME:20221111T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/13
DESCRIPTION:Title: C
omputing limit mixed Hodge structures\nby Emre Can Sertöz (Hannover)
as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nConside
r a smooth family of varieties over a punctured disk that is extended to a
flat family over the whole disk\, e.g.\, consider a 1-parameter family of
hypersurfaces with a central singular fiber. The Hodge structures (i.e. p
eriods) of smooth fibers exhibit a divergent behavior as you approach the
singular fiber. However\, Schmid's nilpotent orbit theorem states that thi
s divergence can be "regularized" to construct a limit mixed Hodge structu
re. This limit mixed Hodge structure contains detailed information about t
he geometry and arithmetic of the singular fiber. I will explain how one c
an compute such limit mixed Hodge structures in practice and give a demons
tration of my code.\n
LOCATION:https://researchseminars.org/talk/OBAGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Müfit Sezer (Bilkent)
DTSTART;VALUE=DATE-TIME:20221118T124000Z
DTEND;VALUE=DATE-TIME:20221118T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/14
DESCRIPTION:Title: V
ector invariants of a permutation group over characteristic zero\nby M
üfit Sezer (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\
n\n\nAbstract\nWe consider a finite permutation group acting naturally on
a vector space V over a field k. A well known theorem of Göbe
l asserts that the corresponding ring of invariants k[V]^G is genera
ted by invariants of degree at most dim V choose 2. We point out th
at if the characteristic of k is zero then the top degree of the vec
tor coinvariants k[mV]_G is also bounded above by n choose 2 i
mplying that Göbel's bound almost holds for vector invariants as well in
characteristic zero.\nThis work is joint with F. Reimers.\n
LOCATION:https://researchseminars.org/talk/OBAGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Cesare Veniani (Stuttgart)
DTSTART;VALUE=DATE-TIME:20221125T124000Z
DTEND;VALUE=DATE-TIME:20221125T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/15
DESCRIPTION:Title: N
on-degeneracy of Enriques surfaces\nby Davide Cesare Veniani (Stuttgar
t) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nEnri
ques' original construction of Enriques surfaces involves a 10-dimensional
family of sextic surfaces in the projective space which are non-normal al
ong the edges of a tetrahedron. The question whether all Enriques surfaces
arise through Enriques' construction has remained open for more than a ce
ntury.\n\nIn two joint works with G. Martin (Bonn) and G. Mezzedimi (Hanno
ver)\, we have now settled this question in all characteristics by studyin
g particular configurations of genus one fibrations\, and two invariants c
alled maximal and minimal non-degeneracy. The proof involves so-called `tr
iangle graphs' and the distinction between special and non-special 3-seque
nces of half-fibers.\n\nIn this talk\, I will present the problem and expl
ain its solution\, illustrating further possible developments and applicat
ions.\n
LOCATION:https://researchseminars.org/talk/OBAGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Karaoğlu (Gebze Teknik)
DTSTART;VALUE=DATE-TIME:20221202T124000Z
DTEND;VALUE=DATE-TIME:20221202T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/16
DESCRIPTION:Title: S
mooth cubic surfaces with 15 lines\nby Fatma Karaoğlu (Gebze Teknik)
as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIt is w
ell-known that a smooth cubic surface has 27 lines over an algebraically c
losed field. If the field is not closed\, however\, fewer lines are possib
le. The next possible case is that of smooth cubic surfaces with 15 lines.
This work is a contribution to the problem of classifying smooth cubic su
rfaces with 15 lines over fields of positive characteristic. We present an
algorithm to classify such surfaces over small finite fields. Our classif
ication 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. Classi
fication results for fields of order at most 13 are presented and a verifi
cation using an enumerative formula of Das is performed. Our work is based
on a generalization of the old result due to Cayley and Salmon that there
are 27 lines if the field is algebraically closed.\n\n Smooth cubic surfa
ces with 15 lines\n
LOCATION:https://researchseminars.org/talk/OBAGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Meral Tosun (Galatasaray)
DTSTART;VALUE=DATE-TIME:20221209T124000Z
DTEND;VALUE=DATE-TIME:20221209T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/17
DESCRIPTION:Title: J
ets schemes and toric embedded resolution of rational triple points\nb
y Meral Tosun (Galatasaray) as part of ODTU-Bilkent Algebraic Geometry Sem
inars\n\n\nAbstract\nOne of the aims of J.Nash in an article on the arcs s
paces (1968) was to understand resolutions of singularities via the arcs l
iving 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 essential divis
ors on every resolution. J.Fernandez de Bobadilla and M.Pe Pereira (2011)
have shown his conjecture\, but the proof is not constructive to get the r
esolution from the arc space. We will construct an embedded toric resoluti
on of singularities of type rtp from the irreducible components of the jet
schemes.\n\nThis is a joint work with B.Karadeniz\, H. Mourtada and C.Ple
nat.\n
LOCATION:https://researchseminars.org/talk/OBAGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Özhan Genç (Jagiellonian)
DTSTART;VALUE=DATE-TIME:20221216T124000Z
DTEND;VALUE=DATE-TIME:20221216T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/18
DESCRIPTION:Title: F
inite Length Koszul Modules and Vector Bundles\nby Özhan Genç (Jagie
llonian) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract
\nLet $V$ be a complex vector space of dimension $n\\ge 2$ and $K$ be a s
ubset of $\\bigwedge^2V$ of dimension $m$. Denote the Koszul module by $W(
V\,K)$ and its corresponding resonance variety by $\\mathcal R(V\,K)$. Pap
adima and Suciu showed that there exists a uniform bound $q(n\,m)$ such th
at 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 t
his talk\, we will determine this bound $q(n\,m)$ precisely\, and find an
upper bound for the Hilbert series of these Koszul modules. Then we will c
onsider a class of Koszul modules associated to vector bundles.\n
LOCATION:https://researchseminars.org/talk/OBAGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Salvatore Floccari (Hannover)
DTSTART;VALUE=DATE-TIME:20230303T124000Z
DTEND;VALUE=DATE-TIME:20230303T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/19
DESCRIPTION:Title: S
ixfolds of generalized Kummer type and K3 surfaces\nby Salvatore Flocc
ari (Hannover) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAb
stract\nThe classical Kummer construction associates a K3 surface to any 2
-dimensional complex torus. In my talk I will present an analogue of this
construction\, which involves the two most well-studied deformation types
of hyper-Kähler manifolds in dimension 6. Namely\, starting from any hype
r-Kähler sixfold K of generalized Kummer type\, I am able to construct ge
ometrically a hyper-Kähler manifold of K3^[3]-type. When K is projective\
, the associated variety is birational to a moduli space of sheaves on a u
niquely determined K3 surface. As application of this construction I will
show that the Kuga-Satake correspondence is algebraic for many K3 surfaces
of Picard rank 16.\n
LOCATION:https://researchseminars.org/talk/OBAGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominico Valloni (Hannover)
DTSTART;VALUE=DATE-TIME:20230310T124000Z
DTEND;VALUE=DATE-TIME:20230310T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/20
DESCRIPTION:Title: R
ational points on the Noether-Lefschetz locus of K3 moduli spaces\nby
Dominico Valloni (Hannover) as part of ODTU-Bilkent Algebraic Geometry Sem
inars\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 parametriz
es K3 surfaces $X$ together with a primitive embedding of lattices $L \\ho
okrightarrow \\mathrm{NS}(X)$ 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 given $\\o
verline{ \\mathbb{Q}}$-point of $\\mathcal{F}_L$ has generic Néron-Sever
i lattice (that is\, $\\mathrm{NS}(X) \\cong L$). The criterion is of arit
hmetic nature and only uses properties of covering maps between Shimura va
rieties.\n
LOCATION:https://researchseminars.org/talk/OBAGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slawomir Rams (Jagiellonian)
DTSTART;VALUE=DATE-TIME:20230317T124000Z
DTEND;VALUE=DATE-TIME:20230317T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/21
DESCRIPTION:Title: O
n maximal number of rational curves of bounded degree on certain surfaces
\nby Slawomir Rams (Jagiellonian) as part of ODTU-Bilkent Algebraic Ge
ometry Seminars\n\n\nAbstract\nI will discuss bounds on the number of rati
onal curves of fixed degree on surfaces of various types with special emph
asis on polarized Enriques surfaces. In particular\, I will sketch the pro
of 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. Schue
tt (Hannover)).\n
LOCATION:https://researchseminars.org/talk/OBAGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Türkü Özlüm Çelik (Boğaziçi)
DTSTART;VALUE=DATE-TIME:20230324T124000Z
DTEND;VALUE=DATE-TIME:20230324T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/22
DESCRIPTION:Title: S
ingular curves and their theta functions\nby Türkü Özlüm Çelik (B
oğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstra
ct\nRiemann's theta function becomes polynomial when the underlying curve
degenerates to a singular curve. We will give a classification of such cur
ves accompanied by historical remarks on the topic. We will touch on relat
ions of such theta functions with solutions of the Kadomtsev-Petviashvili
hierarchy if time permits.\n
LOCATION:https://researchseminars.org/talk/OBAGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tolga Karayayla (ODTÜ)
DTSTART;VALUE=DATE-TIME:20230331T124000Z
DTEND;VALUE=DATE-TIME:20230331T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/23
DESCRIPTION:Title: O
n a class of non-simply connected Calabi-Yau 3-folds with positive Euler c
haracteristic-Part 1\nby Tolga Karayayla (ODTÜ) as part of ODTU-Bilke
nt Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will present
a class of non-simply connected Calabi-Yau 3-folds with positive Euler cha
racteristic which are the quotient spaces of fixed-point-free group action
s on desingularizations of singular Schoen 3-folds. A Schoen 3-fold is the
fiber product of two rational elliptic surfaces with section. Smooth Scho
en 3-folds are simply connected CY 3-folds. Desingularizations of certain
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 automor
phism groups of rational elliptic surfaces with section. The smooth Schoen
3-fold case gives 0 Euler characteristic whereas the singular case result
s in positive Euler characteristic for the quotient CY threefolds.\n
LOCATION:https://researchseminars.org/talk/OBAGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tolga Karayayla (ODTÜ)
DTSTART;VALUE=DATE-TIME:20230407T124000Z
DTEND;VALUE=DATE-TIME:20230407T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/24
DESCRIPTION:Title: O
n a class of non-simply connected Calabi-Yau 3-folds with positive Euler c
haracteristic-Part 2\nby Tolga Karayayla (ODTÜ) as part of ODTU-Bilke
nt Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk I will present
a class of non-simply connected Calabi-Yau 3-folds with positive Euler cha
racteristic which are the quotient spaces of fixed-point-free group action
s on desingularizations of singular Schoen 3-folds. A Schoen 3-fold is the
fiber product of two rational elliptic surfaces with section. Smooth Scho
en 3-folds are simply connected CY 3-folds. Desingularizations of certain
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 automor
phism groups of rational elliptic surfaces with section. The smooth Schoen
3-fold case gives 0 Euler characteristic whereas the singular case result
s in positive Euler characteristic for the quotient CY threefolds.\n
LOCATION:https://researchseminars.org/talk/OBAGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig van Coevering (Boğaziçi)
DTSTART;VALUE=DATE-TIME:20230414T124000Z
DTEND;VALUE=DATE-TIME:20230414T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/25
DESCRIPTION:Title: E
xtremal Kähler metrics and the moment map\nby Craig van Coevering (Bo
ğaziçi) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstrac
t\nAn extremal Kähler metric is a canonical Kähler metric\, introduced b
y E.\nCalabi\, which is somewhat more general than a constant scalar curva
ture Kähler metric. The existence of such a metric is an ongoing research
subject and expected to be equivalent to some form of geometric stability
of the underlying polarized complex manifold $(M\, J\, [\\omega])$ –the
Yau-Tian-Donaldson Conjecture. Thus it is no surprise that there is a mo
ment map\, the scalar curvature (A. Fujiki\, S. Donaldson)\, and the probl
em can be described as an infinite dimensional version of the familiar fin
ite dimensional G.I.T.\n\nI will describe how the moment map can be used t
o describe the local space of extremal metrics on a symplectic manifold. E
ssentially\, the local picture can be reduced to finite dimensional G.I.T.
In particular\, we can construct a course moduli space of extremal Kähle
r metrics with a fixed polarization $[\\omega] \\in H^2(M\, \\mathbb{R})$
\, which is an Hausdorff complex analytic space\n
LOCATION:https://researchseminars.org/talk/OBAGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mesut Şahin (Hacettepe)
DTSTART;VALUE=DATE-TIME:20230428T120000Z
DTEND;VALUE=DATE-TIME:20230428T130000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/26
DESCRIPTION:Title: V
anishing ideals and codes on toric varieties\nby Mesut Şahin (Hacette
pe) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nMot
ivated by applications to the theory of error-correcting codes\, we give a
n algorithmic method for computing a generating set for the ideal generate
d by $\\beta$-graded polynomials vanishing on a subset of a simplicial com
plete toric variety $X$ over a finite field $\\mathbb{F}_q$\, parameterize
d by rational functions\, where $\\beta$ is a $d\\times r$ matrix whose co
lumns generate a subsemigroup $\\mathbb{N}\\beta$ of $\\mathbb{N}^d$. We a
lso give a method for computing the vanishing ideal of the set of $\\mathb
b{F}_q$-rational points of $X$. We talk about some of its algebraic invari
ants related to basic parameters of the corresponding evaluation code. Whe
n $\\beta=[w_1 \\cdots w_r]$ is a row matrix corresponding to a numerical
semigroup $\\mathbb{N}\\beta=\\langle w_1\,\\dots\,w_r \\rangle$\, $X$ is
a weighted projective space and generators of its vanishing ideal is relat
ed to the generators of the defining (toric) ideals of some numerical semi
group rings corresponding to semigroups generated by subsets of $\\{w_1\,\
\dots\,w_r\\}$.\n
LOCATION:https://researchseminars.org/talk/OBAGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ekin Ozman (Boğaziçi)
DTSTART;VALUE=DATE-TIME:20230505T124000Z
DTEND;VALUE=DATE-TIME:20230505T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/27
DESCRIPTION:Title: T
he p ranks of Prym varieties\nby Ekin Ozman (Boğaziçi) as part of OD
TU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn this talk we will
start with basics of moduli space of curves\, coverings of curves\, p-ran
ks and mention the differences in characteristics 0 and positive character
istics.Then we'll define Prym variety which is a central object of study i
n arithmetic geometry like Jacobian variety. The goal of the talk is to u
nderstand various existence results about Prym varieties of given genus\,
p-rank and characteristics of the base field. This is joint work with Rach
el Pries.\n
LOCATION:https://researchseminars.org/talk/OBAGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART;VALUE=DATE-TIME:20230512T124000Z
DTEND;VALUE=DATE-TIME:20230512T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/28
DESCRIPTION:Title: C
ounting lines on polarized K3-surfaces\nby Alexander Degtyarev (Bilken
t) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nCoun
ting or estimating the number of lines or\, more generally\, low degree\nr
ational curves on a polarized algebraic surface is a classical problem goi
ng\nback almost 1.5 centuries. After a brief historical excurse\, I will t
ry to\ngive an account of the considerable progress made in the subject in
the last\ndecade or so\, mainly related to various (quasi-)polarizations
of\n$K3$-surfaces: \n\n$\\bullet$\nlines on $K3$-surfaces with any polariz
ation\,\n\n$\\bullet$\nlines on low degree $K3$-surfaces with singularitie
s\,\n\n$\\bullet$\nconics on low degree $K3$-surfaces.\n\nIf time permits\
, I will briefly discuss other surfaces/varieties as well.\n\nSome parts o
f this work are joint projects\n(some still in progress) with Ilia Itenber
g\, Slavomir Rams\, Ali\nSinan Sertöz.\n
LOCATION:https://researchseminars.org/talk/OBAGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Degtyarev (Bilkent)
DTSTART;VALUE=DATE-TIME:20231013T124000Z
DTEND;VALUE=DATE-TIME:20231013T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/30
DESCRIPTION:Title: S
ingular real plane sextic curves without real points\nby Alexander Deg
tyarev (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\n(joint with Ilia Itenberg)\nIt is a common understanding that an
y reasonable geometric question about K3\n-surfaces can be restated and so
lved in purely arithmetical terms\, by means of an appropriately defined h
omological type. For example\, this works well in the study of singular co
mplex sextic curves in P2 or quartic surfaces in P3 (see [1\,2])\, as we
ll as in that of smooth real ones (see [4\,6]). However\, when the two are
combined (both singular and real curves or surfaces)\, the approach fails
as the `"obvious'' concept of homological type does not fully reflect 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 generall
y\, have no real singular points\; then\, one can indeed confine oneself t
o the homological types consisting of the exceptional divisors\, polarizat
ion\, and real structure.\n\nStill\, the resulting arithmetical problem is
not quite straightforward\, but we manage to solve it and obtain a satisf
actory classification in the case of empty real part\; it matches all know
n results obtained by an alternative purely geometric approach. In the gen
eral case of smooth real part\, we also have a formal classification\; how
ever\, establishing a correspondence between arithmetic and geometric inva
riants (most notably\, the distribution of ovals among the components of a
reducible curve) still needs a certain amount of work.\n\nThis project wa
s conceived and partially completed during our joint stay at the Max-Planc
k-Institut für Mathematik\, Bonn. The speaker is partially supported by T
ÜBİTAK project 123F111.\n\nREFERENCES\n\n[1]. Ayşegül Akyol and Alex D
egtyarev\, Geography of irreducible plane sextics\, Proc. Lond. Math. Soc.
(3) 111 (2015)\, no. 6\, 13071337. MR 3447795\n\n[2]. Çisem Güneş Akt
aş\, Classi\ncation of simple quartics up to equisingular deformation\, H
iroshima Math. J. 47 (2017)\, no. 1\, 87112. MR 3634263\n\n[3]. I. V. Ite
nberg\, Curves of degree 6 with one nondegenerate double point and groups
of monodromy of nonsingular curves\, Real algebraic geometry (Rennes\, 199
1)\, Lecture Notes in Math.\, vol. 1524\, Springer\, Berlin\, 1992\, pp. 2
67288. MR 1226259\n\n[4]. V. M. Kharlamov\, On the classi\ncation of nons
ingular surfaces of degree 4 in RP3\n with respect to rigid isotopies\, Fu
nktsional. Anal. i Prilozhen. 18 (1984)\, no. 1\, 4956. MR 739089\n\n[5].
Sébastien Moriceau\, Surfaces de degré 4 avec un point double non dég
énéré dans l'espace projectif réel de dimension 3\, Ph.D. thesis\, 200
4.\n\n[6]. V. V. Nikulin\, Integer symmetric bilinear forms and some of th
eir 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://researchseminars.org/talk/OBAGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Turgay Akyar (METU)
DTSTART;VALUE=DATE-TIME:20231020T124000Z
DTEND;VALUE=DATE-TIME:20231020T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/31
DESCRIPTION:Title: S
pecial linear series on real trigonal curves\nby Turgay Akyar (METU) a
s part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nFor a gi
ven trigonal curve $C$\, geometric features of the Brill-Noether variety
$W_d^r(C)$ parametrizing complete linear series of degree $d$ and dimensio
n 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 basic pro
perties 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://researchseminars.org/talk/OBAGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:İzzet Coşkun (UIC)
DTSTART;VALUE=DATE-TIME:20231027T124000Z
DTEND;VALUE=DATE-TIME:20231027T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/32
DESCRIPTION:Title: D
ense orbits of the PGL(n)-action on products of flag varieties\nby İz
zet Coşkun (UIC) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\
nAbstract\nIt is a classical and very useful fact that any n+2 linearly ge
neral points in P^n are projectively equivalent. In this talk\, I will con
sider generalizations of this statement to higher dimensional linear space
s. The group PGL(n) acts on products of Grassmannians or more generally fl
ag varieties. I will discuss cases when this action has a dense orbit. Thi
s talk is based on joint work with Demir Eken\, Abuzer Gündüz\, Majid Ha
dian\, Chris Yun and Dmitry Zakharov.\n
LOCATION:https://researchseminars.org/talk/OBAGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Çisem Güneş Aktaş (Abdullah Gül)
DTSTART;VALUE=DATE-TIME:20231103T124000Z
DTEND;VALUE=DATE-TIME:20231103T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/33
DESCRIPTION:Title: G
eometry of equisingular strata of quartic surfaces with simple singulariti
es\nby Çisem Güneş Aktaş (Abdullah Gül) as part of ODTU-Bilkent A
lgebraic Geometry Seminars\n\n\nAbstract\nThe geometry of the equisingular
strata of curves\, surfaces\, etc. is one of the central problems of K3-s
urfaces. Thanks to the global Torelli theorem and surjectivity of the per
iod map\, the equisingular deformation classification of singular projecti
ve models of K3-surfaces with any given polarization becomes a mere comput
ation. The most popular models studied intensively in the literature are p
lane sextic curves and spatial quartic surfaces. Using the arithmetical re
duction\, Akyol and Degtyarev [1] completed the problem of equisingular de
formation classification of simple plane sextics. Simple quartic surfaces
which play the same role in the realm of spatial surfaces as sextics do fo
r curves\, are a relatively new subject\, promising interesting discoverie
s.\n\nIn this talk\, we discuss the problem of classifying quartic surface
s with simple singularities up to equisingular deformations by reducing th
e problem to an arithmetical problem about lattices. This research [3] or
iginates from our previous study [2] where the classification was given o
nly for nonspecial quartics\, in the spirit of Akyol ve Degtyarev [1]. Ou
r principal result is extending the classification to the whole space of s
imple quartics and\, thus\, completing the equisingular deformation classi
fication of simple quartic surfaces.\n\n [1] Akyol\, A. ve Degt
yarev\, A.\, 2015. Geography of irreducible plane sex- tics. Proc. Lond. M
ath. Soc. (3)\, 111(6)\, 13071337. ISSN 0024-6115. doi:10.1112/plms/pdv053
.\n [2] Güneş Aktaş\, Ç\, 2017. Classification of simple qu
artics up to equisin- gular deformation. Hiroshima Math. J.\, 47(1)\, 8711
2. ISSN 0018-2079. doi:10.32917/hmj/1492048849.\n\n [3] Güneş
Aktaş\, Ç\, to appear in Deformation classification of quartic surfaces
with simple singularities. Rev. Mat. Iberoam. doi:10.4171/RMI/1431\n
LOCATION:https://researchseminars.org/talk/OBAGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nurömür Hülya Argüz (Georgia)
DTSTART;VALUE=DATE-TIME:20231110T124000Z
DTEND;VALUE=DATE-TIME:20231110T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/34
DESCRIPTION:Title: Q
uivers and curves in higher dimensions\nby Nurömür Hülya Argüz (Ge
orgia) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\n
Quiver Donaldson-Thomas invariants are integers determined by the geometry
of moduli spaces of quiver representations. I will describe a corresponde
nce between quiver Donaldson-Thomas invariants and Gromov-Witten counts of
rational curves in toric and cluster varieties. This is joint work with P
ierrick Bousseau (arXiv:2302.02068 and arXiv:arXiv:2308.07270).\n
LOCATION:https://researchseminars.org/talk/OBAGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deniz Genlik (OSU)
DTSTART;VALUE=DATE-TIME:20231117T124000Z
DTEND;VALUE=DATE-TIME:20231117T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/35
DESCRIPTION:Title: H
olomorphic anomaly equations for $\\mathbb{C}^n/\\mathbb{Z}_n$\nby Den
iz Genlik (OSU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nA
bstract\nIn this talk\, we present certain results regarding the higher ge
nus Gromov-Witten theory of $\\mathbb{C}^n/\\mathbb{Z}_n$ obtained by stud
ying its cohomological field theory structure in detail. Holomorphic anoma
ly equations are certain recursive partial differential equations predicte
d by physicists for the Gromov-Witten potential of a Calabi-Yau threefold.
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 holomorphi
c anomaly equations in arbitrary dimension\, a result beyond the considera
tion of physicists. The proof of this fact relies on showing that the Grom
ov-Witten potential of $\\mathbb{C}^n/\\mathbb{Z}_n$ lies in a certain pol
ynomial ring. This talk is based on the joint work arXiv:2301.08389 with H
sian-Hua Tseng.\n
LOCATION:https://researchseminars.org/talk/OBAGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Ulaş Özgür Kişisel (METU)
DTSTART;VALUE=DATE-TIME:20231124T124000Z
DTEND;VALUE=DATE-TIME:20231124T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/36
DESCRIPTION:Title: R
andom Algebraic Geometry and Random Amoebas\nby Ali Ulaş Özgür Kiş
isel (METU) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstr
act\nRandom algebraic geometry studies variable properties of typical alge
braic varieties as opposed to invariant properties or extremal properties.
For instance\, a complex algebraic projective plane curve is always topol
ogically connected\, which is an invariant property\; a real algebraic pr
ojective plane curve of degree $d$ has\, by a classical theorem of Harnack
\, at most $\\displaystyle{g+1=(d-1)(d-2)/2+1}$ connected components where
$g$ denotes genus\, which is an extremal property\; whereas a random real
algebraic projective degree $d$ plane curve in a suitable precise sense (
to be explained in the talk) has an expected number of connected component
s 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 t
hen proceed to discuss some of our results on the expected properties of a
moebas of random complex algebraic varieties\, based on a joint work with
Turgay Bayraktar\, and another joint work with Jean-Yves Welschinger.\n
LOCATION:https://researchseminars.org/talk/OBAGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nil Şahin (Bilkent)
DTSTART;VALUE=DATE-TIME:20231201T124000Z
DTEND;VALUE=DATE-TIME:20231201T134000Z
DTSTAMP;VALUE=DATE-TIME:20231130T080259Z
UID:OBAGS/37
DESCRIPTION:Title: M
onotonicity of the Hilbert Functions of some monomial curves\nby Nil
Şahin (Bilkent) as part of ODTU-Bilkent Algebraic Geometry Seminars\n\n\n
Abstract\nLet $S$ be a 4-generated pseudo-symmetric semigroup generated 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 corresponding s
emigroup ring and\n$I_S$ be the defining ideal of $S$. $f_*$ being the hom
ogeneous summand of $f$\, tangent cone of $S$ is $k[S]/{I_S}_*$ where ${I_
S}_* =< f_*|f \\in I_S >$. We will show that the "Hilbert function of the
local ring (which is isomorphic to the tangent cone) for a 4 generated ps
eudo-symmetric numerical semigroup $$ is always non-de
creasing when $n_1