ODTÜ-BİLKENT Algebraic
Geometry Seminar
(See all past talks ordered according
to speaker or date)
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**** 2026 Spring Talks ****
This
semester we plan to have all of our seminars online
Öznur
Turhan - [Galatasaray & Polish Academy] - Newton-nondegenerate line singularities, Lê
numbers and Bekka (c)-regularity
| Abstract: Consider an
analytic function $f(t,z)$ defined in a
neighbourhood of the origin of
$\mathbb{C}\times\mathbb{C}^n$ such that for
all $t$, the function $f_t(z):=f(t,z)$ defines a
hypersurface of $\mathbb{C}^n$
with a line singularity at $0\in\mathbb{C}^n$. Denote by
$V(f)$ the hypersurface of $\mathbb{C}\times\mathbb{C}^n$ defined by
$f(t,z)$ and write $Σf$ for its singular locus. We
assume that $f_t$ is ''quasi-convenient'' and
Newton nondegenerate. Within this framework, we
show that if the Lê numbers of $f_t$ are
independent of $t$ for all small $t$, then $Σf$ is
smooth and $V(f)\backslash Σf$ is Bekka
(c)-regular over $Σf$. This is a version for line
singularities of a result of Abderrahmane
concerning isolated singularities. As a corollary, we obtain that any family of quasi-convenient, Newton non-degenerate, line singularities with constant Lê numbers as above is topologically equisingular. In particular, this applies to families with non-constant Newton diagrams, and therefore extends, in some direction, a result previously observed by Damon. This is a joint work with Christophe Eyral. |
Meral Tosun - [Galatasaray] - McKay Quivers Beyond ADE
|
Abstract: The classical
McKay correspondence relates finite subgroups of
SL(2,C) to affine ADE Dynkin diagrams and Du Val
surface singularities. In this talk, we extend
this perspective to small finite subgroups of
GL(2,C) whose quotients produce isolated surface
singularities. Using character theory and a
product formula for McKay quivers, we give an
explicit description of the quivers associated
with the natural two-dimensional representation. |
|
Abstract: Using
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 arbitrary, not-necessarily toric,
rational surfaces and propose a conjectural
relation with refined Donaldson-Thomas
invariants. This is joint work with Hulya Arguz. |
|
Abstract:
In 1876, Axel Harnack proved in a
foundational article that |
|
Abstract: Let $F$
be the finite field with $q$ elements and $K$
be its algebraic closure. The ring
$S=F[x_0,x_1,x_2]$ is graded via
$\deg(x_i)=w_i$, for $i=0,1,2$, where $w_0,
w_1$ and $w_2$ generate a numerical semigroup!
We study some linear codes obtained from the
weighted projective plane $P(w_0,w_1,w_2)$
over $K$. |
|
Abstract: The
classical Noether-Lefschetz theorem claims
that a very general degree $d>3$ surface in
$\mathbb{P}^3$ has Picard 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 of
irreducible components. For $d>4$, it is
classical result due independently to Green
and Voisin, that the unique component of
highest codimension corresponds to the locus
of surfaces which contain lines. The natural generalization of
this question to higher dimensional
hypersurfaces of the 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 Structure to
compute (and bound) the dimension of its
Zariski tangent space. A natural stronger version of
the linear cycles conjecture is that the Hodge
loci with maximal tangent space are those
corresponding to linear cycles. In this talk I will report on
recent results disproving this conjecture for
all degrees and dimensions. This is a joint work with
Jorge Duque Franco. |
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ODTÜ talks are either at Hüseyin Demir Seminar room
or at Gündüz İkeda seminar room at
the Mathematics building of ODTÜ.
Bilkent talks are at room 141 of Faculty of
Science A-building at Bilkent.
Zoom talks are online.
Talks of previous
years
