ODTÜ-BİLKENT Algebraic
Geometry Seminar
(See all past talks ordered according
to speaker or date)
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**** 2026 Fall Talks ****
This
semester we plan to have all of our seminars online
Demir Eken - [Michigan] - Positivity, Adjoint Linear Systems, and Jet
Separation
| Abstract: Positivity of
line bundles allows us to construct morphisms and
projective embeddings, and more generally global
sections with prescribed Taylor coefficients. This
raises a quantitative question: how much
positivity is needed for global generation, very
ampleness, or separation of higher-order jets? In
this expository talk, I will discuss these
questions for adjoint line bundles $K_X+mA$ with
$A$ ample, starting from Fujita’s conjectures. I
will also present global and local criteria for
$k$-jet separation and the role of Seshadri
constants in measuring local positivity. |
Anatoly Libgober - [UIC] - Pencils of curves on algebraic surfaces with reducible fibers
|
Abstract: We describe
constraints on the pencils of curves having
sufficiently many reducible members, depending on
the surface and the numerical classes of
irreducible components. In the case of pencils of
curves in linear systems with a small degree of
the discriminant we give a classification of these
pencils. This follows from the description of
polarized simply connected surfaces with the
degree of discriminant less than 13. |
|
Abstract: A
period is an absolutely convergent integral of a
rational function over a domain defined by
polynomial inequalities, all with rational
coefficients. The conjectural category of
motives organizes periods by their cohomological
origin. In this talk, we will discuss Aomoto
polylogarithms and a conjecture of Beilinson
identifying their bialgebra with the Hopf
algebra of mixed Tate motives. Working with
motives in the sense of Nori, we will then
present a new candidate for this Hopf algebra,
compatible with Beilinson’s conjecture. |
|
Abstract: In this talk I will
consider a moduli space of
projective varieties enhanced with a
certain frame of their cohomology
bundles. In many examples such as
elliptic curves, abelian varieties,
Calabi-Yau varieties, and
conjecturally in general, this
moduli space is a quasi-affine
scheme over ${\mathbb
Z}[\frac{1}{N}]$ for some natural
number N. The ring of global regular
functions on this quasi-affine
variety is called the ring of CY
modular forms and it gives us
natural generalizations of modular
and quasi-modular forms. In the case
of Calabi-Yau threefolds, it
includes the genus g topological
string partition function encoding
genus g Gromov-Witten invariants. We
can also rewrite the BCOV anamally
equation using certain vector fields
on this moduli space which are
algebraic incarnation of
differential equations of
automorphic forms. After taking
modulo p of this moduli space for p
coprime with N, I will discuss an
outline of a project how to prove
the p-integrality of Calabi-Yau
modular forms beyond the established
cases of hypergeometric Calabi-Yau
varieties (after Yau, Lian,
Krattenthaler among many others). The
talk is based on my book "Modular
and Automorphic Forms &
Beyond, Monographs in
Number Theory, World Scientific
(2021)" in which the Tupi name
ibiporanga (pretty land) for such a
moduli space is suggested. |
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Abstract: Upon completing the
deformation classification of simple real
plane sextic curves with smooth real part,
we observed certain distinctive lacunas in
our list of topological types. These lacunas
are very similar to those in the smooth
case, which originally led to the discovery
of the Gudkov--Rokhlin congruence. However,
ours depend on the set of singularities and,
therefore, need a new dedicated congruence;
we suggest one. |
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
