ODTÜ-BİLKENT Algebraic
Geometry Seminar
(See all past talks ordered according
to speaker or date)
Refresh this page to see recent changes, if any
**** 2025 Fall Talks ****
This
semester we plan to have all of our seminars online
Bayram Tekin - [Bilkent] - A rank-4 tensor Riemann would have loved
plus spinor-techniques in differential geometry
| Abstract: I would like
to discuss two topics that have proved very useful
in the parts of differential geometry used 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
plain sight up until our paper ( Phys.
Rev. D 99 (2019) 4, 044026). The second
topic will include formulating differential
geometry in terms of Weyl spinors which are
fundamental representations of SL(2,C). |
Türkü Özlüm Çelik - [Max Planck] - Interaction Networks via Grassmannians
|
Abstract: When can a
network of mutually reinforcing N components
remain stable? To approach such questions, we
describe the interactions through generalized
Lotka–Volterra equations—a broad class of
dynamical systems modeling how components
influence one another over time. This formulation
leads to a family of semi-algebraic sets
determined by the sign pattern of the parameters.
These sets encode positivity conditions defining
regions of potential coexistence, with polynomial
degrees growing exponentially in N. Embedding the
parameter space into the real Grassmannian
Gr(N,2N) transforms these conditions into sign
relations governed by the Grassmann–Plücker
equations and oriented matroids. This geometric
reformulation yields a realization problem through
which we detect impossible interaction networks
and study the algebraic structure underlying
stability. If time permits, we will also touch on
how these structures connect to algebraic curves.
This talk is based on our recent work arXiv:2509.00165. |
|
Abstract: Graphs can be
viewed as (non-archimedean) analogs of Riemann
surfaces. For example, there is a notion of
Jacobians for graphs. More classically, graphs can
be viewed as electrical networks. I will explain
the interplay between these points of view and
some applications in arithmetic geometry. |
|
Abstract: The number of
numerical semigroups with given Frobenious number
(or conductor, or genus) is one of the topics that
is studied by many researchers. In our previous
works, we have given parametrizations of Arf
numerical semigroups of small multiplicity 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 conductor
c is (eventually) constant for some m
(especially for prime m) when restricted to some
congruence classes of c modulo m. In a recent work
with N. Tutaş, we have characterized those
multiplicities m and congruence 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 enumeration of
Arf numerical semigroups with given multiplicity
and conductor, Semigroup Forum 110, 308-316.]
where the above characterization is given. |
|
Abstract: One 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 degree obtained by Miyaoka in
2009. After recalling the necessary notions,
in my talk I will present various results
concerning the question whether the above
bound is sharp for rational (resp.
smooth rational) curves on K3-surfaces of
high degree. |
|
Abstract: In this talk,
we explore some number theoretic aspects of
hyperelliptic 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 isomorphism classes.
We also present explicit constructions of
hyperelliptic Jacobian varieties with rational
torsion points of prescribed order. |
|
Abstract: The
Birch–Swinnerton-Dyer conjecture relates the
behavior of the L-function of an elliptic curve at
its central point to the rank of its group of
rational points. The Bloch–Kato conjecture
generalizes this principle to a broad family of
motivic Galois representations, predicting a
precise relationship between the order of
vanishing of motivic L-functions at integer values
and the structure of the associated Selmer groups.
Since the foundational work of Kolyvagin in the
nineties, Euler systems have played a central role
in approaching these conjectures, and in recent
years their scope has expanded significantly
within the automorphic setting of Shimura
varieties. |
|
Abstract: A numerical semigroup S is called Sally type if its multiplicity is one more than its width. In this talk, we will analyze the properties 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 we determine the minimal generators. Joint work with Dubey, Goel, Singh
and Srinivasan |
|
Abstract: |
|
Abstract: TBA |
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
