ODTÜ-BİLKENT Algebraic
Geometry Seminar
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to speaker or date)
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**** 2024 Spring Talks ****
This
semester we plan to have most of our seminars online,
except the last one!
Pınar Mete-[Balıkesir]
- On some invariants of the tangent
cones of numerical semigroup rings
Abstract: The minimal free resolution
is a very useful tool for extracting information about
modules. Many important numerical invariants of a module
such as Hilbert function and Betti numbers can be
deduced 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 numerical
semigroup S. He also stated the problem of describing
the Betti numbers and the minimal free resolution for
the tangent cone when S is 4-generated semigroup which
is symmetric. In this talk, I will first give some 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 of the Apery table of the
numerical semigroup to determine some properties of its
tangent cone. DI. STAMATE, Betti numbers for numerical semigroup rings. Multigraded Algebra and Applications, 238, 133-157, Springer Proceedings in Mathematics and Statistics, Springer, Cham 2018. |
Turgay
Bayraktar-[Sabancı] - Equidistribution for Zeros of Random Polynomial
Systems
Abstract: A 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 coefficients.
The talk is based on the joint work with Çiğdem
Çelik. |
Abstract: Given
a connected reductive algebraic group G over a
number field F, the global Langlands (reciprocity)
conjecture roughly predicts that, there should be
a correspondence between (automorphic side) the
isomorphism classes of (cuspidal,
cohomological) automorphic 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. |
Abstract: In
1927, van der Waerden proved a theorem regarding
the existence of arithmetic progressions in any
partition of the positive integers with finitely
many classes. In 1936, a strengthening of van der
Waerden's theorem was conjectured by Erdös and
Turan, which states that any subset of positive
integers with a positive upper density contains
arbitrarily long arithmetic progressions. In 1975,
Szemeredi developed his combinatorial method to
resolve this conjecture, and the affirmative
answer to Erdös and Turan's conjecture is now
known as Szemeredi's theorem. As well as in the
integers, Szemeredi-type problems have been
extensively studied in subsets of finite fields.
While much work has been done on the problem of
whether subsets of finite fields contain
arithmetic progressions, in this talk we
concentrate on how many arithmetic progressions we
have in certain subsets of finite 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 best possible when k is small, owing to
the Sato-Tate conjecture. This work is supported
by the Scientific and Technological Research
Council of Turkey with the project number 122F027. |
Abstract: We are
dealing with a hypersurface $X\subset
\mathbb{C}^3$ having non-isolated singularities.We
construct an embedded toric resolution of $X$
using some specific vectors in its dual Newton
polyhedron. To do this, we first define the
profile of a full dimensional cone and we
establish a relation between the jet vectors and
the integer points in the profile. This is a part of the joint work
with C. Plénal and M. Tosun. References |
Abstract: For
curves over the field of p-adic numbers, there are
two notions of p-adic integration:
Berkovich-Coleman integrals which can be performed
locally, and Vologodsky integrals with desirable
number-theoretic properties. These integrals 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
reduction. Moreover, there are practical
algorithms available to compute Coleman integrals. |
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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