ODTÜBİLKENT
Algebraic Geometry Seminar
(See all past talks
ordered according to speaker
and date)
**** 2015 Fall Talks ****

Alexander Degtyarev[Bilkent]
 Lines on smooth quartics
Abstract:
In 1943, B. Segre proved that a smooth quartic surface
in the complex projective space cannot contain more
than 64 lines. (The champion, socalled Schur's
quartic, has been known since 1882.) Even though a gap
was discovered in Segre's proof (Rams, Schütt, 2015),
the claim is still correct; moreover, it holds over
any field of characteristic other than 2 or 3. (In
characteristic 3, the right bound seems to be 112.) At
the same time, it was conjectured that not any number
between 0 and 64 can occur as the number of lines in a
quartic. 
Ali Sinan Sertöz[Bilkent]
 The basic theory of elliptic
surfacesI
Abstract: This term we will be running a learnin seminar on elliptic surfaces with a view toward "lines on quartic surfaces". We will be mainly following Miranda's classical notes but other sources will not be excluded. 
Ali Sinan Sertöz[Bilkent]  The basic theory of elliptic surfacesII
Abstract: We continue our learning seminar talk on elliptic surfaces. We will also mention how this topic shows up in the search for lines on quartic surfaces in $\mathbb{P}^3$. 
Ergün Yalçın[Bilkent]  Group actions on spheres with rank one isotropy
Abstract: Actions of finite groups on spheres can be studied in various different geometrical settings, such as (A) smooth Gactions on a closed manifold homotopy equivalent to a sphere, (B) finite Ghomotopy representations (as defined by tom Dieck), and (C) finite GCW complexes homotopy equivalent to a sphere. These three settings generalize the basic models arising from unit spheres S(V) in orthogonal or unitary Grepresentations. In the talk, I will discuss the group theoretic constraints imposed by assuming that the actions have rank 1 isotropy (meaning that the isotropy subgroups of G do not contain $\mathbb{Z}/p \times \mathbb{Z}/p$, for any prime $p$). This is joint work with Ian Hambleton. 
Özgün Ünlü[Bilkent]
 Free group actions on products of
spheres
Abstract: In this talk we will discuss the problem of finding group theoretic conditions that characterizes the finite groups which can act freely on a given product of spheres. The study of this problem breaks up into two aspects: (1) Find group theoretic restrictions on finite groups that can act freely on the given product. (2) Construct explicit free actions of finite groups on the given product. I will give a quick overview of the first aspect of this topic. Then I will discuss some recently employed methods of constructing such actions. 
Recep Özkan[ODTÜ] Concrete sheaves and continuous spaces
Abstract:
This is a talk from the speaker's recent
dissertation. After he summarizes the historical
background and the recent developments in the field he
will motivate his dissertation problems. Time
permitting he will talk about the ideas behind the
proof of his main theorem. 
Cem Tezer[ODTÜ]
 Anosov diffeomorphisms : Revisiting
an old idea
Abstract: Introduced by D. V. Anosov as the discrete time analogue of geodesic flows on Riemann manifolds of negative sectional curvature, Anosov diffeomorphisms constitute one of the leitmotivs of contemporary abstract dynamics. It is conjectured that these diffeomorphisms occur on very exceptional homogeneous spaces. The speaker will delineate the basic facts and briefly mention his own recent work towards settling this conjecture. 
Haydar Göral[Université Lyon 1]  Primality via Height Bound
Abstract: Height functions are of fundamental importance in Diophantine geometry. In this talk, we obtain height bounds for polynomial ring over the field of algebraic numbers. This enables us to test the primality of an ideal. Our approach is via nonstandard methods, so the mentioned bounds will be ineffective. We also explain the tools from nonstandard analysis. 
Alperen Ergür[Texas A&M]  Tropical Varieties for Exponential Sums
Abstract:
We define a variant of tropical varieties for
exponential sums. These polyhedral complexes can
be used to approximate, within an explicit distance
bound, the real parts of complex zeroes of exponential
sums. We also discuss the algorithmic efficiency of
tropical varieties in relation to the computational
hardness of algebraic sets. Our proof involves
techniques from basic complex analysis, inequalities
and some recent probabilistic estimates on projections
that might be of interest to analyst. 
Ali Ulaş Özgür Kişisel[ODTÜ] Moduli space of elliptic curves
Abstract: The aim of this talk is to view the moduli space of elliptic curves in different contexts. After briefly discussing the classical setting, we will see how it can be viewed as an orbifold and as an algebraic stack. 
Mesut Şahin[Hacettepe]
 On Pseudo Symmetric Monomial Curves
Abstract: In this talk,
we introduce monomial curves, toric ideals and
monomial algebras associated to 4generated pseudo
symmetric numerical semigroups. We give a
characterization of indispensable binomials of
these toric ideals, and of these monomial algebras
to have strongly indispensable minimal graded free
resolutions. We also discuss when the tangent
cones of these monomial curves at the origin are
CohenMacaulay in which case Sally's conjecture
will be true. 
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
Abuilding at Bilkent.
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2015 Spring Talks (349360) 