Symposium in Algebraic Geometry Date: 2015. 12. 28 (Mon) ~ 12. 29 (Tue) Place: Busan, Haeundae Rivera Hotel |
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Title: Cohomology ring of the moduli space of stable sheaves supported on
quartic curves
Calabi-Yau threefold suggested by S. Katz, we compute the cohomology
ring of the moduli space of stable sheaves with Hilbert polynomial 4m+1
on the projective plane. As a byproduct, we obtain the total Chern class and
Euler characteristics of all line bundles, which provide a numerical data for
the strange duality on the plane. This is joint work with Han-Bom Moon.
Speaker: 김영락
Title : Ulrich bundles on rational and Enriques surfaces
Abstract : An Ulrich bundle on an n-dimensional smooth projective variety X
is a vector bundle which has the same cohomology table as the trivial bundle
on n-dimensional projective space. Ulrich bundles have several different
motivations from linear algebra, commutative algebra, and projective
geometry.Eisenbud and Schreyer made a comprehensive study and
conjectured that every variety carries an Ulrich bundle. Nevertheless,
the existence problem is wildly open, even for smooth surfaces.
In this talk, we will briefly discuss how to construct an Ulrich bundle
on some rational surfaces using Lazarsfeld-Mukai bundle techniques
suggested by Aprodu, Farkas and Ortega. We will also discuss the
existence problem on Enriques surfaces.
Speaker: 이경석
Title : Semiorthogonal decompositions of derived categories of algebraic varieties
coherent sheaves on algebraic varieties and its applications.
Then I will discuss the notion of semiorthogonal decomposition
and many examples of semiorthogonal decompositions of derived categories
of algebraic varieties. Finally I will discuss Fano visitor problem.
Speaker: 이병호
Title: G-braided spaces
Abtract: I will discuss about the definition of G-braided spaces and its
motivation. It will include a survey of the algebraic aspects of the theory of
Frobenius manifolds, and the problem of orbifolding Frobenius manifolds.
models of C^n/G can be realised as moduli spaces of G-constellations.
After introducing G-bricks and round down functions, I present some
new results.
Title: Stability of nets of quadrics in P^5 and associated discriminants
Abstract: Let S be a complete intersection surface defined by a net N of
quadrics in P^5. In this talk we analyze GIT stability of nets of quadrics
in P^5 up to projective equivalence and discuss some connections
between a net of quadrics and the associated discriminant sextic curve.
In particular, we prove that if S is normal and the discriminant of S
is stable then N is stable. And we prove that if S has the reduced
discriminant and the discriminant is stable then N is stable.
Moreover, we prove that if S has simple singularities then the
discriminant has simple singularities.
which is also ubiquitous in natural sciences and many areas of applications.
Recently, it turned out that there is a natural way to consider sets of some
interesting tensors geometrically.
some related problems to audience with modest backgrounds. As an
example, we consider the problem of `complexity of matrix
multiplication’ from this algebro-geometric viewpoint, where one
could see that the naive way to multiply two matrices is not
computationally optimal for matrices of large size and how to
find an optimal way to do it approximately. Next, we consider
the problem todetermine border ranks of monomials and report
recent results, which is based on the joint work with Luke Oeding
in progress.