WORKSHOP FOR YOUNG RESEARCHERS
IN MATHEMATICS
May 21 - 24, 2015
http://math.univ-ovidius.ro/workshop/2015/WYRM/
Organized by: the Faculty of Mathematics and Computer Science, Ovidius University Constanta,
the Mathematical Institute of the Romanian Academy Bucharest and
Department of Mathematics of University of Wisconsin - Madison, USA
ABSTRACTS
Heegaard-Floer homology and cuspidal multiple planes
Cristian ANGHEL
IMAR, Romania
Heegaard-Floer homology has been used recently in problems concerning cuspidal
plane curves. We intend to review these results and some connections with the theory
of ramified coverings of the complex projective plane. This is joint work in progress
with Cristina A-M. Anghel.
Gorenstein binomial edge ideals associated with scrolls
Ajdin HALILOVIC
IMAR, Romania
Let IG be the binomial edge ideal on the generic 2 × n - Hankel matrix associated
with a closed graph G on the vertex set [n]. We characterize the graphs G for which
IG has maximal regularity and is Gorenstein.
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Motivic Infinite Cyclic Covers
Laurent¸iu MAXIM
University of Wisconsin - Madison, USA
To an infinite cyclic cover of a punctured neighborhood of a simple normal crossing
divisor on a complex quasi-projective manifold we associate (assuming certain finiteness
conditions are satisfied) an element in the equivariant Grothendieck ring of varieties,
called motivic infinite cyclic cover, which satisfies birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex
hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively. This is joint work with M. Gonzalez Villa and A. Libgober.
Resonance varieties and nilpotent Lie algebras
Radu Clement POPESCU
IMAR, Romania
The space of g-valued flat connections, where g is a Lie algebra, has a filtration by
the resonance varieties associated to a representation of g. I present results concerning
the space of sl2 -valued flat connections and the resonance varieties for the ChevalleyEilenberg cochain algebra of a finite dimensional nilpotent Lie algebra.
Lattice based cryptography
Miruna ROS
¸ CA
Bitdefender, Romania
Lattice based cryptography has drawn a lot of attention in the last two decades,
especially after Craig Gentry’s breakthrough paper in 2009. The aim of this talk is to
motivate the interest of the cryptographic community in these abstract objects.
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Filtrations for Koszul rings
DUMITRU STAMATE
University of Bucharest, Romania
One of the methods introduced for checking that a standard graded algebra is Koszul
is the existence of a so called Koszul filtration. We are interested in semigroup rings
R = K[H], which are not usually standard graded. In this context we introduce the
strongly Koszul property, extending in a natural way the similar concept of Herzog,
Hibi and Restuccia for standard graded K-algebras. We show that if K[H] is strongly
Koszul, then its associated graded ring grK[H] is a Koszul ring in the classical sense
and that the two rings have the same Poincare series. Our toolbox includes sequentially
Cohen-Macaulayness and shellability for posets.
This is a preliminary report on work in progress with Juergen Herzog, Essen, Germany.
On the envelope of α-sections of a convex body
Costin VˆILCU
IMAR, Romania
This talk is based on a joint work with Nicolas Chevallier and Augustin Fruchard
(Universit´e de Haute Alsace, Mulhouse).
Let K be a planar convex body af area |K|, and take 0 < α < 1. An α-section of K
is an oriented line ∆ cutting K in two compact parts, one to the right, denoted by K − ,
of area |K − | = α|K|, and the other to the left, K + , of area |K + | = (1 − α)|K|. Denote
by mα the envelope of all α-sections of K, and by Kα the intersection of all K + .
The aim of the talk is to present properties of mα and its relation to Kα . Some connections will also be mentioned, to outer billiards, floating bodies, and fair partitioning.
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