28th National School on Algebra, Bucharest
June 8 - June 12
The National School on Algebra, the 28th edition, will take place in Bucharest, 8-12th of June, right after the conference, part of the same event and thus having the same title “Homological trends in Commutative Algebra and Algebraic Geometry”.
The website for the school is math.univ-ovidius.ro/sna/edition.aspx?cat=GeneralInfo&itemID=15 .
There will be 5 mini-courses, three one-hour lectures each, delivered by Alexandru Constantinescu (Freie Universität Berlin, Germany), Florian Enescu (Georgia State University, USA), Gavril Farkas (Humboldt-Universität zu Berlin, Germany), Claudiu Raicu (Notre Dame University, USA), Jerzy Weyman (Jagiellonian University, Poland).
Here are the mini-abstracts of each of the 5 mini-courses:
Alexandru Constantinescu: The deformation theory of an affine singularity is governed by the so-called versal deformation. This is an object through which all other deformations factor. In the setting of affine toric geometry, this whole process can be translated in the language of semigroups. Our first aim will be to construct abstractly a universal (flat) extension of a pair of semigroups. We will then see how this universal extension explicitly looks like for semigroups arising from affine toric singularities, and how it relates to Minkowski decompositions of polyhedra. Finally, we will connect these universal objects to the graded components of the versal deformation of a toric singularity.
Florian Enescu: Homological methods in positive characteristic commutative algebra. In the past several decades, there has been a flurry of developments in commutative algebra and algebraic geometry in positive characteristic related to the Frobenius homomorphism. New theories such as tight closure theory and Hilbert-Kunz theory have brought numerous advances and applications. A significant part of these ideas rely on homological methods, in connection to local cohomology and injective hulls of local rings, and they currently represent an exciting area of research in commutative algebra.
Gavril Farkas: TBA
Claudiu Raicu: TBA
Jerzy Weyman: TBA