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Equivariant topology in algebraic geometry

Objective

In physical sciences, a very challenging problem is the understanding of sudden changes caused by smooth alterations of parameters. For instance, water suddenly boils, or ice melts. The back of the camel breaks suddenly under a load of just one more straw. These abrupt changes are not only present in dynamical systems, but also in biology (e.g. population models, cell growth), and human society (e.g. stock markets). The proposer studies the mathematical theory of these phenomena, namely uses topological methods to understand how global topology forces singularities. The governing notion of global singularity theory is "Thom polynomial". The proposer has a strong research record on computing and applying Thom polynomials in various topological settings, eg. differentiable maps, forms, quivers, discriminants. The objective of the proposal is to support the proposer's career development by extending his expertise from {\em topology} to modern geometry and related geometric and algebraic combinatorics. Visiting the Renyi Mathematical Institute in Budapest for a year, doing training and research under the supervision of A. Nemethi (scientist in charge) will significantly develop and widen the competences of the researcher. The equivariant techniques Rimanyi used in the theory of singularities is proposed to be applied in geometrically relevant situations. The two concrete proposed projects are the study of matroid versions of linear Gromov-Witten invariants, and the geometry of natural stratifications on punctual Hilbert schemes of high dimension spaces.

Field of science

  • /natural sciences/mathematics/pure mathematics/topology
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/physical sciences
  • /natural sciences/mathematics/applied mathematics/dynamical systems
  • /natural sciences/mathematics/pure mathematics/algebra/algebraic geometry

Call for proposal

FP7-PEOPLE-IEF-2008
See other projects for this call

Funding Scheme

MC-IEF - Intra-European Fellowships (IEF)

Coordinator

RENYI ALFRED MATEMATIKAI KUTATOINTEZET
Address
Realtanoda Street 13-15
1053 Budapest
Hungary
Activity type
Other
EU contribution
€ 78 532,63
Administrative Contact
Andras Nemethi (Prof.)