1. Classes of combinatorial objects: from structure to algorithms (CCOSA)

ERC-2010-StG_20091028; 60 months; 01/12/2010 - 30/11/2015

MFF, RNDr. Daniel Král, PhD.

Abstract

The proposed project aims at analyzing fundamental problems from combinatorics using the most current methods available and at providing new structural and algorithmic insights to such problems. The problems considered will be treated on a general level of classes of combinatorial objects of the same kind and the developed general methods will also be applied to specific open problems. Classes of dense and sparse objects will be treated using different techniques.

Dense combinatorial objects appear in extremal combinatorics and tools developed to handle them found their applications in different areas of mathematics and computer science. The project will focus on extending known methods to new classes of combinatorial objects, in particular those from algebra, and applying the most current techniques including Razborov flag algebras to problems from extremal combinatorics. Applications of the obtained results in property testing will also be considered.

On the other hand, algorithmic applications often include manipulating with sparse objects. Examples of  sparse objects are graphs embeddable in a fixed surface and more general minor-closed classes of graphs. The project objectives include providing new structural results and algorithmic metatheorems for classes of sparse objects using both classical tools based on the theory of graph minors as well as new tools based on the framework of classes of nowhere-dense structures.

2. Ion Spectroscopy of Reaction Intermediates ( ISORI)

ERC-2010-StG_20091028; 60 months; 01/01/2011 - 31/12/2016

PřF; Mgr. Jana Roithová, Ph.D.

Abstract

Modern chemistry experiences a fast development of new reactions with dominance in organometallics and recently also organocatalysis. The massive synthetic progress however greatly foreruns mechanistic studies and the deeper insight is often rather limited. This large unexplored area accordingly challenges pioneering research and formulation of new concepts in chemistry. The present research project uses the most powerful tools of several research disciplines and aims towards the investigation of the elementary steps in organic reactions by means of mass spectrometry (MS) in combination with electrospray ionization (ESI) and quantum chemistry with a particular focus on ion spectroscopy.

The research will concentrate on elementary reactions in catalysis, e.g. the interaction of catalysts with substrates or bimolecular reactions of reactant/catalyst complexes. A major innovative contribution consists in applying ion spectroscopy for the structural characterization of reaction intermediates using a newly proposed tandem mass spectrometer with a cooled linear ion trap, which will allow two-photon experiments with IR and UV tunable lasers. The experiments will provide specific information about various intermediates and will help to disentangle even complicated mixtures or isomeric ions. In addition, an innovative experiment is designed, in which bimolecular reactivity of isobaric ions will be studied individually. Kinetics of selected reactions in solution will also be followed by ESI/MS. The combined efforts of these different approaches will provide a comprehensive understanding of the reaction mechanisms and will lead to the formulation of new general concepts in organic and organometallic reactivity.