This award will partially support the international research conference, entitled ``Order, Algebra and Logics'', to be held at Vanderbilt University during June 12-16, 2007. This conference is unusual both for the broad range of contemporary mathematics it targets and the specific set of subdisciplines it encompasses. It is expected to attract upwards of 150 mathematicians, logicians and computer scientists.
Recent years have witnessed increased research activity on the interface between logic and universal algebra. In particular, the use of algebraic methods has proved to be fruitful in the study of non-classical logics - such as modal logic, fuzzy logic, and substructural logics - with ordered structures playing a central role in this relationship. A profound study of the connection between commutator theories and the shapes of congruences lattices of algebras, over any variety, has been completed by K. Kearnes and E. Kiss, and the central open question in the representation theory of lattices, asking whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice, has been given a negative solution by F. Wehrung. Methods of universal algebra have generated deep new results on certain decidability questions, and on complexity questions for algorithmic problems in finite algebras.
The conference aims to bring together researchers from all these research fields in order to foster collaboration and further research. The featured areas include, but are not limited to, the following (in alphabetical order):
- Algebraic logic - Algebraic theory of quasivarieties - Algorithmic problems in algebra - Applications of universal algebra to logics - Binary systems - Complexity and other algorithmic problems - Duality theory for algebraic structures - Finite axiomatizability problems - Modal logics - Non-classical logics - Numerical invariants of locally finite varieties - Ordered algebraic structures - Ordered topological spaces - Representations of lattices - Residuated structures - Substructural logics - Tame congruence theory and applications - Topological methods in algebra and logic
The scientific program of the conference will include invited lectures, contributed talks and tutorials. The organizers will make strong efforts to ensure a substantial participation by recent Ph.D. recipients and graduate students, for whom attendance at such a meeting can significantly promote career development and integration into the mathematics community.
