International Conference on Order, Algebra and Logics

该奖项将部分支持将于2007年6月12日至16日在范德比尔特大学举行的名为“秩序、代数和逻辑”的国际研究会议。这次会议的不同寻常之处在于它所针对的当代数学的广泛范围和它所涵盖的具体的子学科。预计将吸引150多名数学家、逻辑学家和计算机科学家。近年来，人们对逻辑和泛代数之间的接口进行了越来越多的研究。特别是，代数方法的使用已被证明在非经典逻辑的研究中是富有成效的-例如模态逻辑，模糊逻辑和子结构逻辑-有序结构在这种关系中起着中心作用。K. Kearnes和E. Kiss完成了对易子理论与任意代数同余格形状之间联系的深入研究，并且F. Wehrung给出了格表示理论中关于是否每一个代数分配格都同构于一个格的同余格的中心开放问题的负解。普遍代数方法在某些可判定性问题和有限代数算法问题的复杂性问题上产生了深刻的新结果。会议旨在汇集所有这些研究领域的研究人员，以促进合作和进一步的研究。特色区域包括但不限于以下（按字母顺序排列）：代数逻辑-拟变的代数理论-代数中的算法问题-通用代数在逻辑中的应用-二元系统-复杂性和其他算法问题-代数结构的对偶理论-有限公性问题-模态逻辑-非经典逻辑-局部有限变的数值不变量-有序代数结构-有序拓扑空间-格的表示-剩余结构-子结构逻辑-驯服同余理论及其应用-代数和逻辑中的拓扑方法会议的科学计划将包括邀请讲座，专题演讲和辅导。组织者将努力确保最近的博士学位获得者和研究生的大量参与，对他们来说，参加这样的会议可以显著促进职业发展和融入数学界。

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.