Konferenzen  >  Mathematik  >  Mathematische Logik, Grundlagen der Mathematik

The 13th International School of Rewriting will be held in Tbilisi, Georgia, September 19–24, 2022. The school will be organized by Ivane Javakhishvili Tbilisi State University (TSU) and will be part of the Computational Logic Autumn Summit (CLAS 2022). Term Rewriting is a simple but powerful model of computation with numerous applications in computer science and mathematics. It is heavily used in symbolic computation, formal reasoning, and program verification. Rewriting-based techniques are useful in many other fields as well, for instance, in quantum computing, biology, music.... The 13th International School on Rewriting (ISR 2022) is aimed at students, researchers and practitioners interested in the use or the study of rewriting and its applications

Informationstheorie und Grundlagen der Informatik,    Kurse und Veranstaltungen für Studenten der Mathematik

Logical and semantic frameworks are formal languages used to represent logics, languages and systems. These frameworks provide foundations for the formal specification of systems and programming languages, supporting tool development and reasoning.

Informationstheorie und Grundlagen der Informatik,    Wissenschaftliche Philosophie

Inductive reasoning is one of the most important reasoning techniques for humans and formalises the intuitive notion of "reasoning from experience". It has thus influenced both theoretical work on the formalisation of rational models of thought in Philosophy as well as practical applications in the areas of Artificial Intelligence and, in particular, Machine Learning. The First International Conference on Foundations, Applications, and Theory of Inductive Logic (FATIL2022) aims at bringing together experts from all fields concerned with inductive reasoning.

Informationstheorie und Grundlagen der Informatik,    Wissenschaftliche Philosophie

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to connecting two parallel approaches towards the study of the complexity of equivalence relations. On the one hand, a popular tool for classifying equivalence relations on standard Borel spaces is Borel reducibility. Invariant descriptive set theory, centered around this notion, is a vibrant field which shows deep connections with topology, group theory, combinatorics, and ergodic theory. On the other hand, a natural effectivization of Borel reducibility, named computable reducibility, appears in computability theory. Computable reducibility has proven to be a key notion for measuring the complexity of equivalence relations on the natural numbers, with fruitful applications in a variety of fields, such as: the metamathematics of arithmetic, the study of word problems for groups, the theory of numberings, and computable model theory. Despite the analogy between Borel and computable reducibility, there has been so far little effort to directly connect techniques, knowledge, and researchers of these separate fields. To counter this lack of communication, the proposed workshop will assemble a diverse group of mathematical logicians - drawn from both experts in invariant descriptive set theory and experts in computability theory working on computable reduction - to discuss on how their tools can align.

The Research Institute for Mathematical Sciences (RIMS)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

This is a workshop in commutative algebra, broadly interpreted, with a focus on three areas, all concerned with resolutions in various forms. One is the resolution of singularities of algebraic varieties, which remains a vibrant topic of research. The second is the theory of noncommutative resolution of singularities. Introduced two decades ago, this subject has witnessed remarkable growth developing connections to algebraic geometry, commutative algebra, cluster algebras, and the representation theory of algebras, both commutative and noncommutative, among others. The third intended meaning of the word “resolution” is as in free resolutions of algebras and modules in commutative algebra.

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Stability theory, in the sense of mathematical logic, consists of a collection of technical methods first developed to address the logical problem of classifying abstract models of mathematical theories. Stability theory has proven to be applicable to other mathematical problems such as understanding rational solutions of algebraic equations. It has recently been shown that the techniques and methods used for the classification described above can be used in much more general settings with applications to other areas of mathematics such as algebraic geometry, additive combinatorics and extremal graph theory. Researchers at this meeting will study these developments to deepen these applications, and to extend the scope of stability theory to an even wider range of mathematical theories.

CIRM – Centre International de Rencontres Mathématiques

The debate between Hilbert and Brouwer, which took place at the beginning of the 20th century, is without doubt one of the most important events in the history of foundations of mathematics. In that debate Brouwer rejected transcendent proof methods and insisted on the exclusive use of intuitionist (or constructive) arguments for a conceptually correct development of mathematics. Hilbert, on the contrary, viewed these transcendental and non-effective proofs as the very essence of mathematical thinking. He introduced proof theory in the hope to justify these transcendent methods by purely effective means. While Gödel’s second incompleteness theorem is generally said to contravene Hilbert’s hopes, it is remarkable that Gödel himself insisted on the fact that his result does not contradict at all Hilbert’s program. In fact, the impact of Gödel’s result on Hilbert’s program was the topic of a discussion between Gödel, Herbrand and Neumann about the fundamental question of the scope of constructive mathematics. Recent results in different fields of mathematics, such as proof theory, type theory, constructive algebra and categorical logic, shed new light on this question. For instance, proof theory seems to indicate precise limits to intuitionistic type theory, while on the other hand the Univalence Axiomallows for a rather unexpected extension of constructive methods. The goal of this workshop is precisely to bring together experts in these different fields to evaluate the impact of those new results on foundations of mathematics.

The Fields Institute

This workshop will be less focused in nature and will bring together small groups of experts centered around emerging applications of set theory. This will include applications of set-theory in algebraic topology and homological algebra, operator algebras (for instance Koszmider's solution to Anderson's conjecture), Keisler's order in model theory, and the geometry of Banach spaces.

Casa Matemática Oaxaca (CMO)

The workshop is designed to explore the interactions that exists between set theory, topology, and algebra. The focus of the workshop will be on the study of topological problems of set-theoretic flavor arising in topological algebra and algebraic topology, as well as the study of topological games and homogeneity.

The Fields Institute

Scheduled as part of Thematic Program on Operator Algebras and Applications

Casa Matemática Oaxaca (CMO)

In the recent development of Mathematics, the study of symmetry of highly singular objects has contributed to the simultaneous understanding of symmetries and groups. The aims of the Workshop are the study of symmetries of the Cantor set, and the understanding of the groups arising as symmetries of the Cantor set.

CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)