Reverse Mathematics addresses the question of which axioms of mathematics are necessary in order to prove a specific theorem or develop a specific branch of mathematics. This often reveals new insights on these theorems and branches, such as connections with other parts of mathematics, generalizations, and explicit proofs that provide additional information on the objects constructed. The program will gather experts who have contributed to the development of the field in its first 50 years in order to discuss recent advances and future directions, as well as explore and expand its connections with other fields of mathematics.

The program will last 10 weeks and include visits from researchers, collaborations, talks, and four weeks of focus workshops. 

Week 2 (June 30–July 4). Workshop "Reverse Mathematics and Higher Computability Theory."
Higher Computability Theory (or Higher Recursion Theory) investigates generalized notion of computability, e.g., carried out over the real numbers, abstract structures, or in infinite time, as well as its connections with definability, notions of complexity, and model theory. By establishing connections with computability in the usual sense, Higher Computability Theory has deep interactions with Reverse Mathematics. This will be the topic of the workshop.

Week 6 (July 28–August 1). Summer School "Reverse Mathematics: New Paradigms."

The summer school will feature courses by the following lecturers:

Damir Dzhafarov (UConn). From topology to combinatorics, via reverse mathematics.
Ekaterina Fokina (TU Wien). Computable structure theory.
Anton Freund (U Würzburg). The strength of better-quasi-orderings, via ordinal analysis.
Ludovic Patey (Paris). Lowness and avoidance: a guide to separation.
Keita Yokoyama (Tohoku). Reverse mathematics for
analysis: an introduction

Week 7 (August 4–8). Workshop "Reverse Mathematics: New Paradigms."
The "Big Five" systems of Reverse Mathematics are commonly said to suffice for capturing the strength of "most" mathematical theorems. The New Paradigms workshop will welcome explorations into recent and future developments beyond the Big Five involving stronger axiomatic systems, weaker axiomatic systems, or "adjacent" axiomatic systems, as well as new potential approaches to Reverse Mathematics, e.g., in terms of higher-type or higher-order systems, or systems based on more languages other than arithmetic.

Week 10 (August 25–29). Workshop "Reverse Mathematics: Beyond Logic."
This workshop will welcome aspects of Reverse Mathematics which relate to other branches of mathematics such as topology, algebra and order theory, finite and infinite combinatorics, analysis, as well as connections with computer science, philosophy, physics, game theory, and more.