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)
Ekaterina Fokina (TU Wien)
Anton Freund (U Würzburg)
Ludovic Patey (Paris)
Keita Yokoyama (Tohoku)
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.
Coming soon.
Organizers
Name | Affiliation |
---|---|
Juan Aguilera | Technical University of Vienna |
Linda Brown Westrick | The Pennsylvania State University |
Noam Greenberg | Victoria University of Wellington |
Denis Hirschfeldt | University of Chicago |
Attendees
Name | Affiliation |
---|---|
Miguel Aguilar | TU Wien |
Alessandro Andretta | University of Torino |
Heidi Benham | University of Connecticut |
Kenza Benjelloun | Université Côte d'Azur |
Sapir Ben-Shahar | University of Wisconsin-Madison |
Raphaël Carroy | University of Torino |
William Chan | Technical University of Vienna |
Peter Cholak | University of Notre Dame du Lac |
Chris Conidis | City University New York |
Andrew DeLapo | University of Connecticut |
Andres Diaz Rojas | Universitat de Barcelona, ICCUB |
Isabel Diaz Rojas | University of Sheffield |
Natasha Dobrinen | University of Notre Dame du Lac |
Gavin Dooley | University of Notre Dame du Lac |
François Dorais | University of Vermont |
Damir Dzhafarov | University of Connecticut |
Luca Facchinetti | University of Udine |
David Fernández-Duque | University of Barcelona |
Ekaterina Fokina | TU Wien |
Johanna Franklin | Hofstra University |
Anton Freund | University of Würzburg |
Sy David Friedman | University of Vienna |
Yuxiao Fu | University of Connecticut |
Elijah Gadsby | City University New York |
Mariami Gamsakhurdia | TU Wien |
Su Gao | Nankai University |
Giorgio Genovesi | University of Leeds |
Oriola Gjetaj | Ghent University |
Sarah Gleghorn | University of Cambridge |
Jun Le Goh | National University of Singapore |
David Gonzalez | University of California, Berkeley |
Zakkai Goriely | University of California, Berkeley |
Vassilios Gregoriades | National and Technical University of Athens |
Piotr Gruza | University of Warsaw |
Ellen Hammatt | TU Wien |
Jeffry Hirst | Appalachian State University |
Edward Hou | Caltech University |
Martina Iannella | TU Wien |
Corrie Ingall | University of Connecticut |
Josiah Jacobsen-Grocott | Nanyang Technological University |
Hanul Jeon | Cornell University |
Liling Ko | TU Wien |
Ulrich Kohlenbach | Technical University Darmstadt |
Leszek Kołodziejczyk | University of Warsaw |
Thibaut Kouptchinsky | TU Wien |
Jan Kruschewski | TU Wien |
Vlad Lazar | Ghent University |
Dominique Lecomte | University Paris Jussieu |
Ludovic Levy Patey | CNRS Paris |
Lu Liu | Central South University |
Robert Lubarsky | Florida Atlantic University |
Philipp Lücke | University of Hamburg |
Alberto Marcone | University of Udine |
Andrew Marks | University of California, Berkeley |
Russell Miller | City University of New York |
Antonio Montalbán | University of California, Berkeley |
Carl Mummert | Marshall University |
Antonio Nakid Cordero | University of Wisconsin-Madison |
Selwyn Ng | Nanyang Technological University |
Orazio Nicolosi | University of Torino |
Andre Nies | University of Auckland |
Gian Marco Osso | University of Udine |
Fedor Pakhomov | Ghent University |
Aristotelis Panagiotopoulos | University of Vienna |
Konstantinos Papafilippou | Ghent University |
Alvaro Pintado | University of Pennsylvania |
Nicholas Pischke | Technical University Darmstadt |
Philipp Provenzano | Ghent University |
Dino Rossegger | TU Wien |
Sam Sanders | Ruhr-Universität Bochum |
Philipp Schlicht | University of Siena |
Paul Shafer | University of Leeds |
Aeacus Sheng | Carnegie Mellon University |
Borja Sierra | University of Bern |
Giovanni Soldà | Ghent University |
Grigorii Stepanov | TU Wien |
Patryk Szlufik | University of Warsaw |
Catalina Torres | University of Barcelona |
Henry Towsner | University of Pennsylvania |
Daniel Turetsky | Victoria University of Wellington |
Manlio Valenti | Swansea University |
José Jeremías Valenzuela Morales | George Washington University |
Java Darleen Villano | University of Connecticut |
Andrea Volpi | University of Udine |
Wei Wang | Sun Yat-sen University |
Jin Wei | Technical University Darmstadt |
Andreas Weiermann | Ghent University |
Philip Welch | University of Bristol |
Keita Yokoyama | Tohoku University |
Liang Yu | Nanjing University |
Miroslav Zeleny | Charles University Prague |