Homotopy, rationality, and geometry

Conference - Homotopy, rationality, and geometry

Homotopic methods have deepened our understanding of rationality phenomena, from rational obstructions (non-abelian Chabauty, section conjecture, Brauer–Manin) to estimates in dimension growth and height estimates (IUT, Heath-Brown-Serre conjecture, Batyrev-Manin conjecture, Malle conjecture) and non-rationality (Hilbert specialization property).

Moduli situations (Hurwitz spaces and SL2-torsors) provide new contexts for geometry and arithmetic to interact. Anabelian algorithms reveal new structures (e.g., monoids and quasi-tripods) and new models for central objects of number theory (e.g., BGT subgroups wrt the absolute Galois group of rational numbers).

• Lior Bary -Soroker, Tel Aviv University, IL
• Alexander Betts, Cornell University, US
• Benjamin Collas, RIMS, Kyoto University, JP
• Raf Cluckers, Université de Lille – CNRS, FR
• Pierre Dèbes, Université de Lille, FR
• Cyril Demarche, IMJ-PRG (Sorbonne Université), FR
• Arno Fehm, TU Dresden, DE
• David Harbater, University of Pennsylvania, US
• Yuichiro Hoshi, RIMS, Kyoto University, JP
• Diego Izquierdo, IMJ-PRG (Sorbonne Université), FR
• Ariyan Javanpeykar, Radboud University Nijmegen, NL
• Joachim König, Korea National University of Education, KR

• Jochen Koenigsmann, University of Oxford, UK
• Emmanuel Lepage, IMJ-PRG (Sorbonne Université), FR
• Shinichi Mochizuki, RIMS, Kyoto University, JP
• Danny Neftin, Technion – Israel Institute of Technology, IL
• Christopher Rasmussen, Wesleyan University, US
• Mohamed Saïdi, University of Exeter, UK
• Koichiro Sawada, RIMS, Kyoto University, JP
• Shota Tsujimura, RIMS, Kyoto University, JP
• Craig Westerland, University of Minnesota, US
• Takehiko Yasuda, Osaka University, JP
• Yu Yang, RIMS, Kyoto University, JP
• Umberto Zannier*, Scuola Normale Superiore di Pisa, IT