IMPA, Rio de Janeiro, March 17 – 21

The study of Geometry proposes many problems of comparison between the volume of a space and the length/area of curves/surfaces of a certain type that it contains. There are many examples of such problems. Every convex billiard limited in the plane contains periodic orbits, in particular one with a shorter period. By varying the billiard, but keeping the area fixed, which one has the largest periodic orbit with the shortest period? All the spheres contain an immersed periodic geodesic, in particular a shorter one. Among spheres with the same area, how large can the length of this shortest geodesic be? Each compact surface has a spectrum associated with its Laplacian operator, and this contains a smallest positive eigenvalue. Among surfaces of the same area, how big can this first eigenvalue be? These and other very similar questions have been investigated by mathematicians from different specialties and using different techniques from Differential Geometry, Analysis and Simplified Geometry. Despite great progress towards establishing optimal inequalities for the quantities discussed above, many basic conjectures about them remain. The event “Systolic and Diastolic Geometry” will be dedicated to disseminating the state of the art on the main conjectures about problems such as those described above, and to bringing together different specialties to motivate future research in which innovative techniques, inspired by the analogies between these problems, enable significant advances and the solution of fundamental problems in Geometric Analysis and Simplified Geometry.

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Program

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Guest Speakers

  • Alberto Abbondandolo (Bochum)
  • Alexey Balitskiy (Luxembourg)
  • Alexander Nabutovsky (Toronto)
  • André Neves (UChicago)
  • Florent Balacheff (Autònoma de Barcelona)
  • Gabriele Benedetti(VU Amsterdam)
  • Johanna Bimmerman (Bochum)
  • Juan Carlos Alvarez-Paiva (Lille)
  • Luca Asselle (Bochum)
  • Mikhail Karpukhin (UCL)
  • Pazit Haim-Kislev (Tel Aviv)
  • Rafael Montezuma (UFC)
  • Regina Rotman (Toronto) – Romain Petrides (Paris Cité)
  • Shira Tanny (IAS)
  • Stéphane Sabourau (Paris-Est Créteil)
  • Xin Zhou (Cornell)
  • Yaron Ostrover (Tel Aviv)
  • Yevgeny Liokumovich (Toronto)
Scientific Committee
  • Lucas Ambrozio (IMPA)
  • Vinicius Ramos (IMPA)
  • Umberto Hryniewicz (Aachen)

Organizing Committee

  • Lucas Ambrozio (IMPA)
  • Vinicius Ramos (IMPA)
  • Umberto Hryniewicz (Aachen)

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