19/03/2025

IMPA promotes the 1st edition of 'Systolic and Diastolic Geometry'

The first edition of the event “Systolic and Diastolic Geometry” began this Monday (17) at IMPA and will run until next Friday (21). The workshop brings together researchers from around the world for a debate on geometric themes based on two main specialties: geometric analysis and symplectic geometry. Organised by IMPA researchers Lucas Ambrózio, Vinícius Ramos and Umberto Hryniewicz (Technical University of Aachen), the event has 61 registered participants.

“The fields of geometric analysis and symplectic geometry have objects in common, but not only that: there are a number of problems in these two areas that, abstractly, are very similar. These specific problems relate to the comparison of volume with other geometric quantities that I like to call, metaphorically, “systoles” and “diastoles,” explained Ambrose.

The workshop aims to disseminate the main research and advances made in attempting to solve common problems in geometry. Most of these deal with the comparison between the volume of a space and the length/area of curves/surfaces of a certain type.

The event also encourages the sharing of perspectives and insights among experts from different areas of geometry. "If all goes well, this meeting will foster new collaborations, suggest new lines of research, and perhaps create the right environment for someone to have that idea that will solve one of the great open conjectures about these systolic and diastolic problems in geometry," added Ambrózio.

The program features 21 speakers from institutions such as the University of Paris, the University of Chicago, and the Free University of Amsterdam.

A PhD from IMPA, Professor Brayan Ferreira, from the Federal University of Espírito Santo (UFES), returned to the institute this week to participate in the workshop and give a “short talk” this Monday (17). “This event has a good interface with symplectic geometry, which is my area. Vinicius Ramos, who is organizing the event, was my advisor and I was invited to give a short talk. The expectation is to see new ideas, to see how to bridge the areas and, in addition, the speakers are exceptional. I think it will be very cool.”

Bryan Ferreira

During the event's opening, Ramos welcomed the participants. “We are very happy that you are all here. We hope you have a great week and that we can interact, especially with people we don't normally see at conferences. We want people to come together and talk about similar things. So, don't miss the opportunity to talk to people, especially those you don't know. For those who are in Rio for the first time, I hope you enjoy it and make the most of the city.”