IMPA hosts events on algebraic geometry and differential equations

This week, IMPA hosted two scientific meetings that brought together researchers from different institutions in Brazil and abroad to discuss central themes in contemporary mathematics. On Thursday (14) and Friday (15), the Institute hosted the final stage of the Conference on Hodge theory, birational geometry and atomsan international series of conferences focused on algebraic geometry. On Friday (15), the Rio de Janeiro Colloquium on Analysis and Differential Equations (CRANED) was also held, a meeting that seeks to strengthen integration between research groups in the state of Rio de Janeiro.

A Conference on Hodge theory, birational geometry and atoms connected research centers in North and South America, passing through the University of Miami, the Institute of Mathematical Sciences of the Americas (IMSA) and Unicamp, until arriving at IMPA. The meeting brought together experts in algebraic geometry to discuss recent developments, especially in the interaction between Gromov-Witten theory and Hodge theory, an area that has been driving new research directions. This movement culminates in the so-called “theory of atoms”, developed in works by Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev and Tony Yu, and later expanded to the context of GGG-equivariant birational geometry in the article Atoms meet symbolsby Leonardo Cavenaghi, Ludmil Katzarkov and Maxim Kontsevich.

IMPA researcher and one of the organizers of the event, Miikhail Verbitskiy highlighted the relevance of the conference both for the dissemination of results and for strengthening the Institute’s international collaborations.

“IMPA is one of the most important research centers in algebraic geometry in Brazil and Latin America. With this conference, we brought to the Institute the important new theory of atoms developed by Katzarkov, Kontsevich, Pantev and Yu, allowing these results to be appreciated by local specialists in birational geometry and related subfields,” he said.

Maria Eduarda Martins, a doctoral student at IMPA, highlighted the interdisciplinary nature of the meeting. “I found the event interesting because it addressed a new and more modern area, which has recently emerged from the dialog between different fields – including my area of research, Birrational Geometry. There are a lot of cool intersections being worked on,” he said.

Juan Pablo Campo, also a doctoral student at IMPA, highlighted the most important lectures for his research. “The event caught my attention because it was in my field. I was interested in attending some of the lectures, such as the one by Oliver Martin, my advisor, as well as those by Jorge Vitório and Vladimiro Benedetti”, he said.

The event was also attended by Carolina Araujo (IMPA), Giovane Neto (ICMS), Jérémy Guéré (Grenoble), Leonardo Cavenaghi (ICMS), Ludmil Katzarkov (UM/ICMS), Shaowu Zhang (Caltech), Alexey Elagin (Edinburgh), Antoine Pinardin (Basel) and Lino Grama (Unicamp).

CRANED was held this Friday (15)

Also on Friday (15), IMPA hosted the Rio de Janeiro Colloquium on Analysis and Differential Equations (CRANED), organized jointly by IMPA and the institutions FGV EMAp, UFRJ, UFF, Uerj and PUC-Rio. The event aims to bring together the different research groups working in the areas of mathematical analysis and partial differential equations (PDEs) in the state of Rio de Janeiro.

Rio de Janeiro Colloquium on Analysis and Differential Equations (CRANED)

Pavel Petrov, a researcher at IMPA and one of the organizers of the meeting, stressed that the colloquium seeks to strengthen links between institutions and expand opportunities for scientific collaboration. “The colloquium seeks to connect all the universities in Rio that have strong research groups in analysis and EDPs,” he explained.

According to the researcher, CRANED functions as a space for researchers from different institutions to come together, allowing collaborations to emerge that can mature over the years.

“There is also the opportunity to get to know the work of colleagues from FGV, UFRJ, UFF and other institutions better, finding points of contact between the research. CRANED can be seen as a ground where we try to plant seeds of collaboration. The impact of these connections may come a long time later, but it is important to invest effort in building these relationships,” he said.

The researcher also highlighted the diversity of topics in the area of analysis and EDPs, which brings together both theoretical and numerical approaches. “The number of challenges in the area is enormous, because the field itself is very broad. EDPs and analysis connect very diverse approaches, both analytical and numerical. I think it’s important to preserve this spirit of diversity and promote a kind of fusion between different lines of research,” he concluded.