Juanita Pinzón Caicedo, an assistant professor in the Department of Mathematics, had wanted to do something for the Colombian mathematical community since she left the country in 2008.
She voiced her aspirations at the Colombian Congress of Mathematics and was later selected as a keynote speaker for the 2023 meeting. Her undergraduate advisor introduced her to the group and promptly put her in contact with professors who shared her interests. That same year, she joined the organizing committee of the first iteration of the Colombian Meeting of Geometry and Topology (ECOGyT) program in Bogotá, Colombia, with a plan to bring the two-week summer school to a new city every two years.
ECOGyT is dedicated to fostering intellectual discourse and community for Colombian topologists and geometers and their international counterparts, she said.
Pinzón Caicedo conceded that she didn’t know most of the other co-organizers of ECOGyT very well, but that their similar vision of bringing Latin Americans and the topology community together helped foster their own relationships with one another.
“We just felt this familiarity,” said Pinzón Caicedo, who received an undergraduate degree from the Universidad Los Andes in Bogotá and completed her doctorate at Indiana University before joining the University of Notre Dame in 2020. “We had a shared dream, right? And all of a sudden, this dream was coming true.”
The first week of the school offered four mini-courses, which allowed students to brush up on different areas of research. Pinzón Caicedo’s course on knots and surfaces introduced methods to construct algebraic objects that can tell different knots apart.
The second week then featured a series of lectures on novel developments and concepts in topology, with lecturers from universities in Brazil, Chile, Colombia, Germany and the United States.
She stressed the importance of bringing Colombian topologists together, but was fervent that invitations to the congress be made worldwide. International students arrived from Spain, Mexico, Brazil, and the U.S. Over 100 students attended the event, with mini-courses and lectures given by over two dozen professors.
These efforts were hampered by Colombia’s own geography, with Pinzón Caicedo joking that “the Andes enter Colombia to die.” Where Colombia borders Ecuador, located to its southwest, the mountain range becomes divided into three smaller ranges which run straight through the country. This makes land travel exceedingly difficult and expensive, but the event remained successful.
To help transform the outpouring of new faces into a community, ECOGyT included several social events.
“We tried to open spaces so that we would help different styles of learners and different types of people,” Pinzón Caicedo said. “Some people shine in social situations … but some people just want to think about math.”
These strategies appeared to pay off, with students offering a warm reception to the conference in their feedback to organizers. The participants sent the organizers a digital card which featured a drawing of a heart-shaped knot, and their individual signatures.
David Galvin, professor and chair of the Department of Mathematics at Notre Dame, spoke highly of Pinzón Caicedo, describing her as an innovative teacher and expert in her field of low-dimensional topology.
He praised ECOGyT as a “lab of mathematics,” where students are given the opportunity to gain new perspectives on topology through a week of shared academic and social experiences with researchers from all over the world.
Galvin also highlighted the challenges of organizing these types of conferences in South America, emphasizing that the continent is underrepresented on the international stage despite an abundance of talented researchers and professors like Pinzón Caicedo.
“Mathematics is absolutely a global subject. The homotopy group of the sphere (in topology, two continuous functions from one topological space to another are called “homotopic”) is the same whether you’re in South America or West Africa or Northern Europe or Australia,” he said.
Looking to future years, Pinzón Caicedo’s primary goal is to sponsor as many students as possible. However, this requires additional funding or grants for transportation and lodging expenses.
“If [anyone] wants to give me $20, I am telling you, those $20 could potentially pay for one night of a shared hotel room for one participant. And that’s just amazing,” she said.
Her request not only identifies a call to action for the mathematical community, but it's a testament to her commitment to making ECOGyT a longstanding institution.
About the author: Gray Nocjar is a junior electrical engineering major with minors in energy studies and in the Gallivan Program for Journalism, Ethics and Democracy at the University of Notre Dame.