Complexes of Surfaces in Low Dimensional Topology (26w5641)

The Casa Matemática Oaxaca (CMO) will host the "Complexes of Surfaces in Low Dimensional Topology" workshop in Oaxaca, from May 17 to May 22, 2026.

Two-dimensional objects, known as surfaces, are prevalent in physical systems. For example, surfaces arise as isothermals dividing between hotter regions and colder ones and also as frontiers between two media such as oil-and-water. These surfaces may evolve either as the choice of temperature of isothermal is varied or as the frontier undulates and forms connects or separates. Understanding these surfaces and the ways they may evolve provides valuable knowledge about physical systems. Additionally, the study of surfaces is instrumental in exploring higher-dimensional shapes, particularly in three- and four-dimensional spaces.

A common technique to analyze special surfaces is to construct a graph where the vertices represent the surfaces of interest. Two vertices are connected by an edge if their corresponding surfaces are related by elementary moves. The topological properties of this graph, such as connectedness and symmetry, help explain how surfaces organize themselves within a three- or four-dimensional manifold.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta Technology and Innovation. The research station in Oaxaca is funded by UNAM and IIMAS.