Characteristic and Obstruction classes in Mass partition problems

Characteristic and obstruction classes represent natural invariants of vector and fiber bundles. They are widely used tools in classical algebraic topology. In this talk, we will present how they can help give answers to some mass partition problems. Ham sandwich theorem, a staple mass partition result, says that d nice measures in R^d can be simultaneously equipartitioned by an affine hyperplane. Over time, other mass partition results were considered, some of them being generalizations or extensions of the ham sandwich theorem. However, many questions in the field remain completely open. We will focus on several results of this type, which we approach with methods from equivariant topology. The talk is based on joint works with Pavle Blagojević and with Pablo Soberón.