Recorded 09 January 2024. Kent Vashaw of the Massachusetts Institute of Technology presents "A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories" at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Abstract: Carlson's connectedness theorem for cohomological support varieties is a fundamental result which states that the support variety for an indecomposable module of a finite group is connected. In this talk, we will discuss a generalization, where it is proved that the Balmer support for an arbitrary monoidal triangulated category satisfies the analogous property. This is shown by proving a version of the Chinese remainder theorem in this context, that is, giving a decomposition for a Verdier quotient of a monoidal triangulated category by an intersection of coprime thick tensor ideals. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/symmetric-tensor-categories-and-representation-theory/?tab=overview