Chinese Remainder Theorem and Carlson's Theorem for Monoidal Triangulated Categories

Explore a lecture on advanced mathematical concepts in category theory and representation theory. Delve into Kent Vashaw's presentation on "A Chinese remainder theorem and Carlson's theorem for monoidal triangulated categories" from the Massachusetts Institute of Technology. Discover how Carlson's connectedness theorem for cohomological support varieties is generalized to monoidal triangulated categories. Examine the proof of a Chinese remainder theorem in this context, which provides a decomposition for Verdier quotients of monoidal triangulated categories by intersections of coprime thick tensor ideals. Gain insights into the Balmer support for arbitrary monoidal triangulated categories and its analogous properties to Carlson's theorem. This 52-minute talk, part of IPAM's Symmetric Tensor Categories and Representation Theory Workshop, offers a deep dive into cutting-edge mathematical research connecting various areas of algebra and topology.