Wednesdays at 11:00AM in South Hall 6635
April 18 | Sherilyn Tamagawa (UCSB)
Quandles and Friends
Quandles encode knots as algebraic structures. In this introductory talk, I will describe quandles and some of the ways we use them to study knots. I will also describe some algebraic structures closely related to quandles.
May 23 | Alan Tran (UCSB)
April 4 | Wade Bloomquist (UCSB)
Quantum Representations of Mapping Class Groups and Their Applications
A ``quantum" representation of the mapping class group of a surface is one coming from a 2+1 TQFT. Certain quantum representations can be built using colored ribbon graph invariants. For special families of these representations a second meaning arises for ``quantum". In particular, for these families, in the limit of a parameter classical topological information can be recovered (a property called asymptotic faithfulness). After introducing these representations and discussing asymptotic faithfulness we will dive into some applications both within mathematics and topological quantum computing.