LdT Seminar - Tomorrow (Room 136)

[Rafael Torres]

Speaker:  Lucrezia Beatrice Lorenzi (SISSA)

Title: Extending the Jones polynomial to a 3-manifold invariant

Abstract: Reshetikhin and Turaev's theorems on the interplay of algebra representations and ribbon tangles allow for introducing families of closed 3-manifold invariants. Via this interplay, such families are related to some categories, called modular, whose structure is linked to low-dimensional topology, as the name might hint to (think of the modular group).
In this seminar, we are going to study a specific instance of Reshetikhin-Turaev invariant, which extends the Jones polynomial to a closed 3-manifold invariant. After having topologically analyzed the generic formula following from Reshetikhin and Turaev theorems, and how does it find a manifold invariant, we will shift to the relation with modular categories, which will be thoroughly defined, and contextualized in a LdT setting. After a quick break, we will study our suitable choice of modular category, namely that of finite-dimensional representations of the quantum group over sl_2, where the formal parameter q is evaluated at a root of unity. In conclusion, we will find out how does the Jones polynomial arise as an invariant associated to this choice of category.
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Date: Thursday March 13th, 2025
Time: 11:00 am
Venue: Room 136