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Explore the mathematical construction of Turaev-Viro invariants derived from the quantum group $U_{q}sl(2;\mathbb{R})$ in this 56-minute conference talk presented at ICBS2025. Delve into the theoretical foundations of quantum topology and learn how these invariants are computed using representations of the quantum universal enveloping algebra of $sl(2;\mathbb{R})$. Examine the relationship between quantum groups and topological invariants, understanding how the real form of the quantum special linear group contributes to the development of these mathematical tools. Gain insights into advanced topics in quantum topology, including the role of quantum deformation parameters and their applications in three-dimensional topology through the lens of Turaev-Viro theory.
