Mathematical Sciences
Departmental Weekly Events
August 25 – August 29, 2025
Agenda
Monday, August 25
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*Please note change in time for the whole of the fall 2025 semester.
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Tuesday, August 26
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Wednesday, August 27
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Thursday, August 28
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Friday, August 29
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Abstract: The quantum automorphism group of a graph is a natural generalization of the notion of automorphism group of a graph in the framework of compact quantum groups. What makes these objects particularly interesting is their interplay with the Graph Isomorphism nonlocal game from quantum information theory. However, explicit computation of quantum automorphism groups of graphs is quite difficult and few general results were known a few years ago. In this talk, we shall explore algebraic and combinatorial tools which enable us to compute quantum automorphism groups of larger graphs from those of simpler ones. In particular, we give explicit algorithms for computing quantum automorphism groups of large families of graphs such as forests, outerplanar graphs, and block graphs, and study quantum automorphism groups of lexicographic products of graphs. |
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| Abstract: In 2006, Przytycki observed that Khovanov’s homology theory for links in S^3 coincided with an older invariant of associative algebras, called Hochschild homology, on a certain class of links. Since then, Hochschild homology has been used frequently as a tool to study Khovanov homology. Conversely, our work with variants of Khovanov homology has motivated a novel generalization of Hochschild homology to a particular class of non-associative algebras. In this talk, I will survey the interactions between these two homology theories and, time willing, define the generalized Hochschild complex. |
Notes:
August 29th
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