The UC Berkeley Representation theory and tensor categories seminar |
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| DATE | SPEAKER | TITLE (click to show abstract) |
| January 21 | Nicolai Reshetikhin , UC Berkeley and BIMSA |
Invariants of tangles with a flat connection in the complement I.Abstract: The construction of these invariants based on properties of quantum groups at roots of unity and it was proposed in a joint work with R. Kashaev. It is related to homotopy quantum field theory by V. Turaev. In this talk, I will recall the construction of these invariants, and I will explain why Poisson structures on the center of quantum groups at a root of unity that appear are natural from the geometry of flat connections in the complement to a tangle. |
| January 28 | No seminar | |
| February 4 | Nicolai Reshetikhin , UC Berkeley and BIMSA |
Invariants of tangles with a flat connection in the complement II.Continuation of the previous talk. Abstract: The construction of these invariants based on properties of quantum groups at roots of unity and it was proposed in a joint work with R. Kashaev. It is related to homotopy quantum field theory by V. Turaev. In this talk, I will recall the construction of these invariants, and I will explain why Poisson structures on the center of quantum groups at a root of unity that appear are natural from the geometry of flat connections in the complement to a tangle. |
| February 11 | Christian Gaetz, UC Berkeley |
SL(n) web bases from hourglass plabic graphsAbstract: The SL(3) web basis is a special diagrammatic basis for certain spaces of tensor invariants developed in the late 90’s by Kuperberg as a tool for computing quantum link invariants. Since then this basis has found connections and applications to cluster algebras, dimer models, quantum topology, and tableau combinatorics. A main open problem has remained: how to find a basis replicating the desirable properties of this basis for SL(4) and beyond? I will describe joint work with Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Josh Swanson in which we construct such a basis for SL(4). Modified versions of plabic graphs and the six-vertex model and new tableau combinatorics will appear along the way. |
| February 18 |
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| February 25 |
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| March 4 | Dmytro Matvieievskyi, Kavli IMPU |
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| March 11 |
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| March 18 |
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| March 25 | Spring Recess | |
| April 1 |
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| April 8 |
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| April 15 |
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| April 22 | Agustina Czenky, USC |
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| April 29 |
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