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Alain Connes27/06/2022, 10:00
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Dietmar Bisch27/06/2022, 11:30
The hyperfinite II_1 factor contains a wealth of subfactors that give rise to many new and fascinating mathematical structures.
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Vaughan Jones discovered that the unitary tensor category generated by the standard representation of a subfactor has a planar structure and can be described as what he called a ``planar algebra''. It is a complete invariant for amenable subfactors by a deep result... -
David Evans27/06/2022, 14:30
Groups can act as symmetries of physical systems and on their mathematical models as in conformal field theory.
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Vaughan's subfactor theory provides a framework for quantum symmetries beyond those arising from groups or their deformations as quantum groups or loop groups. The accepted position was that the Haagerup system, associated with the a subfactor at index $(5+ \sqrt(13))/2$, was... -
Christian Blanchet28/06/2022, 09:30
We will review fundamental contributions of Vaughan Jones in the genesis of Quantum Topology. Then we will focus on representations of Mapping Class Groups highlighting a contribution of Vaughan Jones in genus 2. We will finally discuss homological models producing new representations.
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Helen Wong28/06/2022, 11:00
In the case of a closed surface, there is a rich body of work describing how the Kauffman bracket skein algebra can be regarded as a quantization of Teichmuller space. In order to generalize to a surface with punctures, Roger and Yang defined a skein algebra with extra generators and relations that they conjectured to be a quantization of Penner's decorated Teichmuller space. In joint work...
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Dror Bar-Natan28/06/2022, 13:30
Reporting on joint work with Roland van der Veen, I'll tell you some stories about ρ1, an easy to define, strong, fast to compute, homomorphic, and well-connected knot invariant. ρ1 was first studied by Rozansky and Overbay, it is dominated by the coloured Jones polynomial (but it isn't lesser!), it has far-reaching generalizations, and I wish I understood it.
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Pavel Safronov28/06/2022, 15:00
Skein modules were defined by Przytycki and Turaev as a way to generalize the Jones polynomial and the Kauffman bracket to links in manifolds other than the 3-sphere. In this talk I will review some recent structural results, such as the fact that the skein module of a closed 3-manifold is finite-dimensional for generic quantum parameters. I will also describe a work in progress joint with...
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Jean-Claude Hausmann29/06/2022, 09:30
We consider the following problem: when is a CW-space X homotopy equivalent to a CW-complex without j-cells for k<j<r ?
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We show that this is equivalent to some cohomology condition together with the vanishing of an algebraic K-theory "cell-dispensability obstruction", analogous but not equal to the Wall finiteness obstruction. A similar theory holds for closed manifolds, replacing ``cells''... -
Martin Bridson29/06/2022, 11:00
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Paul Wedrich30/06/2022, 09:30
The Temperley-Lieb algebra describes the local behaviour of the Jones polynomial and gives rise to the Kauffman bracket skein modules of 3-manifolds. Going up by one dimension, Bar-Natan's dotted cobordisms describe the local behaviour of Khovanov homology and, likewise, give rise to skein modules of 4-manifolds. I will describe the construction of these skein modules and methods to compute...
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Lisa Piccirillo30/06/2022, 11:00
In this talk I will discuss a classification of topological 4-manifolds with boundary and fundamental group Z, under some mild assumptions on the boundary. I will apply this classification classify surfaces in simply-connected 4-manifolds with 3-sphere boundary, where the fundamental group on the surface complement is Z. I will also compare these homeomorphism classifications with the smooth...
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Cameron Gordon30/06/2022, 13:30
It is well known that the ADE graphs arise in many classification problems in mathematics. In 2019 Michel Boileau, Steve Boyer and I conjectured a modest addition to this list: the fibered links that induce the tight contact structure on S^3 and have a cyclic branched cover whose fundamental group is left-orderable. We will describe the conjecture, its background, and some recent results that...
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Hans Wenzl30/06/2022, 15:00
{Abstract:}\textit{The famous Schur-Weyl duality states that the commutant of the action of
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$Gl(V)$ on $V^{\otimes n}$ is generated by the obvious action of the symmetric group $S_n$
on $V^{\otimes n}$. We will first give a survey of quantum groups $U_q{\mathfrak g}$ and representations $V$,
where the commutant of the action of $U_q{\mathfrak g}$ on $V^{\otimes n}$ is (almost) generated by... -
Mikhail Khovanov01/07/2022, 09:30
Skein modules were defined by Przytycki and Turaev as a way to generalize the Jones polynomial and the Kauffman bracket to links in manifolds other than the 3-sphere. In this talk I will review some recent structural results, such as the fact that the skein module of a closed 3-manifold is finite-dimensional for generic quantum parameters. I will also describe a work in progress joint with...
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Aaron Lauda01/07/2022, 11:00
There is a rich interplay between two-dimensional topological phases in quantum mechanical systems and topological quantum field theory. This interaction is further enriched as topological structures inherent in TQFT lead to novel features, such as non-abelian braiding statistics for low energy excitations, when expressed in the corresponding quantum mechanical models. In this talk, we will...
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