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{\Large Department of Mathematics, BGU}

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\textbf{On} \emph{Wednesday, November  6, 2024}
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\textbf{At} \emph{14:10 -- 15:10}
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\textbf{In} \emph{-101}

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{\large\scshape Nadav Gropper 
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  (University of Haifa)
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will talk about
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{\Large\bfseries TQFTs for pro-p Poincare duality groups\par}
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\textsc{Abstract:}
In the talk, I will discuss the Turner-Turaev formalism for unoriented Topological Quantum Field Theory (TQFT). Building upon this formalism, I will introduce an analogous version for (d+1)-dimensional TQFT for pro-p Poincare duality groups.
In the case of d = 1, this enables us to study cobordisms and TQFTs for both the maximal pro-p quotient of absolute Galois groups of p-adic fields and pi\_1(X)\^{}p, the pro-p completions of fundamental groups of surfaces. 
This generalisation gives a framework for arithmetic TQFTs and strengthens the analogies within arithmetic topology, which relates p-adic fields to surfaces (oriented mod p\^{}r). I will explain the classification of TQFTS for the (1+1)-dimensional case, in terms of Frobenius algebras with some extra structure.

If time permits, I will explain how we define a Dijkgraaf Witten like theory, to get formulas for counting G-covers of X, where X is either a surface, or a p adic field, and G is a p-group (these formulas are similar to the ones given by Mednykh for surfaces using TQFTs, and by Masakazu Yamagishi using a more algebraic approach). I will also try to outline how we plan to also get similar formulas for Hom(\textbackslash{}pi\_1(X)\^{}p,G), where G=GL\_n(k) for k=F\_\{p\^{}r\} or Z/p\^{}rZ.

The talk is based on joint work with Oren Ben-Bassat.








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