#  Seminar, Pavel Etingof (MIT), New symmetric tensor categories in positive characteristic 

 



####  calendar\_today Date and Time 

 **September 25, 2018** 

 04:00PM - 05:00PM EDT 

####  pin\_drop Location 

 **Jefferson 356**  



 

 



 

   ![Pavel Etingof](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/etingof_pavel.png?itok=Z9uMo5SB) 

 

 **Title.** New symmetric tensor categories in positive characteristic

 **Abstract**. We construct and study a nested sequence of finite symmetric tensor  
categories \\({\\rm Vec}=\\mathcal C\_0\\subset \\mathcal C\_1\\subset\\cdots\\subset \\mathcal C\_n\\subset\\cdots\\)  
over a field of characteristic 2 such that \\(\\mathcal C\_{2n}\\) are  
incompressible, i.e., do not admit tensor functors into  
tensor categories of smaller Frobenius--Perron dimension.  
This generalizes the category \\(\\mathcal C\_1\\) described by S. Venkatesh and the category \\(\\mathcal C\_2\\) defined by V. Ostrik.  
The Grothendieck rings of the categories \\(\\mathcal C\_{2n}\\) and \\(\\mathcal C\_{2n+1}\\) are both isomorphic to the ring of real cyclotomic integers defined by a primitive \\(2^{n+2}\\)-th root of unity, \\({\\mathcal O}\_n=\\Bbb Z\[2\\cos(\\pi/2^{n+1})\]\\). We expect that the category \\(\\mathcal C\_{2n}\\) is a reduction to characteristic 2 of the Verlinde category at the \\(2^n\\)-th root of unity, and that there exists similar non-semisimple reduction of the Verlinde category at the \\(p^n\\)-th root of unity to characteristic p when . This is joint work with Dave Benson.





 

 



 

 

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