On super exterior powers and Berezinians
| Dates: | 5 October 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Speaker: | Theodore Voronov (Manchester) |
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Abstract:
I will speak about power expansions of the function $R(z)=\mathrm{Ber}(E+ zA)$, where A is a linear operator in a superspace (or a supermatrix). Berezinian is the superanalog of determinant. Unlike the classical case, is not a polynomial in the matrix entries but a rational function. Also, it cannot be described in terms of the top exterior power because no such top power exists in the super case. However, a non-obvious connection between these notions exists, and it is encoded in the properties of the expansions of $\mathrm{Ber}(E+ zA)$. (Due to Khudaverdian and myself, also earlier work of Th. Schmitt.) For example, "vanishing of top power" is replaced by "universal recurrent relations" (satisfied by the supertraces or in the Grothendieck ring), and $\mathrm{Ber} A$ is expressed as the ratio of certain Hankel determinants built of supertraces of exterior powers. There has been some interesting new development (due to Ekanayaka-Shemyakova), which I can also speak about if time permits.
Speaker
Theodore Voronov (Manchester)
Travel and Contact Information
Find event
Frank Adams room 1
Alan Turing Building
Manchester
