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Tuesday, 9 April 2024 - 10:00 to 11:30 <br />
Place: IM, konÃrna
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Speaker: Michael Kompatscher, Univerzita Karlova<br />
Title: Interpolation over finite algebraic structures
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Abstract <br />
<p><br></p><p>It is a well-known fact that the polynomials F[x1,...,xn] over a finite field F can be used to interpolate any partial operation F^n -> F. Moreover, such interpolating polynomials can be constructed fairly easily. In this talk, I would like to discuss, for which other finite algebraic structures A analogous statements hold. As it is quite rare that then _every _partial operation can be interpolated by A, we focus on the following two computational questions: For which A can we efficiently decide, whether a given partial operation can be interpolated by a term of A? When can we even efficiently compute such interpolating terms?</p><p><br></p><p>In particular, I want to discuss the complexity for so-called Mal'tsev algebras, a big class of algebraic structures that includes groups, rings, fields, Boolean algebras, quasigroups, etc. Mal'tsev algebras are conjectured to admit polynomial time algorithms for both problems.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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