BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:Europe/Budapest END:VTIMEZONE BEGIN:VEVENT UID:2o9s47ifspevlifg5b8gru3dov@google.com CATEGORIES:{lang hu}Algebra szeminárium{/lang}{lang en}Algebra seminar{/lang} SUMMARY:Ágnes Szendrei (University of Colorado, Boulder): Introduction to the Subpower Membership Problem - Part 2 LOCATION:Riesz Lecture Hall, 1st Floor, Bolyai Institute, Aradi Vértanúk tere 1., Sz eged DESCRIPTION;ENCODING=QUOTED-PRINTABLE:Abstract. Let A be a fixed finite algebra with finitely many basic operatio ns. The Subpower Membership Problem for A is the following combinatorial de cision problem SMP(A):
Input: k+1 elements a_1, … , a_k, b of A^n (for some integers k,n>0).
Question: Is b in the subalgebra of A^n generated by a_1, … , a_k?

In the talks I plan to survey what is currently known about this problem, emphasizing how purely algebraic results have con tributed to making progress. The outline is as follows:

1. The nai ve algorithm; applications of more efficient algorithms.
2. An efficien t algorithm for classical structures (groups, rings, modules).
3. The l argest class of algebras for which a similar `generalized Gaussian eliminat ion’
algorithm might work: forks, few subpowers, edge/parallelogram terms.
4. A sufficient condition for a finite algebra A with a paralle logram term so that there
exists an efficient algorithm for SMP(A).
5. Next steps? DTSTAMP:20211129T175552Z DTSTART;TZID=Europe/Budapest:20210924T101500 DTEND;TZID=Europe/Budapest:20210924T121500 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR