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:20240329T131345Z
DTSTART;TZID=Europe/Budapest:20210924T101500
DTEND;TZID=Europe/Budapest:20210924T121500
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR