BEGIN:VCALENDAR
METHOD:REQUEST
PRODID:Microsoft Exchange Server 2010
VERSION:2.0
BEGIN:VTIMEZONE
TZID:FLE Standard Time
BEGIN:STANDARD
DTSTART:16010101T040000
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
RRULE:FREQ=YEARLY;INTERVAL=1;BYDAY=-1SU;BYMONTH=10
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:16010101T030000
TZOFFSETFROM:+0200
TZOFFSETTO:+0300
RRULE:FREQ=YEARLY;INTERVAL=1;BYDAY=-1SU;BYMONTH=3
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
ORGANIZER;CN=Kushnerchuk Nataliia:mailto:nataliia.kushnerchuk@aalto.fi
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=FALSE;CN=agc-math-
 aalto@list.aalto.fi:mailto:agc-math-aalto@list.aalto.fi
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=FALSE;CN=matlait-h
 enkilosto@helsinki.fi:mailto:matlait-henkilosto@helsinki.fi
DESCRIPTION;LANGUAGE=en-GB:We would like to invite you to the next talk of 
 autumn in the Aalto AGC (Algebra\, Geometry and Combinatorics) Seminar!\n\
 nThe talk is on\nMon 05.10. at 14:15-15:00\nin\nM3 (M234)\, Otakaari 1.\n\
 nThe speaker is\nVanni Nocerini (Aalto)\ngiving the talk\nRosenbrock's The
 orem characterizes Prüfer domains\n\nAbstract:\nUnder coprimality assumpt
 ions on certain submatrices\, Rosenbrock's Theorem relates the invariant f
 actors of a matrix P to those of its "transfer function" (an engineering t
 erm that denotes the Schur complement of a leading principal submatrix\, a
 ssumed invertible) G. Motivated by applications in systems theory\, Rosenb
 rock first proved this result in the 1960s for P \\in \\R[x]. In 1974\, Co
 ppel proved Rosenbrock's Theorem in much broader generality\, assuming tha
 t the base ring is a PID.\n\nI would like to discuss some recent results o
 n this theorem:\n\n\n  1.\nEven Coppel's assumptions can be weakened furth
 er to show that Rosenbrock's Theorem holds over any elementary divisor dom
 ain (EDD). This is relevant for engineering applications over the ring of 
 entire functions. Moreover\, even when the assumptions of the theorem do n
 ot hold\, it is possible to estimate the relation between the invariant fa
 ctors of P and G.\n  2.\nBecause the Smith and Smith-McMIllan forms are on
 ly guaranteed to exist over an EDD (or its field of fractions)\, the resul
 t in part (a) means that Rosenbrock's Theorem holds for every integral dom
 ain over which its original statement makes sense. However\, it possible t
 o reopen the question by translating the statement in the language of frac
 tional ideals. One can then prove that this "ideal-theoretic Rosenbrock's 
 Theorem" holds if and only if the underlying ring is a Prüfer domain. For
  more general rings\, several interesting partial results can also be stat
 ed\, some of which are still motivated by applications to engineering. Som
 e connections with the Quillen-Suslin theorem also arise.\n\n\n\nPart (a) 
 is based on joint work with Dopico and Zaballa\; part (b) is based on a si
 ngle authored paper.\n\n\n
UID:040000008200E00074C5B7101A82E008000000009548BA108951DD01000000000000000
 010000000B9891EDA360CA74596547B9E2BE6FA63
SUMMARY;LANGUAGE=en-GB:[Aalto AGC seminar] Vanni Noferini | Rosenbrock's Th
 eorem characterizes Prüfer domains | Mon 05.10 at 14.15
DTSTART;TZID=FLE Standard Time:20261005T141500
DTEND;TZID=FLE Standard Time:20261005T150000
CLASS:PUBLIC
PRIORITY:5
DTSTAMP:20261001T094143Z
TRANSP:OPAQUE
STATUS:CONFIRMED
SEQUENCE:0
LOCATION;LANGUAGE=en-GB:Otakaari 1\, M234
X-MICROSOFT-CDO-APPT-SEQUENCE:0
X-MICROSOFT-CDO-OWNERAPPTID:2125072877
X-MICROSOFT-CDO-BUSYSTATUS:TENTATIVE
X-MICROSOFT-CDO-INTENDEDSTATUS:BUSY
X-MICROSOFT-CDO-ALLDAYEVENT:FALSE
X-MICROSOFT-CDO-IMPORTANCE:1
X-MICROSOFT-CDO-INSTTYPE:0
X-MICROSOFT-ONLINEMEETINGEXTERNALLINK:
X-MICROSOFT-ONLINEMEETINGCONFLINK:
X-MICROSOFT-DONOTFORWARDMEETING:FALSE
X-MICROSOFT-DISALLOW-COUNTER:TRUE
X-MICROSOFT-REQUESTEDATTENDANCEMODE:DEFAULT
X-MICROSOFT-ISRESPONSEREQUESTED:FALSE
X-MICROSOFT-LOCATIONDISPLAYNAME:Otakaari 1\, M234
X-MICROSOFT-LOCATIONSOURCE:None
X-MICROSOFT-LOCATIONS:[{"DisplayName":"Otakaari 1\, M234"\,"LocationAnnotat
 ion":""\,"LocationUri":""\,"LocationStreet":""\,"LocationCity":""\,"Locati
 onState":""\,"LocationCountry":""\,"LocationPostalCode":""\,"LocationFullA
 ddress":""}]
BEGIN:VALARM
DESCRIPTION:REMINDER
TRIGGER;RELATED=START:-PT15M
ACTION:DISPLAY
END:VALARM
END:VEVENT
END:VCALENDAR