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CALSCALE:GREGORIAN
METHOD:PUBLISH
UID:e51905a7-8593-49ce-8b3e-cc1d660a215a
X-WR-CALNAME:Seminaire SYNTHESE\, Blaise Genest
X-WR-TIMEZONE:Europe/Paris
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TZID:Europe/Paris
TZUNTIL:20270328T010000Z
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DTSTART:20241027T030000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
RDATE:20251026T030000
RDATE:20261025T030000
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DTSTART:20250330T020000
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RDATE:20260329T020000
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UID:e51905a7-8593-49ce-8b3e-cc1d660a215a
DTSTAMP:20260511T110304Z
CLASS:PUBLIC
DESCRIPTION:Titre: 'ON ROBUSTNESS FOR THE SKOLEM and related PROBLEMS'\nBla
 ise Genest (IPAL\, Singapore)\n\n\nabstract:\nThe Skolem problem is a long
 -standing open problem in linear dynamical systems: can a linear recurrenc
 e sequence (LRS) ever reach 0 from a given initial configuration? Similarl
 y\, the positivity problem asks whether the LRS stays positive from an ini
 tial configuration. Deciding Skolem (or positivity) has been open for half
  a century: the best known decidability results are for LRS with special p
 roperties (e.g.\, low order recurrences). On the other hand\, these proble
 ms are much easier for “uninitialised” variants\, where the initial config
 uration is not fixed but can vary arbitrarily: checking if there is an ini
 tial configuration from which the LRS stays positive can be decided by pol
 ynomial time algorithms (Tiwari in 2004\, Braverman in 2006). In this talk
 \, we consider problems that lie between the initialised and uninitialised
  variants. More precisely\, we ask if 0 (resp. negative numbers) can be av
 oided from every initial configuration in a neighbourhood of a given initi
 al configuration. This can be considered as a robust variant of the Skolem
  (resp. positivity) problem. We show that these problems lie at the fronti
 er of decidability: if the neighbourhood is given as part of the input\, t
 hen robust Skolem and robust positivity are Diophantine hard\, i.e.\, solv
 ing either would entail major breakthroughs in Diophantine approximations\
 , as happens for (non-robust) positivity. Interestingly\, this is the firs
 t Diophantine hardness result on a variant of the Skolem problem. On the o
 ther hand\, if one asks whether such a neighbourhood exists\, then the pro
 blems turn out to be decidable in their full generality\, with PSPACE comp
 lexity. Our analysis is based on the set of initial configurations such th
 at positivity holds\, which leads to new insights into these difficult pro
 blems\, and interesting geometrical interpretations.\n\nJoint work with S.
  AKSHAY\, HUGO BAZILLE\, and MIHIR VAHANWALA.\n\n\nImport automatique depu
 is https://framagenda.org/remote.php/dav/public-calendars/D3yqF7nwys9amfyY
 ?export par sync_icals_to_drupal.py pour M2F
DTSTART;TZID=Europe/Paris:20250623T140000
DTEND;TZID=Europe/Paris:20250623T150000
LOCATION:salle 381
SEQUENCE:0
SUMMARY:Seminaire SYNTHESE\, Blaise Genest
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR
