BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//ox.ac.uk//NONSGML oxford.event//EN
X-WR-TIMEZONE:Europe/London
BEGIN:VTIMEZONE
TZID:Europe/London
X-LIC-LOCATION:Europe/London
BEGIN:DAYLIGHT
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=3
TZNAME:BST
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
END:DAYLIGHT
BEGIN:STANDARD
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYDAY=-1SU;BYMONTH=10
TZNAME:GMT
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
SUMMARY:Scaling limits for a population model with growth\, division and c
 ross-diffusion
DTSTART;TZID=Europe/London:20260612T110000
DTEND;TZID=Europe/London:20260612T120000
DTSTAMP:20260610T195357Z
UID:c8f338b9-8f44-f111-bec7-7c1e52046848
CREATED:20260430T122552Z
DESCRIPTION:Motivated by the modeling of bacteria microcolony morphogenesi
 s across multiple scales\, we explore in this talk models for a spatial po
 pulation of interacting\, growing and dividing particles. Starting from a 
 microscopic stochastic model\, we first write the corresponding stochastic
  differential equation satisfied by the empirical measure\, and rigorously
  derive its mesoscopic (mean-field) limit. We then take an interest in the
  so-called localization limit\, to reach a macroscopic (large-scale) model
 . The scaling consists in assuming that the range of interaction between i
 ndividuals is very small compared to the size of the domain. In proving th
 e localization limit using compactness arguments\, the difficulties are tw
 ofold: first\, growth and division render the system non-conservative\, pr
 eventing the use of energy estimates. Second\, the size of the particles\,
  being a continuous trait\, leads to new difficulties in obtaining compact
 ness estimates. We first show rigorously the localization limit in the cas
 e without growth and fragmentation\, under smoothness and symmetry assumpt
 ions for the interaction kernel. We then perform a thorough numerical stud
 y in order to compare the three modeling scales and study the different li
 mits in situations not covered by the theory yet. These works provide a be
 tter understanding of the link between the micro- meso- and macro- scales 
 for interacting particle systems. \n\nCo-authors: Marie Doumic (Ecole Poly
 technique and Inria\, CMA)\, Sophie Hecht (CNRS\, Sorbonne Université) an
 d Marc Hoffmann ( University Paris-Dauphine )
LAST-MODIFIED:20260430T122738Z
LOCATION:Mathematical Institute - L4\, L4 Mathematical Institute Woodstock
  Road Oxford Oxfordshire OX2 6GG United Kingdom
SPEAKER:Dr Diane Peurichard (INRIA Paris)
END:VEVENT
END:VCALENDAR