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DTSTAMP:20200125T151357Z
UID:5c8a5b8a6bdba599784853@ist.ac.at
DTSTART:20190807T130000
DTEND:20190807T141500
DESCRIPTION:Speaker: Moritz Lang\nAbstract: The sandpile group\, also refer
red to as the critical group\, is a refinement of the number of spanning t
rees on a given undirected multigraph. The study of the sandpile group ori
ginated in the physical literature\, specifically in the analysis of the s
o called sandpile model\, a cellular automaton which serves as the archety
pical example for self-organized criticality\, an important phenomenon in
physics\, biology\, neuroscience and many other fields. The concept of cri
ticality is based on the idea that certain systems show "similar" spatio-t
emporal dynamics at different scales\, which lead to the development of re
normalization group theory and similar mathematical concepts describing th
e limits of certain properties of such systems on infinite domains (graphs
). Despite this backdrop\, no mathematical definition for the scaling-limi
t of the sandpile group itself yet exists. In this talk\, we introduce a t
iling problem with finite open convex polyforms. We show that\, if there e
xists a tiling of the polyform P2 by P1\, one can construct a monomorphism
between the sandpile groups corresponding to the respective polyforms. Th
e direct limits of infinite series of such tilings then provide the first
definitions of scaling-limits of the sandpile group on the standard square
lattice\, and on similar infinite domains. At the end of the talk\, we di
scuss the open question if these limits are independent of the sequence of
polyforms.Joint work with Mikhail Shkolnikov.
LOCATION:Mondi Seminar Room 3\, Central Building\, IST Austria
ORGANIZER:hwagner@ist.ac.at
SUMMARY:GeomTop Seminar: "\;Sandpile monomorphisms and scaling limits&q
uot\;
URL:https://talks-calendar.app.ist.ac.at/events/2049
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