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DESCRIPTION: The upcoming Thematic Einstein Semester entitled "Geometric an
d Topological Structure of Materials" will focus on recent advancements in
computational materials science. In this talk\, we will present two interes
ting areas where algebra can play a role in future research. First\, in the
design and analysis of novel materials\, questions of rigidity of framewor
ks arise. For generic configurations\, matroid-theoretic and combinatorial
techniques can be used to study rigidity. But the frameworks arising in app
lications are rarely generic\, therefore deciding local rigidity presents a
difficult computational problem which connects to the numerical algebraic
geometry of varieties and semi-algebraic sets. Second\, both point configur
ations and also polycrystalline materials give rise to cellular decompositi
ons of 3-dimensional space. We will discuss how a Fourier-type analysis of
these cells can be used to understand their approximate symmetry. The repre
sentation theory of SO(3) and its finite subgroups can be used to extract F
ourier coefficients from the surface normal density of a given cell.
DTSTAMP:20191129T152200
DTSTART:20191216T160000
CLASS:PUBLIC
LOCATION:Technische Universität Berlin\n Institut für Mathematik\n Straße d
es 17. Juni 136\n 10623 Berlin\n Room MA 041 (Ground Floor)
SEQUENCE:0
SUMMARY:Alexander Heaton (Max Planck Institut Leipzig): Applications of alg
ebra to the geometry of materials
UID:95692799@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20191216-C-Heaton.html
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