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講演会
過去の記録 ～04/18｜次回の予定｜今後の予定 04/19～
2012年10月30日(火)
17:00-18:00 数理科学研究科棟(駒場) 470号室
Frank Lutz 氏 (ベルリン工科大学)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
Frank Lutz 氏 (ベルリン工科大学)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
[ 講演概要 ]
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).
For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct ``complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
``complicatedness'' of complexes.
Our first aim is to use methods from discrete and geometric topology
to recover structural information from the composition of
monocrystalline materials that have a periodic foam structure
(such as gas hydrates and transition metal alloys) and also of
polycrystalline materials (such as metals and certain ceramics).
For more general complexes, even with a billion of faces, homological
information can be obtained with computational homology packages
such as CHomP or RedHom. These packages extensively use discrete Morse
theory as a preprocessing step. Although it is NP-hard to find optimal
discrete Morse functions, most data appears to be easy and it is
in fact hard to construct ``complicated'' examples. As we will see,
random discrete Morse theory will allow us to measure the
``complicatedness'' of complexes.
