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Lectures
Seminar information archive ～09/12｜Next seminar｜Future seminars 09/13～
2012/10/30
17:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Frank Lutz (Technische Universität Berlin)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
Frank Lutz (Technische Universität Berlin)
Discrete Topologgy of Cellular Microstructures
and Complicatedness Measurements for Cell Complexes (JAPANESE)
[ Abstract ]
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.
