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DTSTAMP:20210308T200000Z
UID:1614953543349@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20210308T200000Z
DTEND:20210308T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
Shiwen Zhang, U Minnesota, will be speaking.\n
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The presentation title is "The landscape law
for tight binding Hamiltonians."\n
\n
Contact
Jeffrey Hudson Schenker (schenke6@msu.edu) for
more information.\n
\n
The localization landscape
theory, introduced in 2012 by Filoche and
Mayboroda, considers the so-called the landscape
function u solving Hu=1 for an operator
H. The landscape theory has remarkable power
in studying the eigenvalue problems of H and
has led to numerous landscape baked'' results
in mathematics, as well as in theoretical
and experimental physics. In this talk, we will
discuss some recent results of the landscape
theory for tight-binding Hamiltonians H=-Delta+V
on Z^d. We introduce a box counting function,
defined through the discrete landscape
function of H. For any deterministic bounded
potential, we give estimates for the integrated
density of states from above and below by
the landscape box counting function, which
we call the landscape law. For the Anderson model,
we get a refined lower bound for the IDS,
throughout the spectrum. We will also discuss
some numerical experiments in progress on
the so-called practical landscape law for the
continuous Anderson model. This talk is based
on joint work with D. N. Arnold, M. Filoche,
S. Mayboroda, and Wei Wang.\n\n
Price: free\n
Sponsor: Department of Mathematics\n
Sponsor's Homepage: https://www.math.msu.edu/\n
Contact name: Department of Mathematics\n
Contact phone: (517) 353-0844\n
for more info visit the web at:\n
https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Online via Zoom
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