Events Mini Calendar

Go to previous month Go to next month
  S M T W R F S
W9 28 1 2 3 4 5 6
W10 7 8 9 10 11 12 13
W11 14 15 16 17 18 19 20
W12 21 22 23 24 25 26 27
W13 28 29 30 31 1 2 3


Today is:
Sat, Oct 16, 2021


MSU Events Calendar

 
 Choose Calendar view:   Day   Week   Month     Search   Filter

3:00pm
to
4:00pm
Math Seminar Series  (Conferences / Seminars / Lectures)

Shiwen Zhang, U Minnesota, will be speaking.

The presentation title is "The landscape law for tight binding Hamiltonians."

Contact Jeffrey Hudson Schenker (schenke6@msu.edu) for more information.

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.

more information...


Location: Online via Zoom [map]
Price: free
Sponsor: Department of Mathematics
Contact: Department of Mathematics
phone pic (517) 353-0844