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TZOFFSETFROM:-0500
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DTSTART:20230312T070000
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DTSTART:20231105T060000
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UID:event.906124.www.amherst.edu
DTSTART;TZID=America/New_York:20240220T160000
SEQUENCE:0
TRANSP:TRANSPARENT
DTEND;TZID=America/New_York:20240220T170000
LOCATION:Science Center\, A011
SUMMARY:Ivan Contreras (Amherst College Mathematics and Statistics)
CLASS:PUBLIC
DESCRIPTION:Title: Discrete Quantum Mechanics: Can we hear the shape of a g
raph?\n\nAbstract: Can we hear the shape of a drum? This question has prom
pted\na fundamental area of research in modern mathematics. One of the mai
n\ncharacters in this story is the Laplace operator (aka the Laplacian)\,\
nthat can be defined using basic tools of calculus.In this talk we will\ne
xplore the graph Laplacian\, a discrete version of the Laplace\noperator\,
which has broad applications in graph theory\, combinatorics\nand mathema
tical physics. In particular\, we will present a discrete\nversion of the
Schrödinger and Dirac equations and how it connects\nwith some of the pr
operties of a graph (connectivity\, cycles/trees and\nwalks) that can be e
xtracted from the graph Laplacian\, as well as\nrecent work with undergrad
uate students on Dirac and Laplace operators\non graphs. This will give us
an opportunity towards the end of the\ntalk to discuss different ways in
which students can get involved with\nundergraduate research in mathematic
al physics.\n
DTSTAMP:20240415T160140Z
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