<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=iso-8859-1"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:#954F72;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-family:"Calibri",sans-serif;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal style='margin-bottom:3.0pt'><b><span style='font-size:14.0pt'>Approximate spectral theory in heterogeneous media, asymptotic ballistic transport, and beyond?<o:p></o:p></span></b></p><p class=MsoNormal><span lang=FR style='font-size:12.0pt'>Speaker: Antoine Gloria, Sorbonne University, Laboratoire Jacques-Louis Lions<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:12.0pt'>Time/Room: 3:30pm - 4:30pm/Dilworth Room<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>In this talk I’ll consider the Schrödinger in heterogeneous media and shall discuss long-time transport properties of localized initial conditions, and more precisely the regime of asymptotic ballistic transport. To this aim I’ll introduce an approximate spectral theory inspired by the Floquet theory for periodic media that allows to diagonalize the Schrödinger operator up to an error that we control by energy estimates combined with estimates on "correctors". This yields asymptotic ballistic results for quasiperiodic potentials up to stretched exponential times, as well as fine results in the random setting. To conclude I'll discuss what direction could be taken to tackle larger time scales.<br> <br>This is joint work with Mitia Duerinckx and Christopher Shirley (Université Libre de Bruxelles).<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Abstract Link: <a href="http://www.math.ias.edu/seminars/abstract?event=137597">http://www.math.ias.edu/seminars/abstract?event=137597</a><o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>