<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><br class=""></div><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><blockquote type="cite" class=""><div class="">Begin forwarded message:</div><br class="Apple-interchange-newline"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;" class=""><b class="">From: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Henry Yuen <<a href="mailto:hyuen@CS.COLUMBIA.EDU" class="">hyuen@CS.COLUMBIA.EDU</a>><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;" class=""><b class="">Subject: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><b class="">Fwd: Mathematics of Waves and Quantum Materials</b><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;" class=""><b class="">Date: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">August 27, 2025 at 8:07:32 PM EDT<br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;" class=""><b class="">To: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class=""><a href="mailto:QUANTUM@LISTS.COLUMBIA.EDU" class="">QUANTUM@LISTS.COLUMBIA.EDU</a><br class=""></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;" class=""><span style="font-family: -webkit-system-font, "Helvetica Neue", Helvetica, sans-serif;" class=""><b class="">Reply-To: </b></span><span style="font-family: -webkit-system-font, Helvetica Neue, Helvetica, sans-serif;" class="">Quantum <<a href="mailto:QUANTUM@LISTS.COLUMBIA.EDU" class="">QUANTUM@LISTS.COLUMBIA.EDU</a>><br class=""></span></div><br class=""><div class=""><div dir="ltr" class="">Course announcement for this Fall.<br class=""><br class=""><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">---------- Forwarded message ---------<br class="">From: <strong class="gmail_sendername" dir="auto">Michael I. Weinstein</strong> <span dir="auto" class=""><<a href="mailto:miw2103@columbia.edu" class="">miw2103@columbia.edu</a>></span><br class="">Date: Wed, Aug 27, 2025 at 10:33 AM<br class="">Subject: Mathematics of Waves and Quantum Materials<br class="">To: <<a href="mailto:henry.yuen@columbia.edu" class="">henry.yuen@columbia.edu</a>><br class="">Cc: Michael I Weinstein <<a href="mailto:miw2103@columbia.edu" class="">miw2103@columbia.edu</a>><br class=""></div><br class=""><br class=""><div style="line-break:after-white-space" class=""><span style="font-size:14px" class="">Dear Henry, I hope all is well with you.</span><div class=""><span style="font-size:14px" class="">Below is information on an Applied Math course I’m teaching this semester. </span><div style="font-size:14px" class="">Please forward to anyone you think may be interested. </div><div style="font-size:14px" class="">Best wishes, Michael</div><div style="font-size:14px" class=""><br class=""></div><div style="font-size:14px" class="">Michael I. Weinstein<br class="">Department of Applied Physics <br class=""> & Applied Mathematics, and<br class="">Department of Mathematics<br class="">Columbia University<br class="">New York, New York 10027<br class=""><br class=""><a href="http://www.columbia.edu/~miw2103/" target="_blank" class="">www.columbia.edu/~miw2103/</a><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><div style="font-size:14px" class=""><b class="">Fall 2025, Applied Mathematics E4990, Section 001</b></div><div style="font-size:14px" class="">Tuesday and Thursdays 10:10-11:25am</div><div style="font-size:14px" class="">Location: 253 Engineering Terrace (SW Mudd Building)</div><div style="font-size:14px" class="">Special Topics in Applied Mathematics</div><div class=""><span style="font-size:14px" class="">Instructor: Michael I Weinstein</span></div><div class=""><blockquote type="cite" style="" class=""><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><p style="font-size:16px;margin:12px 0px;color:rgb(39,53,64);font-family:"Lato Extended",Lato,"Helvetica Neue",Helvetica,Arial,sans-serif;font-variant-ligatures:normal;background-color:rgb(255,255,255);text-decoration-style:initial;text-decoration-color:initial" class=""><b class="">Course Title:</b> Mathematics of Waves and Quantum Materials</p></blockquote></div></blockquote><span style="font-size:14px" class=""><b class="">Course description:</b> In this course we will study mathematical aspects of wave phenomena in classical and quantum</span></div><div style="font-size:14px" class="">physics, with a view toward models (PDE, discrete,..) of quantum materials, and their metamaterial analogues.</div><div style="font-size:14px" class="">Topics include: Wave phenomena (non-dispersive and dispersive);</div><div style="font-size:14px" class="">wave, Schroedinger, Dirac equations, </div><div style="font-size:14px" class="">Spectral theory of periodic operators (Floquet-Bloch) and the band structure of crystals.</div><div style="font-size:14px" class="">Multiple scale methods and applications to wave-packets and their dynamics.</div><div style="font-size:14px" class="">Effective Hamiltonians arising in homogenization and strong binding (high contrast) regimes.</div><div style="font-size:14px" class="">Case study of quantum materials: graphene. 2D materials in a magnetic field.</div><div style="font-size:14px" class="">Basics of symmetries, band structure degeneracies, symmetry breaking perturbations,</div><div style="font-size:14px" class="">and topological wave phenomena in 2D materials.</div><div style="font-size:14px" class=""><br class=""></div><div style="font-size:14px" class=""><b class="">Prerequisites:</b> The following courses or equivalents: </div><div style="font-size:14px" class="">Applied Analysis APMA 4100, Applied Functional Analysis APMA 4150, Partial Differential Equations APMA 4200,</div><div style="font-size:14px" class="">or permission of the instructor.</div></div></div></div></div></div>
</div></blockquote></div><br class=""></div></div></div><br class=""></body></html>