BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//jEvents 2.0 for Joomla//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VTIMEZONE
TZID:America/New_York
BEGIN:STANDARD
DTSTART:20230306T153000
RDATE:20230312T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20231105T010000
RDATE:20240310T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20241103T010000
RDATE:20250309T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20251102T010000
RDATE:20260308T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20261101T010000
RDATE:20270314T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20271107T010000
RDATE:20280312T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:STANDARD
DTSTART:20281105T010000
RDATE:20290311T030000
TZOFFSETFROM:-0400
TZOFFSETTO:-0500
TZNAME:America/New_York EST
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:20230312T030000
RDATE:20231105T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
BEGIN:DAYLIGHT
DTSTART:20240310T030000
RDATE:20241103T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
BEGIN:DAYLIGHT
DTSTART:20250309T030000
RDATE:20251102T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
BEGIN:DAYLIGHT
DTSTART:20260308T030000
RDATE:20261101T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
BEGIN:DAYLIGHT
DTSTART:20270314T030000
RDATE:20271107T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
BEGIN:DAYLIGHT
DTSTART:20280312T030000
RDATE:20281105T010000
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:America/New_York EDT
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
UID:c46f7b6297d00fdc0c1ddde9c227b26f
CATEGORIES:Colloquia
CREATED:20240227T091514
SUMMARY:Some unconventional PDE problems from photonics
LOCATION:Hill 705
DESCRIPTION:Speaker: Robert Kohn (Courant Institute)Title: Some unconventional PDE prob
 lems from photonicsAbstract: Electromagnetic waves are described by Maxwell
 's equations. For transverse-magnetic waves in a time-harmonic setting, the
  Maxwell system reduces to a simple-looking divergence-form Helmholtz equat
 ion: div( a(x,omega) grad u) + omega^2 m(x, omega) u = 0. Here u is scalar 
 valued, omega is the frequency, and the coefficients a(x,omega) and m(x,ome
 ga) represent the material properties of the medium -- specifically, a(x,om
 ega) is 1/(dielectric permittivity) and m(x,omega) is the magnetic permeabi
 lity. One might think that we have, by now, a full understanding of the mat
 hematical issues raised by this equation -- but in fact it isn't so. Indeed
 , due to the frequency-dependence of the permittivity, there are materials 
 for which the dielectric permittivity is near zero or even negative at freq
 uencies of practical interest. The analysis of devices made by combining su
 ch materials with ``ordinary'' dielectrics (for which the permittivity is p
 ositive) raises numerous PDE issues that are still not well understood.\n
X-ALT-DESC;FMTTYPE=text/html:<p><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (Wes
 t European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helve
 tica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-weig
 ht: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent:
  0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norm
 al; background-color: #ffffff; float: none;">Speaker: Robert Kohn (Courant 
 Institute)</span><br aria-hidden="true" style="color: #242424; font-family:
  'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, Bli
 nkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px
 ; font-style: normal; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: left; text-indent: 0px; text-transform: none; widows: 2; word-
 spacing: 0px; white-space: normal; background-color: #ffffff;"><br aria-hid
 den="true" style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (W
 est European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Hel
 vetica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-we
 ight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-inden
 t: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: no
 rmal; background-color: #ffffff;"><span style="color: #242424; font-family:
  'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, Bli
 nkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px
 ; font-style: normal; font-weight: 400; letter-spacing: normal; orphans: 2;
  text-align: left; text-indent: 0px; text-transform: none; widows: 2; word-
 spacing: 0px; white-space: normal; background-color: #ffffff; float: none;"
 >Title: Some unconventional PDE problems from photonics</span><br aria-hidd
 en="true" style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (We
 st European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helv
 etica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-wei
 ght: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent
 : 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: nor
 mal; background-color: #ffffff;"><br aria-hidden="true" style="color: #2424
 24; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -a
 pple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font
 -size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: nor
 mal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; 
 widows: 2; word-spacing: 0px; white-space: normal; background-color: #fffff
 f;"><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (We
 st European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helv
 etica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-wei
 ght: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent
 : 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: nor
 mal; background-color: #ffffff; float: none;">Abstract: Electromagnetic wav
 es are described by Maxwell's equations.&nbsp;</span><span style="color: #2
 42424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI',
  -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; f
 ont-size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: 
 normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: non
 e; widows: 2; word-spacing: 0px; white-space: normal; background-color: #ff
 ffff; float: none;">For transverse-magnetic waves in a time-harmonic settin
 g, the Maxwell&nbsp;</span><span style="color: #242424; font-family: 'Segoe
  UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSy
 stemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-
 style: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: left; text-indent: 0px; text-transform: none; widows: 2; word-spacing
 : 0px; white-space: normal; background-color: #ffffff; float: none;">system
  reduces to a simple-looking divergence-form Helmholtz equation:&nbsp;</spa
 n><span style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West
  European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvet
 ica Neue', sans-serif; font-size: 14.6667px; font-style: normal; font-weigh
 t: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 
 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: norma
 l; background-color: #ffffff; float: none;">div( a(x,omega) grad u) + omega
 ^2 m(x, omega) u = 0. Here u is scalar&nbsp;</span><span style="color: #242
 424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -
 apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; fon
 t-size: 14.6667px; font-style: normal; font-weight: 400; letter-spacing: no
 rmal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none;
  widows: 2; word-spacing: 0px; white-space: normal; background-color: #ffff
 ff; float: none;">valued, omega is the frequency, and the coefficients a(x,
 omega) and&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI'
 , 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystem
 Font, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-styl
 e: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align
 : left; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0p
 x; white-space: normal; background-color: #ffffff; float: none;">m(x,omega)
  represent the material properties of the medium --&nbsp;</span><span style
 ="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)', 
 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sa
 ns-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; lette
 r-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-tra
 nsform: none; widows: 2; word-spacing: 0px; white-space: normal; background
 -color: #ffffff; float: none;">specifically, a(x,omega) is 1/(dielectric pe
 rmittivity) and m(x,omega)&nbsp;</span><span style="color: #242424; font-fa
 mily: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system
 , BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6
 667px; font-style: normal; font-weight: 400; letter-spacing: normal; orphan
 s: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2; 
 word-spacing: 0px; white-space: normal; background-color: #ffffff; float: n
 one;">is the magnetic permeability. One might think that we have, by now, a
 &nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', 'Segoe U
 I Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Robo
 to, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: normal;
  font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; te
 xt-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-s
 pace: normal; background-color: #ffffff; float: none;">full understanding o
 f the mathematical issues raised by this equation --&nbsp;</span><span styl
 e="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European)',
  'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue', s
 ans-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; lett
 er-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-tr
 ansform: none; widows: 2; word-spacing: 0px; white-space: normal; backgroun
 d-color: #ffffff; float: none;">but in fact it isn't so. Indeed, due to the
  frequency-dependence of the&nbsp;</span><span style="color: #242424; font-
 family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-syst
 em, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 14
 .6667px; font-style: normal; font-weight: 400; letter-spacing: normal; orph
 ans: 2; text-align: left; text-indent: 0px; text-transform: none; widows: 2
 ; word-spacing: 0px; white-space: normal; background-color: #ffffff; float:
  none;">permittivity, there are materials for which the dielectric permitti
 vity&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', 'Seg
 oe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, 
 Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: nor
 mal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left
 ; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; whi
 te-space: normal; background-color: #ffffff; float: none;">is near zero or 
 even negative at frequencies of practical interest. The&nbsp;</span><span s
 tyle="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West European
 )', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica Neue'
 , sans-serif; font-size: 14.6667px; font-style: normal; font-weight: 400; l
 etter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text
 -transform: none; widows: 2; word-spacing: 0px; white-space: normal; backgr
 ound-color: #ffffff; float: none;">analysis of devices made by combining su
 ch materials with ``ordinary''&nbsp;</span><span style="color: #242424; fon
 t-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-sy
 stem, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 
 14.6667px; font-style: normal; font-weight: 400; letter-spacing: normal; or
 phans: 2; text-align: left; text-indent: 0px; text-transform: none; widows:
  2; word-spacing: 0px; white-space: normal; background-color: #ffffff; floa
 t: none;">dielectrics (for which the permittivity is positive) raises numer
 ous PDE&nbsp;</span><span style="color: #242424; font-family: 'Segoe UI', '
 Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFon
 t, Roboto, 'Helvetica Neue', sans-serif; font-size: 14.6667px; font-style: 
 normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: l
 eft; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; 
 white-space: normal; background-color: #ffffff; float: none;">issues that a
 re still not well understood.</span></p>
CONTACT:Robert Kohn (Courant Institute)
DTSTAMP:20260829T012812
DTSTART;TZID=America/New_York:20240306T153000
DTEND;TZID=America/New_York:20240306T163000
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR