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: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:20240408T154500
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:a06b11278572f0d262ba3abfa5596ae4
CATEGORIES:Colloquia
CREATED:20250210T134303
SUMMARY:Probing Inside: Inverse Problems, Nonlinearity, and Nonlocality
LOCATION:HILL 705
DESCRIPTION:<p style="border: 0px; font-weight: 400; font-size: 12pt; line-height: inhe
 rit; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, 
 Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-align: baseline;
  letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; t
 ext-transform: none; widows: 2; word-spacing: 0px; white-space: normal; bac
 kground-color: #ffffff;" data-olk-copy-source="MessageBody">Inverse boundar
 y problems aim to determine the internal properties of a medium from measur
 ements made at its boundary. Mathematically, this amounts to recovering the
  coefficients of a partial differential equation inside a domain from infor
 mation about solutions on the boundary. Such problems arise in numerous app
 lications, from medical imaging to exploration geophysics. A celebrated exa
 mple is the Calderon problem, which asks whether one can recover the electr
 ical conductivity of a medium from voltage and current measurements on the 
 boundary. This foundational question has inspired decades of research in th
 e field.</p><p style="border: 0px; font-weight: 400; font-size: 12pt; line-
 height: inherit; font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontServic
 e, Calibri, Helvetica, sans-serif; margin: 0px; padding: 0px; vertical-alig
 n: baseline; letter-spacing: normal; orphans: 2; text-align: start; text-in
 dent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space:
  normal; background-color: #ffffff;">&nbsp;</p><p style="border: 0px; font-
 weight: 400; font-size: 12pt; line-height: inherit; font-family: Aptos, Apt
 os_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; margi
 n: 0px; padding: 0px; vertical-align: baseline; letter-spacing: normal; orp
 hans: 2; text-align: start; text-indent: 0px; text-transform: none; widows:
  2; word-spacing: 0px; white-space: normal; background-color: #ffffff;">In 
 this talk, we will offer an introduction to the field of inverse boundary p
 roblems, beginning with the Calderon problem and then turning to recent adv
 ances in inverse problems for both nonlinear and nonlocal elliptic operator
 s. Perhaps surprisingly, the presence of nonlinearity or nonlocality can ac
 tually be beneficial, allowing one to solve inverse problems that remain op
 en in their linear or local counterparts. In particular, we present a compl
 ete solution to the fractional anisotropic Calderon problem on smooth compa
 ct Riemannian manifolds without boundary: the source-to-solution map of the
  fractional Laplacian, known on an arbitrarily small open subset, determine
 s the manifold up to isometry. This provides a nonlocal analog of the class
 ical anisotropic Calderon problem, which remains one of the central open qu
 estions in dimensions three and higher.</p>
CONTACT:Katya Krupchyk (UC Irvine)
DTSTAMP:20260828T081111
DTSTART;TZID=America/New_York:20250409T154500
DTEND;TZID=America/New_York:20250409T164500
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
END:VCALENDAR