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UID:f3f8da3a7eefd0a305913496a902ae64
CATEGORIES:Mathematical Physics Seminar
CREATED:20260601T002414
SUMMARY:Webinar: Robert McCann - Trading linearity for ellipticity: a low regularity Lorentzian splitting theorem
LOCATION:Zoom
DESCRIPTION:Robert McCann – University of Toronto \nWednesday, June 24, 2026\nZoom open
 s: 10:30AM EDT\nSeminar begins: 10:45AM EDT\nTrading linearity for elliptic
 ity: a low regularity Lorentzian splitting theorem\n \nWhile Einstein's the
 ory of gravity is formulated in a smooth setting, the celebrated singularit
 y theorems of Hawking and Penrose describe many physical situations in whic
 h this smoothness must eventually breakdown. It is thus of great interest t
 o study the theory in low regularity settings. In the lecture, we establish
  a low regularity splitting theorem by sacrificing linearity of the d'Alemb
 ertian to recover ellipticity. We exploit a negative homogeneity $p$-d'Alem
 bert operator for this purpose. The same technique yields a simplified proo
 f of Eschenberg (1988) Galloway (1989) and Newman's (1990) confirmation of 
 Yau's (1982) conjecture, bringing all three Lorentzian splitting results in
 to a framework closer to the Cheeger-Gromoll splitting theorem from Riemann
 ian geometry. Based on joint work with Mathias Braun, Nicola Gigli, Argam O
 hanyan, and Clemens Saemann: 1) arXiv 2501.00702 2) arXiv 2408.15968 3) arX
 iv 2410.12632 4) arXiv 2507.06836\n
X-ALT-DESC;FMTTYPE=text/html:<p style="text-align: center;"><strong>Robert McCann – University of Toront
 o&nbsp;</strong></p><p style="text-align: center;"><strong>Wednesday,&nbsp;
 June 24,&nbsp;2026</strong></p><p style="text-align: center;"><strong>Zoom 
 opens: 10:30AM EDT</strong></p><p style="text-align: center;"><strong>Semin
 ar begins: 10:45AM EDT</strong></p><p style="text-align: center;"><strong>T
 rading linearity for ellipticity: a low regularity Lorentzian splitting the
 orem</strong></p><p>&nbsp;</p><p>While Einstein's theory of gravity is form
 ulated in a smooth setting, the celebrated singularity theorems of Hawking 
 and Penrose describe many physical situations in which this smoothness must
  eventually breakdown. It is thus of great interest to study the theory in 
 low regularity settings. In the lecture, we establish a low regularity spli
 tting theorem by sacrificing linearity of the d'Alembertian to recover elli
 pticity. We exploit a negative homogeneity $p$-d'Alembert operator for this
  purpose. The same technique yields a simplified proof of Eschenberg (1988)
  Galloway (1989) and Newman's (1990) confirmation of Yau's (1982) conjectur
 e, bringing all three Lorentzian splitting results into a framework closer 
 to the Cheeger-Gromoll splitting theorem from Riemannian geometry. Based on
  joint work with Mathias Braun, Nicola Gigli, Argam Ohanyan, and Clemens Sa
 emann: 1) arXiv 2501.00702 2) arXiv 2408.15968 3) arXiv 2410.12632 4) arXiv
  2507.06836</p>
DTSTAMP:20260828T090945
DTSTART;TZID=America/New_York:20260624T104500
DTEND;TZID=America/New_York:20260624T120000
SEQUENCE:0
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