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DTSTART:20211107T020000
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UID:calendar.1386259.field_date.0@bhi.fas.harvard.edu
DTSTAMP:20210806T024945Z
DESCRIPTION:\n Jared Speck (Mathematics) \;- Vanderbilt University\n\n\n
\n \n\n\n\n Title: \;Cosmological Singularities in General Relativity: T
he Complete Sub-Critical Regime\n\n\n\n Abstract: \;The celebrated theo
rems of Hawking and Penrose show that under appropriate assumptions on the
matter model\, a large\, open set of initial data for Einstein's equation
s lead to geodesically incomplete solutions. However\, these theorems are
'soft' in that they do not yield any information about the nature of the i
ncompleteness. Despite the uncertainty\, in the mathematical physics liter
ature\, there are heuristic results\, going back 50 years\, suggesting tha
t whenever a certain 'sub-criticality' condition holds\, the Hawking-Penro
se incompleteness is caused by the formation of a cosmological Big Bang si
ngularity\, that is\, curvature blowup along an entire spacelike hypersurf
ace. In recent joint work with I. Rodnianski and G. Fournodavlos\, we have
given a rigorous proof of this phenomenon\, i.e.\, a proof of stable mono
tonic curvature blowup along a spacelike hypersurface in the complete regi
me where the heuristics suggest it might occur. More precisely\, our resul
ts apply to Sobolev-class perturbations -- without symmetry -- of generali
zed Kasner solutions whose exponents satisfy the sub-criticality condition
. Our main theorem shows that -- like the generalized Kasner solutions --
the perturbed solutions develop Big Bang singularities. In this talk\, I w
ill provide an overview of our result and explain how it is tied to some o
f the main themes of investigation by the mathematical general relativity
community\, including the remarkable work of Dafermos-Luk on the stability
of Kerr Cauchy horizons. I will also discuss the new gauge that we used i
n our work\, as well as intriguing connections to other problems concernin
g stable singularity formation.\n\n\n\n Bio: \;Jared Speck is an Associ
ate Professor of Mathematics at Vanderbilt University. He received his PhD
in Mathematics from Rutgers University in 2008. \; His research inter
ests are nonlinear partial differential equations\, geometry\, general rel
ativity\, fluid mechanics\, and mathematical physics. \; \;\n\n\n
\n \;\n\n\n\n \;\n\n\n\n Link to Zoom\n\n
DTSTART;TZID=America/New_York:20210427T133000
DTEND;TZID=America/New_York:20210427T143000
LAST-MODIFIED:20210427T223445Z
LOCATION:Zoom link in description
SUMMARY:BHI Colloquium
URL;TYPE=URI:https://bhi.fas.harvard.edu/event/bhi-colloquium-56
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