Math & Stats Colloquium – Friday, September 22 @ 3:30 PM CST

University of Saskatchewan Department of Mathematics & Statistics Colloquium and PIMS Applied Mathematics Seminar

The Colloquium Committee cordially invites you to attend the first talk in the 2023-24 Math & Stats Colloquium series.

Date/Time: Friday, September 22 @ 3:30 PM CST

Location: ARTS 206

Speaker: Mohammad Akbar, University of Texas at Dallas

Title: Einstein, Lie, and Black Holes

Abstract: Sophus Lie invented what came to be known as Lie groups to study differential equations systematically. However, while Lie groups gained prominence in mathematics and physics, their original application to differential equations fell into obscurity for about half a century. General Relativity is considered the most nonlinear theory of nature that describes the gravitational field by a set of ten nonlinear second-order partial differential equations, the Einstein equations. Although Lie groups were used by relativists in connection with idealized spacetimes from the beginning --- which made Einstein's equations more tractable --- applying Lie groups to study the "hidden" symmetries of Einstein's equations was not considered until Lie’s original ideas were revived and expanded in the 60s. This led to the search for solution generation techniques in general relativity in which one obtains a solution, or a family of solutions, from a "seed" solution that would otherwise be impossible to obtain. This talk will review static Einstein equations with axial symmetry in vacuum, i.e., Ricci-flat metrics with two commuting hypersurface-orthogonal Killing vector fields. It will present a recently found unexpected symmetry of the system that can be effected algebraically to obtain new solutions and will show how such symmetries are useful in studying black holes and other spacetimes of current physical interest as well as Ricci solitons.

Note: At the speaker’s request, this talk will be in-person only.

Please contact colloquium@math.usask.ca if you have any questions. We hope to see you all on Friday the 22^nd at 3:30PM in ARTS 206!

Colloquium Committee
University of Saskatchewan
Department of Mathematics and Statistics
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