# Physics and Astronomy Colloquium Series

### Next Seminar

*Tuesday, Dec. 6, 2016

*Sac State Physics Majors' Senior Project Talks
Mark Cratty*

*"Hadamard's Method and the Heisenberg Subelliptic Laplacian"*

In 1973, Folland constructed the fundamental solution of the sublaplacian on the Heisenberg group, using the group of dilations and mimicking the case of the Euclidean Laplacian. In our work, we take a different approach. Recent developments in geodesic theory for the sublaplacian lead us to use a different geometric method pioneered by Hadamard. We add an auxiliary term to the sublaplacian to make it a wave-type operator. Then we apply Hadamard's parametrix construction, which Hadamard used to solve the Cauchy problem for the wave equation on a curved space-time. The Hadamard parametrix we construct approximates the fundamental solution for the wave-type modified operator. It is singular along the surface of a conoid. Finally, we take the limit as the auxiliary term goes to zero. We then compare our form of the fundamental solution of the sublaplacian to Folland's.

The Physics and Astronomy Colloquium Series is open to all members of the university. Unless otherwise noted, talks are held on
September 1, 2016 September 8, 2016 Sept. 15, 2016 Sept. 22, 2016 Oct. 6, 2016 October 13, 2016 October 20, 2016 October 27, 2016 November 17, 2016 December 1, 2016 Ashley Luiz "Modeling of Tropomyosin Binding and Polymerization on Filamentous Actin"*Tuesday, December 6, 2016 December 8 2016 Senior Project TalksSergei Mistyuk "Computationally Modeling Microwave Superlenses" andZakery Tridente-Bruns"Exploring Quantum Phase Transitions in SU(N) and SO(N) Models with Quantum Monte Carlo" |

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