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Abstract: Consider the compact Riemannian manifold $(M,g)$ of dimension $n\geq 5$. The $\sigma_2$ Yamabe problem seeks to find a conformal metric to $g$ that has a constant $\sigma_2$ curvature. Sheng-Trudinger-Wang have previously proved the existence of such a metric when $n\geq 5$, while Ge-Wang have provided a constructive proof for $n\geq 9$. In this talk, we will present a constructive proof for the case $n=8$ and discuss the obstruction for such construction when $5\l eq n\leq 7$. The proof is a joint work with Bin Deng and Juncheng Wei.

Seminar website:  Learning Seminar on PDE and Applications     (https://sites.math.rutgers.edu/~yyli/Learningseminar.html)