This dissertation consists of two chapters on behavioral economics.

Chapter one analyzes mutual fund flows from 1999 to 2012 to provide evidence that financial advisers exploit their clients' extrapolative beliefs to sell funds that pay high commissions. Utilizing comparisons between twin retail mutual fund share classes that differ only in commissions, I find a strong positive correlation between commission levels and return chasing. Fund flows from high commission shares show increased purchases of past winners, but no increased redemptions of past losers. This pattern is consistent with the incentives from 12b-1 commissions, which pay advisers to keep clients invested in high commission funds, but is hard to reconcile with alternative explanations such as advisers reducing search costs for quality funds, or return chasers self-selecting into high commission advisers. My findings support the SEC's recent efforts at restructuring 12b-1 commissions, as well as the White House's recent push to require fiduciary duty from all retirement advisers.

Chapter two attempts to isolate the effects of violent video game sales on crime using a novel data set of state-level game sales from 2006 to 2010. The panel database, constructed using NPD group publications and state-level sales weights computed from Google Trends search data, overcomes the time-series data restrictions faced by previous works. However, the state-level variation in this panel data was not enough to disentangle the impact of game sales from time trends because video game sales are highly correlated across states. I document the methodology used to reconstruct the panel data using Google Trends, as this could prove useful in other situations where panel data is difficult or expensive to obtain.

For a formal differential graded algebra, if extended by an odd degree element, we prove that the extended algebra has an $A_\infty$-minimal model with only $m_2$ and $m_3$ non-trivial. As an application, the $A_\infty$-algebras constructed by Tsai, Tseng and Yau on formal symplectic manifolds satisfy this property. Separately, we expand the result of Miller and Crowley-Nordstr\"{o}m for $k$-connected manifold. In particular, we prove that if the dimension of the manifold $n\leq (l+1)k+2$, then its de Rham complex has an $A_\infty$-minimal model with $m_p=0$ for all $p\geq l$.

On a symplectic manifold, Tsai, Tseng, and Yau introduced a coholomogy of differentialforms that is analogous to the Dolbeault cohomology for symplectic manifolds. Such forms are called primitive forms. We develop a Morse theory for these primitive forms, including a Morse-type Cone complex of pairs of critical points that has isomorphic cohomology to the primitive cohomology. The differential of the complex consists of gradient flows and an integration of the symplectic form over spaces of gradient flow lines. We prove that the complex is independent of the choice of metric and Morse function. We also derive Morse style inequalities for the cohomology of the Cone complex and thus the primitive cohomologies. Also, we develop a Witten deformation of the Cone complex, which provides a Witten deformation of the differential operators associated to the cohomology.

We study a symplectic cohomology defined on any symplectic manifold (X, w), introduced by Tseng and Yau. As a main application, we analyze two different fibrations of a link complement M constructed by McMullen-Taubes, and studied further by Vidussi. These examples lead to inequivalent symplectic forms on X = S1 x M, which can be distinguished by the dimension of the primitive cohomologies of differential forms. We provide a general algorithm for computing the monodromies of the fibrations explicitly, which are needed to determine the primitive cohomologies. We also investigate a similar phenomenon coming from fibrations of a class of graph links, whose primitive cohomology provides information about the fibration structure. We then study the A-infinity structure on the differential forms underlying the symplectic cohomology. We use this A-infinity structure to generalize classic notions such as Massey products and twisted differentials. These tools capture more information on certain symplectic 4-manifolds compared to the DGA structure on the de Rham cohomology of X.

Symplectic manifolds have many connections to complex manifolds but lack many of thenice properties that come with a complex structure, especially the fact that symplectic manifolds have no local properties that can differentiate them from other symplectic manifolds. One of the most common global invariants of manifolds is the de Rham cohomology, but this can only detect the topological structure of the manifold and discards the additional symplectic structure. This work expands upon the definition of a cohomology theory specific to symplectic manifolds, specifically based on a viewpoint which comes from the concept of a mapping cone from homological algebra. We demonstrate how common operations on differential forms can be extended to these cone cohomologies with particular focus on the blowup along a symplectic submanifold. Additionally, we show how this approach can be extended to other types of manifolds using nilmanifolds as an example.