Mathematical fairy tales

1. “A survival guide for feeble fish”. How fish can get from $A$ to $B$ in turbulent waters which maybe much fasted than the locomotion speed of the fish provided that there is no large-scale drift of the water flow. This is related to homogenization of the $G$-equation which is believed to govern many combustion processes. Based on a joint work with S. Ivanov and A. Novikov.
2. “What is inside?” Imagine a body with some intrinsic structure, which, as usual, can be thought of as a metric. One knows distances between boundary points (say, by sending waves and measuring how long it takes them to reach specific points on the boundary). One may think of medical imaging or geophysics. This topic is related to the one on minimal fillings, the next one. Joint work with S. Ivanov.
3. How can one discretize elliptic equations without using finite elements, triangulations and such? On manifolds and even “nice” $mm$-spaces. A notion of $\rho$-Laplacian and its stability. Joint with S. Ivanov and Kurylev.
And other.