## Today's seminar

### 2017/12/12

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Alex Mahalov (Arizona State University)
Stochastic Three-Dimensional Navier-Stokes Equations + Waves: Averaging, Convergence, Regularity and Nonlinear Dynamics (English)
[ Abstract ]
We establish multi-scale stochastic averaging, convergence and regularity theorems in a general framework by bootstrapping from global regularity of the averaged stochastic resonant equations. The averaged covariance operator couples stochastic and wave effects. We also present theoretical results for 3D nonlinear dynamics.

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuro Shimizu (RIMS, Kyoto university)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
[ Abstract ]
Let $M$ be a closed oriented $n$-dimensional manifold. We give a geometric proof of that the $k$-times self-intersection of singular set of a Morin map from $M$ to $R^p$ coincides with the corank $k$ singular set of any generic map from $M$ to $R^{p+k-1}$ as homology classes with $Z/2$ coefficient ($n>p+k-2$). As an application we give a description of the signature defect of framed 3-manifold from the point of view of singular sets of maps.