The speaker, Mr. Kota Takeda from Kyoto University, delivered a presentation on data assimilation (DA) from a mathematical perspective. The main result is a theorem proving the mathematical validity of Ensemble Transform Kalman Filter (ETKF)-based DA for dissipative dynamical systems. After explained the mathematical setup for notation and dynamical systems, Mr. Takeda briefly introduced several Kalman filter-based DA methods and some mathematical results related to them. The main theorem states that if the additive inflation parameter is sufficiently large, the error between the analysis and the true states is dominated by the second-order of the observation error. Previous results have established the mathematical validity of DA using additive inflation, but not for multiplicative inflation. This is an advantage of the main result. After his talk, we had a discussion about the main result.