Galaxy survey provides an important window for the exploration of fundamental physics by accurately mapping the large-scale structure of the Universe (LSS), which is expected to lead to great scientific discoveries. In cosmology, LSS encodes abundant key cosmological information (e.g., baryon acoustic oscillations, neutrino masses, primordial non-Gaussianities, gravity properties, and cosmological parameters). How to efficiently extract these valuable information has been an important research topic in galaxy survey science. In order to meet the scientific needs of new-generation surveys, we are developing and optimizing a variety of important cosmological techniques (i.e., non-Gaussian statistics, initial condition reconstruction, and cosmological N-body simulation) by solving several key and urgent problems in this field. In this talk, I will give a compendious introduction to our recent work progresses on this topic (mainly focus on Minkowski functionals). These works are expected to play an important role in the processing and analysis of future galaxy survey data, and ultimately bring more scientific returns.
