With the growing volume of publications in the Computer Science (CS) discipline, tracking the research evolution and predicting the future research trending topics are of great importance for researchers to keep up with the rapid progress of research. Within a research area, there are many top conferences that publish the latest research results. These conferences mutually influence each other and jointly promote the development of the research area. To predict the trending topics of mutually influenced conferences, we propose a correlated neural influence model, which has the ability to capture the sequential properties of research evolution in each individual conference and discover the dependencies among different conferences simultaneously. The experiments conducted on a scientific dataset including conferences in artificial intelligence and data mining show that our model consistently outperforms the other state-of-the-art methods. We also demonstrate the interpretability and predictability of the proposed model by providing its answers to two questions of concern, i.e., what the next rising trending topics are and for each conference who the most influential peer is.