Our research group aims to reveal the mathematics of complex systems arising from nature. With recent technological advancements, nature increasingly hints at underlying mathematical structures through data. Our goal is to extract the essence of these hints from a mathematical perspective, employing both continuous and discrete approaches. Our primary focus is on algebraic and geometric perspectives. We are keen on exploiting advanced computational mathematical tools, including computer algebra. This process is bidirectional: understanding nature not only uncovers new mathematics but also generates mathematical tools to tackle natural phenomena. In our group, we value both sides of this interaction between nature and abstract mathematics.