Türkü Özlüm ÇELİK Group

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.

In our research, we look for algebraic varieties that arise in the sciences. This leads to significant questions in mathematics from algebra to number theory, from geometry to topology. Inspired by recent experiments at our institute, we study these mathematical structures with interest in exploring new insights and machinery for living systems. We make use of tools from research fields, including real, numerical, combinatorial, metric algebraic geometry; (polynomial) optimization; (algebraic) statistics; and discrete mathematics.

Our current research interests include:

• Riemann surfaces, Riemann theta functions, abelian varieties, and Grassmannians; applications in integrable systems
• Real algebraic varieties and semi-algebraic sets; applications in polynomial dynamical systems
• Optimization with respect to distance; applications with Wasserstein distance
• Classification problems in biological systems