Boolean circuits form a simple, natural, and expressive model of computation, powerful enough to capture algorithms and central to many areas of computer science, including algorithms, complexity theory, cryptography, formal verification, hardware design, machine learning, and SAT solving. In this talk, I will survey classical and recent developments in circuit theory, with a focus on results from our group on circuit lower bounds, circuit synthesis, and fine-grained complexity. I will highlight key open problems and outline promising directions for future collaboration.

Alexander Kulikov holds Ph.D. (2009) and Dr.Sci. (2017) degrees from the St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences. Currently, Alexander is a researcher at JetBrains. His scientific interests include algorithms, circuit complexity, and Computer Science education. He coauthored three books and sixteen massive open online courses on algorithms and discrete mathematics with over a million enrolled students.