Courses in Discrete and Computational Geometry

János Pach is a research professor at the Rényi Institute, Budapest. His main fields of interest are discrete and computational geometry, convexity, and combinatorics. He has written more than 350 research papers. His books, "Research Problems in Discrete Geometry'' (with Brass and Moser) and ``Combinatorial Geometry" (with Agarwal) were translated into Japanese, Russian, and Chinese. He is the co-editor-in-chief of Discrete & Computational Geometry. He received the Lester Ford Award from the Mathematical Association of America (1990), the Rényi Prize and the Academy Award from the Hungarian Academy of Sciences (1993, 1998), and the Szele Prize from the Bolyai Mathematical Society (2019). He was elected the ACM Fellow (2011), a member of Academia Europaea (2014) and the Hungarian Academy of Sciences (2022). He was an invited speaker at the International Congress of Mathematicians (2014) and a plenary speaker at the European Congress of Mathematics (2021).    Géza Tóth is a research professor and the head of the Department of Geometry at the Rényi Institute, Budapest, working on problems in discrete and computational geometry and combinatorics. He received his PhD degree at Courant Institute, New York University in 1997, as a student of János Pach, winning the Best Dissertation Prize in mathematics and the Sokol Award, the highest university-wide prize for fresh PhDs. He wrote more than 100 research articles and he is the co-editor-in-chief of Studia Scientiarum Mathematicarum Hungarica and the editor of Computational Geometry and Acta Mathematica Hungarica. Among other distinctions, he received the Erdős Prize of the Hungarian Academy of Sciences in 2008 and the Rényi Prize of the Rényi Institute in 2010.

• Part I. Lecture notes.- Chapter 1. Graph Product Structure Theory with Applications.- Chapter 2. Threshold for the measure of random polytopes.- Chapter 3. Approximation in geometry.- Part II. The Existential Theory of the Reals.- Chapter 4. Intersection graphs of segments and ∃R.- Chapter 5. The Existential Theory of the Reals as a Complexity Class: ACompendium.