Explore the latest developments in Markov bases and their applications in this 51-minute lecture by Sonja Petrović from the Illinois Institute of Technology. Delve into the interconnected realms of sampling, learning, and coloring as they relate to Markov bases. Gain insights into cutting-edge research and practical applications in the field of enumerative geometry. Discover how these mathematical concepts are shaping modern approaches to data analysis, machine learning, and graph theory.