Min Ru (University of Houston) Schmidt's subspace theorem and its generalization
Tue, Oct. 22 12:10pm (MATH …
Jan Mycielski (CU Boulder) Mathematics of human intelligence and related ideas
Tue, Oct. 22 4pm (MATH 350)
Jonathan Quartin (CU) The Moduli Stack of Formal Groups
In recent years, there have been some breakthroughs in extending Schmidt's subspace theorem to non-linear hypersurfaces, made by Corvaja-Zannier, and Evertse-Feretti, etc. In this talk, I will discuss my recent joint work with P. Vojta based on their works, as well as its applications.
A description of the structure of knowledge in the brains of animals, with an outline of the phylogeny of human intelligence. The theory supports some old ideas in the philosophy of mind and it may have applications in artificial intelligence. I will define finite algebraic structures, that I call mental models. They are intended to represent in a realistic way the descriptive component of knowledge (as opposed to its evaluating component). I will define the notions of mental object and of concepts in a mental model. Concepts can be real, like these representing objects and processes of everyday life or studied in science, or they may be imaginary, like these in tales and pure mathematics. Our definitions yields a precise form of Ockham's principle of economy of concepts. The theory suggests some ideas in ontology and pedagogy. Theories of the mind that ignore biology or brain science, or do not propose sufficiently clear notions of meaning, will be criticized.