Title: Gelfand DualityAbstract: If X and Y are locally compact Hausdorff spaces, and C_0(X) and C_0(Y) are the rings of complex-valued functions over the respective spaces that vanish at infinity, then X and Y are homeomorphic if and only if C_0(X) and C_0(Y) are isomorphic as rings. A question arises: is a commutative ring satisfying similar axioms to a ring of complex-valued functions vanishing at infinity (even with no reference to an underlying space in its definition) canonically isomorphic...

Title: Can Computational Modeling Inform Intervention Strategies to Mitigate the Impact of Developmental Abnormalities? Abstract: Branched, tree-like structures, such as the lung airways and mammary ducts, are vital for fluid transport in mammals. They facilitate the secretion and distribution of essential substances, as well as the removal of waste, thereby supporting diverse physiological functions. The formation of these tree-like structures typically begins during embryonic development...

Speaker: Thiago Serra Azevedo Silva, Dept. of Business Analytics

Title: Quantum symmetries old and new.   Abstract: Quantum symmetries is the study of how symmetries of classical objects carry over to their quantizations.  In this lecture I will review the work of De Concini, Kac and Lusztig on how the coadjoint action of an algebra group G carries over to an action of a quantum group at a root of unity on its restricted dual at that root of unity. I will then resolve a recent conjecture in skein theory negatively by analyzing the quantum symmetries...

Title: A model theorist’s perspective on the Connes Embedding Problem (and its resolution)Abstract: In 2020, a group of computer scientists resolved the Connes Embedding Problem (CEP) from von Neumann algebra theory. In this informal talk, I’ll explain how basic ideas from mathematical logic can be used to simplify and strengthen the resolution of the CEP from the computer science result.Professor Goldbring is giving a colloquium talk, Effective metric structure theory and operator algebras, at...

Title: Effective metric structure theory and operator algebrasAbstract: Going back to the work of Turing in the early 20th century, studying what sets and functions are computable has been a fruitful area of research. Usually, such computability-theoretic issues are restricted to countable, discrete objects such as graphs, groups, rings, etc. However, one can transport these ideas to the setting of structures from analysis based on separable metric spaces and in doing so, one can pursue a...

Speaker: Rahul Singh, Dept. of Computer Science

Title: Number theory and cryptography   Abstract:  In this presentation Professor Ye will survey his work and progress in number theory since his last colloquium talk in the department. Topics include the Riemann zeta function, automorphic L-functions, their functoriality, upper bounds, and zero statistics, computational number theory, and its applications to cyberspace security or insecurity.   Short Bio: Professor Yangbo Ye is a professor of Mathematics with expertise in number theory and...