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Events for the weeks of April 27th – May 9th

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Mon, Apr. 28 3:35pm (MATH 3…	Grad Student Seminar Colin Jackson, Sky Jackson (CU Boulder) X In this talk, we will recall some things about Galois groups and look at the "Inverse Galois Problem", which asks which groups appear as Galois groups of polynomials over the rational numbers. The Inverse Galois Problem
Tue, Apr. 29 1:25pm (online)	Algebra/Logic Nebojsa Mudrinski (Novi Sad, Serbia) View Online:https://cuboulder.zoom.us/j/96896272260 X We prove that supernilpotent and nilpotent semirings with absorbing zero are the same and provide a necessary and sufficient condition for supernilpotency (nilpotency). Supernilpotent semirings
Tue, Apr. 29 3:30pm (MATH 3…	Topology Emily Montelius (CU Boulder) X We will cover a brief overview of how to view tiling spaces topologically and then overview different directions that mathematicians expand on this approach. The talk covers chapter 1 of "Topology of Tiling Spaces" by Lorenzo Sadun. It is meant to be a friendly exposition to increase our knowledge of other work in topology, similar to last year's talk "How is knot theory related to topology?". How is tiling related to topology?
Wed, Apr. 30 3:30pm (Math350)	Math Phys Tim Schumacher X The balls-and-bins problem is a fundamental problem in probability theory, analyzing the distribution of m balls randomly placed into n bins. It examines the likelihood of finding a certain number of balls in any given bin. This problem has many practical applications in computer science, such as load balancing in distributed systems. Weighted rendezvous hashing is one approach where bins have different weights (capacities), and the goal is to assign balls to bins such that no bin is unbalanced and, at the same time, all bins are approximately equally utilized. Weighted rendezvous hashing uses a deterministic algorithm to achieve this balance, though the foundations of the algorithm come from probability theory. We will discuss some of the applications and the theory behind these algorithms. Balls in bins
Thu, May. 1 12:30pm (Online)	Rep Theory Juan Villarreal (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk we introduce a canonical decreasing filtration on intertwiners of a vertex algebra. We study the associated graded spaces. Then, we define Poisson vertex intertwiners and Poisson intertwiners. We obtain relations between the associated varieties of modules of a vertex algebra. Intertwiners and filtrations
Thu, May. 1 2:30pm (MATH 3…	Functional Analysis David Blecher (University of Houston) X Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in modern analysis and also in modern quantum physics (such as quantum information theory). They have an extensive theory, and have very important applications in all of these subjects. We present recent work (2025) on the real case of the theory of (complex) operator systems, and also the real case of their remarkable tensor product theory, due in the complex case to Paulsen and his coauthors and students, building on pioneering earlier work of Kirchberg and others. We uncover several notable differences between the real and complex theory, including the absence of minimal and maximal functors in the category of real operator systems. We show how this is related to entanglement. We also develop very many foundational structural results for real operator systems, and elucidate how the complexification interacts with the basic constructions in the subject. We give the real analogues of the Kirchberg conjectures (and of several important related problems that have attracted much interest recently such as the Tsirelson problem on quantum correlations), and the deep relationships between them. Joint work with Travis Russell. Real operator systems
Wed, May. 7 3:30pm (Math350)	Math Phys Andrew Hamilton (CU Boulder Astrophysics) Clifford(11,1) string theory

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