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Events for the weeks of January 29th – February 10th

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Tue, Jan. 31 1:25pm (Online)	Algebra/Logic Žaneta Semanišinová (Technische Universität Dresden) X For a given relational structure $𝔅$ , the constraint satisfaction problem CSP( $𝔅$ ) asks whether a given finite input structure maps homomorphically to $𝔅$ . We study the complexity of CSP( $𝔅$ ), where the domain of $𝔅$ is infinite. Our basic setting is that if we have a complexity classification for the CSPs of first-order expansions of a structure $𝔅$ , then it can be transferred to obtain a classification of the CSPs of first-order expansions of another structure $ℭ$ . We exploit the algebraic product of structures that corresponds to the product of the respective polymorphism clones and present a complete complexity classification of the CSPs for first-order expansions of finite algebraic powers of $ℚ; <)$ . By combining our classification result with classification transfer techniques, we answer several open questions in spatial reasoning from (Balbiani, Condotta, 2002), (Balbiani, Condotta, del Cerro, 1999) and (Balbiani, Condotta, del Cerro, 2002). This is joint work with Manuel Bodirsky, Peter Jonsson, Barnaby Martin and Antoine Mottet. Complexity Classification Transfer for CSPs via Algebraic Products (Click title to connect to Zoom)
Wed, Feb. 1 3:30pm (Math350)	Math Phys Howy Jordan (CU Boulder) X Infinite dimensional manifolds arise naturally even from considerations of finite dimensional spaces. But in general, infinite dimensional topological vector spaces lose many of the nice properties from the finite case that we casually take for granted in differential geometry. In this talk, we consider the nicer cases of Banach and Hilbert spaces and manifolds modeled on these. The basic building blocks of differential geometry (like charts, smooth structures, and tangent vectors) can be easily defined, and we will observe some differences and similarities between the finite theories of submanifolds and vector bundles and their respective general Banach/Hilbert counterparts. Banach and Hilbert Manifolds
Thu, Feb. 2 5pm (MATH 350)	Grad Student Seminar Chase Meadors (CU Boulder) X In this talk, we will start by finding out where the arrows are in algebra so we can turn them all around, yielding a subject called coalgebra. Coalgebra turns out to model various forms of automata and dynamical systems. A "coequation", then, is something that controls, specifies, or constrains the behavior of such systems. We will explore the analogy of "equational logic" for algebras with "modal logic" for coalgebras. Finally, we will proceed to co-solve co-systems of co-linear co-equations and end by learning the co-quadratic formula. Coalgebra 1
Tue, Feb. 7 1:25pm (Online)	Algebra/Logic Will Brian (University of North Carolina at Charlotte) X I will sketch a proof that, assuming 0^† does not exist, if there is a partition of R into ℵ_ω Borel sets, then there is also a partition of R into ℵ_ω+1 Borel sets. (And the same is true for any singular cardinal of countable cofinality in place of ℵ_ω.) This contrasts starkly with the situation for cardinals with uncountable cofinality and their successors, where the spectrum of possible sizes of partitions of R into Borel sets can be made completely arbitrary via forcing. Partitions of the real line into Borel sets (Click title to connect to Zoom)
Wed, Feb. 8 3:30pm (Math350)	Math Phys Rebecah Storms (CU Boulder) Jets and jet bundles
Wed, Feb. 8 4:40pm (MATH 3…	Grad Student Seminar Alex LaJeunesse (CU Boulder) TBA