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Events happening on September 30, 2025

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Tue, Sep. 30 1:25pm (online)	Algebra/Logic Anna Romanowska (Warsaw University of Technology) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we will use an algebraic approach to study convex subsets of affine spaces over the ring of dyadic rationals. Dyadic rationals are rationals whose denominator is a power of 2. A dyadic n-dimensional convex set is defined as the intersection with n-dimensional dyadic space of an n-dimensional real convex set. Such a dyadic convex set is said to be a dyadic n-dimensional polytope if the real convex set is a polytope whose vertices lie in dyadic space. Dyadic convex sets appear as subalgebras of reducts of faithful affine spaces over the ring of dyadic numbers, or equivalently as commutative, entropic and idempotent groupoids (binars or magmas) under the binary operation of arithmetic mean. We will examine algebraic concepts and properties of dyadic polytopes (especially polygons), and contrast their behavior with that of polytopes in real affine space. On the basis of older results about the generation and structure of dyadic polytopes, we will present recent results (obtained with A. Mucka) on the representation, characterization and classification of dyadic triangles. Algebraic properties of dyadic convex polytopes
Tue, Sep. 30 1:30pm (MATH 3…	Homotopy Jackson Morris (University of Washington) X The stable homotopy groups of spheres are an important and complicated invariant. However, there is a filtration which sorts the p-components of this group into vn-periodic layers, known as chromatic heights, which are themselves more computable. The height one piece is the only layer which we fully understand, and an invaluable tool to accessing v1-periodic stable homotopy is the BP<1>-based Adams spectral sequence. In this talk, I will discuss joint work with Petersen and Tatum which focuses on the analogue of this problem in motivic homotopy theory. The key idea is that there are similar periodic layers in the stable homotopy of the motivic sphere. We compute the E1-page of the analogous BPGL<1>-based motivic Adams spectral sequence at all primes p and over a myriad of base schemes. Time permitting, I will discuss future directions in chromatic motivic homotopy theory. Splittings of truncated motivic Brown-Peterson cooperations algebras
Tue, Sep. 30 2:30pm (MATH 3…	Lie Theory Chindu Mohanakumar (University of Colorado Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology
Tue, Sep. 30 2:30pm (MATH 3…	Topology Chindu Mohanakumar (CU Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology
Tue, Sep. 30 2:30pm (MATH 2…	Grad Algebra/Logic Orlando Reyes (CU) Categorical Perspective on Constraint Satisfaction (Part 3)

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