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Events for the weeks of September 28th – October 10th

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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…	Topology 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)
Thu, Oct. 2 11:15am (MATH …	Algebraic Geometry Daniel Lyness X In this talk we will be continuing where we left off last week, having just introduced the Hilbert-Mumford Numerical Criterion. Now we will see how to use this powerful computational tool to do GIT on the space of plane cubic curves. There will be lots of pictures! Then we’ll kick it up a notch to my research question: How to use GIT to find a moduli space for pairs (Q,C) of a conic and cubic plane curve, and how our moduli space will change depending on the ample line bundle used for our embedding in projective space. GIT on plane curves
Thu, Oct. 2 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X The main goal of this set of talks is to introduce twisted crossed products of Banach algebras by locally compact groups. Both talks will be accessible to anyone with basic Functional Analysis knowledge, but Part II will assume familiarity with Part I. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. Part I: We give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. Part II: We now focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. We present a generalization of the so called Packer–Raeburn trick to the L^p-setting, showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one. This is joint work with Carla Farsi and Judith Packer. Twisted Crossed Products of Banach Algebras (Part I)
Fri, Oct. 3 10:10am (Math …	Math Edu Joseph Timmer & Rebekah Jones X In this workshop, we'll analyze examples of teaching statements and discuss what makes a successful teaching statement. We'll also hear directly from faculty who've served on hiring committees about their evaluation process and priorities. Participants can bring their own teaching statements to receive more targeted guidance and feedback. Teaching Statement Workshop
Tue, Oct. 7 1:25pm (online)	Algebra/Logic Andrew Moorhead (TU Dresden, Germany) View Online:https://cuboulder.zoom.us/j/96896272260 X A strong Maltsev class of varieties is a class of varieties for which there exists a finitely presented variety (i.e. a variety in a finite signature satisfying finitely many identities) whose interpretability class is a lower bound to every variety in the interpretability order, while a Maltsev class of varieties is a class for which there exists a countably infinite descending chain of finitely presented varieties and each variety in the Maltsev class is bounded below by some of the chain. A Maltsev term is the original example of a strong Maltsev condition and the identities that define it define the class of congruence permutable varieties. On the other hand, the classes of congruence distributive and congruence modular varieties are not strong Maltsev classes, but rather Maltsev classes (the terms for distributivity were discovered by Jónsson and the terms for modularity were discovered by Day). There has been for some years a fertile area of research which connects Universal Algebra to the complexity theory of constraint satisfaction. While many of these results are largely important for complexity theory, some of them have been important for algebra. In particular, Siggers discovered that the class of locally finite Taylor varieties is captured by a finite package of identities. In 2015, Olsak made the surprising discovery that in fact the class of all Taylor algebras is strong Maltsev. A natural next question was: what about the class of congruence meet semidistributive varieties? This is an important class in fixed template finite domain CSP, since the class of locally finite congruence meet semidistributive varieties is exactly the class of varieties which correspond to CSP templates which can be solved with local consistency methods. Actually, Kozik, Krokhin, Valeriote, and Willard proved that locally finite congruence meet semidistributive varieties are characterized by a finite package of identities. We show that, unlike the class of Taylor varieties, this finiteness does not lift to the general case, that is, there does not exist a strong Maltsev condition that captures every congruence meet semidistirbutive variety. The class of congruence meet semidistributive varieties is not strong Maltsev
Tue, Oct. 7 2:30pm (MATH 2…	Grad Algebra/Logic Omar Al - Khazali (CU Boulder) Graph algebras
Tue, Oct. 7 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X Every permutation is associated to a classical combinatorial object called a Rothe diagram, where the number of points in the diagram is equal to the number of inversions in the permutation. In this talk, we generalize this notion by associating a Rothe diagram to a set of positive orthogonal roots for a finite simply-laced Weyl group. This construction turns out to have many applications to algebraic combinatorics and to the theory of invariant polynomials. This is based on joint work with Tianyuan Xu (University of Richmond). Orthogonal roots and generalized Rothe diagrams
Thu, Oct. 9 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Thu, Oct. 9 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X The main goal of this set of talks is to introduce twisted crossed products of Banach algebras by locally compact groups. Both talks will be accessible to anyone with basic Functional Analysis knowledge, but Part II will assume familiarity with Part I. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. Part I: We give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. Part II: We now focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. We present a generalization of the so called Packer–Raeburn trick to the L^p-setting, showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one. This is joint work with Carla Farsi and Judith Packer. Twisted Crossed Products of Banach Algebras (Part II)
Thu, Oct. 9 3:30pm (Math 3…	Probability Ewan Davies (Colorado State University) X The hard-core model is a well-studied probability distribution in statistical physics and algorithms since it exhibits interesting behavior from probabilistic and algorithmic perspectives. We will survey the underlying mathematical phenomena that drive this interesting behavior and uncover some surprises. A first-order phase transition in the hard-core model
Fri, Oct. 10 10:10am (Math …	Math Edu Hilary Freeman (Colorado State University) X Math 160 Calculus I for Engineers at Colorado State University has been using a version of standards-based grading since Fall of 2020. In this talk I will discuss why I made the change to alternative grading and how I’ve been implementing this grading system and the changes we’ve gone through. I’ll address the particular challenges of coordinating multiple sections with a large total enrollment and what technology I’ve found helpful or not so helpful. Five Years of Standards-Based Grading in a First Semester Calculus Course

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