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Events happening on April 16, 2019

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Apr. 16, 2019 11am (MATH 350)	Number Theory Chong Gyu Lee (Soongsil University) X Spiro showed that multiplicative function which is additive on prime numbers should be the identity function. After Spiro's work, there are many variations. One of such result is work of Chung and Phong; multiplicative function which is additive on triangular numbers should be the identity. But there is non-identity functions which is multiplicative and is additive on square numbers. In this talk, we check the difference of triangular and square numbers and expand it the other polygonal numbers, pentagonal and hexagonal numbers. Multiplicative functions, additive on polygonal numbers
Apr. 16, 2019 12pm (MATH 350)	Kempner Satyan Devadoss (University of San Diego) X A 2-ton interactive sculpture came to life at Burning Man 2018, the world�s most influential large-scale sculpture showcase. Rising 12 feet tall with an 18-foot wingspan in the Nevada desert, the unfolding dodecahedron was illuminated by 16,000 LEDs, requiring 6500 person hours and $40,000 in funds. Its interior, large enough to hold 15 people, was fully lined with massive mirrors, alluding to a possible shape of our universe.� The unfolding exterior points to the 500-year-old work of Albrecht Durer, and the tantalizing open problem of discovering a geometric unfolding for every convex polyhedron.� We discuss the state-of-the-art, and consider higher-dimensional unfolding analogs, with elegant geometric and combinatorial relationships to integer partitions and chord diagrams. Unfolding Mathematics at Burning Man Sponsored by the Meyer Fund
Apr. 16, 2019 12pm (MATH 350)	Topology Satyan Devadoss (University of San Diego) X A 2-ton interactive sculpture came to life at Burning Man 2018, the world�s most influential large-scale sculpture showcase. Rising 12 feet tall with an 18-foot wingspan in the Nevada desert, the unfolding dodecahedron was illuminated by 16,000 LEDs, requiring 6500 person hours and $40,000 in funds. Its interior, large enough to hold 15 people, was fully lined with massive mirrors, alluding to a possible shape of our universe.� The unfolding exterior points to the 500-year-old work of Albrecht Durer, and the tantalizing open problem of discovering a geometric unfolding for every convex polyhedron.� We discuss the state-of-the-art, and consider higher-dimensional unfolding analogs, with elegant geometric and combinatorial relationships to integer partitions and chord diagrams. Unfolding Mathematics at Burning Man Sponsored by the Meyer Fund
Apr. 16, 2019 1pm (MATH 220)	Grad Algebra/Logic Keith Kearnes (CU) Congruence n-permutability is not join prime
Apr. 16, 2019 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (University of Colorado Boulder) X The theory of $P$ -partitions was introduced by Stanley, and a $P$ -partition can be viewed as a generalization of the tableaux. Stembridge introduced enriched $P$ -partitions, and these combinatorial objects are a generalization of the shifted Young tableaux. The polynomials corresponding to the enriched $P$ -partitions produce the peak algebra. We introduce and develop a theory of colored $P$ -partitions and colored enriched $P$ -partitions, and this theory give us tools to define the peak algebra in non-commutating variables.� In the end, we generalize the peak algebra to an arbitrary combinatorial Hopf algebra. This is joint work with Shu Xiao Li. Hopf structures in algebra and combinatorics: The peak algebra in non-commuting variables
Apr. 16, 2019 2pm (MATH 220)	Jordan DuBeau (CU) An uncountable Jonsson Jonsson-Tarski Algebra
Apr. 16, 2019 3pm (MATH 350)	Topology Ezra Getzler (Northwestern University) X The moduli space of vector bundles on a closed oriented surface is a symplectic manifold. More recently, this result has been generalized by To�n and Vezzosi and their collaborators in several directions, in the framework of derived stacks: there is a Chern character in the de Rham complex of differential forms on the moduli space (or derived stack) of finite dimensional complexes on an oriented d-dimensional manifold, and the second Chern character class in this differential form is a shifted symplectic form (of total degree 2-d). In my work with Kai Behrend, I have sought more a constructive approach to this result: the original approach made heavy use of closed model categories and Lurie�s proof of the cobordism hypothesis (for the circle). The goal of these two talks is to explain what a derived stack is, construct some examples explicitly, and explain how to define the Chern character in this setting. To give a small flavor of the subject, here is a typical result from our work: if A is a finite-dimensional differential graded algebra over the complex numbers vanishing in degree -k and below, then its quasi-invertible elements (invertible up to a homotopy) are the objects of a derived k-groupoid. Derived stacks and symplectic forms Sponsored by the Meyer Fund
Apr. 16, 2019 10pm (MATH 350)	PDE/Analysis Taylor Klotz (CU Boulder) X A control system with symmetry is cascade linearizable if its solutions can be determined by �composing� two associated linear systems. One first uses a linearizable quotient of the system by some symmetries to reconstruct the control system as a linear part plus an equation of lie type. One then restricts the reconstructed system along so-called partial contact curves so that the restricted equations are now themselves linearizable as well. In this talk we present new results concerning existence of linearizable partial contact curve reductions. The Partial Contact Curve Reduction Step in Cascade Linearization

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