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Events happening on April 12, 2016

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Apr. 12, 2016 11am (MATH 350)	Number Theory James Ricci (Daemen College) X One of the many interesting algebraic objects associated to a given elliptic curve defined over the rational numbers, E / Q, is its full-torsion representation ρ_E:Gal( Q /Q) → GL₂(Ẑ). Generalizing this idea, one can create another full-torsion Galois representation, ρ_(E₁,E₂): Gal( Q /Q)→(GL₂(Ẑ))² associated to a pair (E₁,E₂) of elliptic curves defined over Q. The goal of this talk is to provide an infinite number of concrete examples of pairs of elliptic curves whose associated full-torsion Galois representation ρ_(E₁,E₂) has maximal image. Elliptic Curves with Maximally Disjoint Division Fields
Apr. 12, 2016 12:10pm (MATH …	Kempner Sandra Laursen (Ethnography & Evaluation Research (E&ER) at CU Boulder) X Mathematics serves as students’ gateway to majors and careers in STEM fields (science, technology, engineering, mathematics), but lack of success in their initial college math courses deters many STEM-intending students from progressing in their desired pathways. While studies across the STEM disciplines support the use of student-centered teaching and learning to increase student learning and persistence, there has been less previous research on these approaches in college mathematics. Our group’s study of inquiry-based learning (IBL) as implemented in over 100 course sections at four universities shows that student-centered approaches can succeed when implemented on a departmental scale (http://www.colorado.edu/eer/research/steminquiry.html ). Despite variation in how IBL was implemented, student outcomes are improved in IBL courses relative to traditionally taught courses, as assessed by general measures that apply across course types. Particularly striking, the use of IBL eliminates a sizable gender gap that disfavors women students in lecture-based courses. Other evidence suggests particular benefits to initially lower-achieving students, and to pre-service K-12 teachers. The study supports IBL teaching as a means to improve learning outcomes and, potentially, student retention in college mathematics. In this session, I will highlight key results from our work that mathematics instructors may find useful to consider and to share with students and colleagues. Student outcomes of inquiry-based learning (IBL) in undergraduate mathematics: Key findings from education research
Apr. 12, 2016 1pm (MATH 220)	Grad Algebra/Logic Nik Ruskuc (University of St Andrews) X Let V be a class of algebras (usually a variety), and let P be an algebraic property. Is it true that the direct product AxB of two algebras from V satisfies the property P if and only if A and B satisfy P? If not, what are the conditions on A and B that make AxB satisfy P? For instance, in the group case the first question has a positive answer for most standard properties P (such as, say, finite generation, finite presentability, residual finiteness, etc.) Peter Mayr and I have been pursuing a project of investigating these questions within the context of Universal Algebra. It turns out that group theoretic results often generalise to much broader classes of algebra, e.g. Malcev varieties and such like. However, it would appear that semigroups by and large tend to remain outside the scope of our general theorems. My aim for this talk is to present it as a kind of 'companion' to our work, in which I will describe the curious landscape for semigroups, and present some remaining open problems. Finiteness properties for direct products of semigroups Sponsored by the Meyer Fund
Apr. 12, 2016 1pm (Math 350)	Functional Analysis Sooran Kang (University of Colorado, Boulder) X As promised in the first lecture, we conclude this series of Ulam lectures by describing the quantum Heisenberg manifolds as twisted groupoid -algebras. First we discuss the definition of a twist groupoid over a groupoid associated to a local homeomorphism and a locally compact Hausdorff space, and discuss the result by Deaconu-Kumjian-Muhly, which says that the twisted groupoid -algebra, , is isomorphic to a Cuntz-Pimsner algebra , where is a Hilbert -correspondence. Combining this result with the result of the isomorphism classes of the QHMs, we show that the QHM can be realized as a twisted groupoid -algebra. Quantum Heisenberg manifolds as twisted groupoid -algebras Sponsored by the Meyer Fund
Apr. 12, 2016 2pm (MATH 220)	Nik Ruskuc (University of St Andrews) X Magnus' solution for the word problem (1932) for one-relator groups is one of the first results in the then-emerging field of combinatorial group theory, and the corresponding problem for one-relation semigroups is perhaps the most easily stated and longest-standing open problem in combinatorial algebra. This talk will be mostly historical in nature, with the aim of outlining the relationship between the two problems, and the present state of knowledge about one-relation semigroups. I will also indicate some possible ways forward, which I am currently pursuing in a project with Robert Gray. One relation groups and semigroups Sponsored by the Meyer Fund
Apr. 12, 2016 4pm (Math220)	Megan Ly (CU Boulder) X Elementary particles such as electrons have an intrinsic angular momentum called "spin". In order to account for spin, we must use the double cover SU(2) of the three dimensional rotation group SO(3) to describe the rotations of fundamental quantum systems. In this talk we construct the irreducible representations of using first and second order differential operators to classify different spin states. Spin and irreducible representations of

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