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Events happening on November 27, 2018

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Nov. 27, 2018 11am (MATH 350)	Number Theory Özlem Ejder (CSU) X The points on the modular curve X_1(n) (roughly) classifies the pairs (E,P) up to isomorphism where E is an elliptic curve and P is a point of order n on E. We call a closed point x on X_1(n) sporadic if there are only finitely many closed points of degree at most deg(x); hence classifying sporadic points on X_1(n) is closely related to determining the torsion subgroups of elliptic curves over a degree d field. When d=1 or 2, Mazur and Kamienny's work show that there are no sporadic points of degree d on X_1(n). In this talk, I will discuss that the sporadic j-invariants of bounded degree is finite. This is joint with A. Bourdon, Y. Liu, F. Odumudu and B. Viray. Sporadic points on modular curves
Nov. 27, 2018 12:10pm (MATH …	Kempner Xudong Chen (CU Boulder) X Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of individual control systems. As a dual, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the (continuum) ensemble. We introduce in the talk a novel class of ensembles of nonlinear control systems, termed distinguished ensemble systems. Every such system has two key components, namely a set of finely structured control vector fields and a set of co-structured observation functions. In the first half of the talk, we demonstrate that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a principle for ensemble system design. In the second half of the talk, we address the issue about existence of a distinguished ensemble system for a given manifold. We will focus on the case where the state space of every individual control system is an arbitrary semi-simple Lie group or its homogeneous space. Structure Theory for Ensemble Control and Estimation of Nonholonomic Systems
CANCELED Nov. 27, 2018	Ulam Erik van Erp (Dartmouth College) X This is joint work with Robert Yuncken. We developed a coordinate-free geometric definition and a unified approach to various pseudodifferential calculi. The starting point of the construction is the identification of an appropriate groupoid, which is a purely geometric object. These groupoids are suitable adaptations of Connes' tangent groupoid. We show how, once the appropriate groupoid has been constructed, the details of the calculus are developed on its foundation. Our construction recovers the classical pseudodifferential calculus as well as, for example, the Heisenberg calculus (on contact manifolds) and its generalizations (to filtered manifolds). A groupoid approach to Pseudodifferential calculi
Nov. 27, 2018 1pm (MATH 220)	Grad Algebra/Logic Peter Mayr X We discuss the final steps in Zhuk's algorithm: reductions for absorbing subuniverses, centers, polynomially complete quotients and linear quotients. CSP linear quotients 1
Nov. 27, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Cofinality Spectrum Problems, Part 2: A motivating example by Malliaris and Shelah
Nov. 27, 2018 3pm (MATH 350)	Topology Paul Lessard X The simplex category, the category of finite totally ordered sets, is a strict test category, meaning that there exists a product preserving Quillen equivalence between simplicial sets, presheaves on the simplex category, and "nice topological spaces". It is not clear however how the combinatorics of the simplex category relate to spectra, the objects which represent cohomology theories for spaces. All the well known models of spectra, Adams spectra, symmetric spectra, L-spectra, etc. may or do use simplicial sets as their presentation for spaces, but only one almost forgotten model, Kan's semisimplicial spectra of 1963 leverage the combinatorics of the simplex category for elegance and insight. We will begin by asking why the simplex category is a strict test category and why the the category of globes is not. We will then then develop a strict test category, the theta category of Joyal, and construct an elegant suspension functor for cellular sets, presheaves on the category theta. We will then present a conjectured new model of spectra based on this category which recovers the best aspects of Kan's semisimplicial spectra. We will also comment on how this model of spectra may provide a universal algebraic lens to the distinction between stable and unstable homotopy theory. A Cellular Suspension Functor for a New Presentation of Spectra
Nov. 27, 2018 4pm (MATH 350)	Topology Andrew Stocker Analytic K-homology

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