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Events for May – September 2015

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May. 15, 2015 2pm (MATH 350)	Number Theory Taku Ishii (Seikei University (Tokyo, Japan)) X I will talk about special functions related to Fourier expansions of Siegel modular forms of degree two, and application to computation of archimedean zeta integrals for some automorphic L-functions on GSp(2). Spherical functions on Sp(2,R) and archimedean zeta integrals
Jul. 14, 2015 11am (Math 220)	Noncomm Geometry Paul Bressler (Universidad de los Andes) Introduction to DG manifolds. Sponsored by the Meyer Fund
Aug. 26, 2015 4pm (MATH 350)	Grad Student Seminar Sebastian Bozlee (CU-Boulder) X An introduction to the categorical conceptualization of mathematics. Categories pt. 1
Aug. 28, 2015 4pm (MATH 350)	Grad Student Seminar Leo Herr X A further welcome to the categorical weltanschauung. Categories pt. 2
Sep. 01, 2015 10am (Math350)	Jonathan Lamar (Colorado) X TBD Intro to algebraic combinatorics: A personal voyage
Sep. 01, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Algebra and Computation: Some Open Problems
Sep. 01, 2015 1pm (Math350)	Stephen Preston Riemannian geometry overview, part 1 of 3
Sep. 01, 2015 2pm (MATH 220)	Keith Kearnes (CU) X This will be the first in a series of talks covering the book ``The structure of finite algebras'' by Hobby and McKenzie. Tame Congruence Theory
Sep. 01, 2015 3pm (Math 350)	Markus Pflaum (CU Boulder) X TBA Introduction to Poisson geometry and deformation quantization
Sep. 02, 2015 4pm (MATH 350)	Grad Student Seminar Robert Hines (CU-Boulder) X In this talk, we will review/introduce simple continued fractions and some ideas from ergodic theory. We will then derive information about the continued fraction expansion of almost every real number by considering the ergodic system (X, T, \mu)=([0,1]\backslash\mathbb{Q}, \{1/x\}, dx/(1+x)). Ergodic Theory of Simple Continued Fractions
Sep. 03, 2015 3pm (MATH 350)	Probability Nicholas Cook (UCLA) X We consider two random matrix ensembles associated to large random regular digraphs: (1) the 0/1 adjacency matrix, and (2) the adjacency matrix with entries weighted by iid signs. Motivated by universality conjectures, we show that the spectral distribution for the latter ensemble is asymptotically described by the circular law, assuming the graph has degree linear in the number of vertices. Towards establishing the same result for the adjacency matrix without iid weights, we prove that it is invertible with high probability. Along the way we make use of Stein's method of exchangeable pairs to establish some graph discrepancy properties. Random regular digraphs: singularity and spectrum
Sep. 08, 2015 10am (Math350)	Katherine Adamyk and Athena Sparks (Colorado) X This introductory talk will cover basic definitions and examples of representation and character theory. It will be accessible to a general math audience. Introduction to Representation Theory
Sep. 08, 2015 1pm (Math350)	Pearce Washabaugh Manifolds of maps
Sep. 08, 2015 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X Set partition statistics have been recently studied as a family be Diaconis et al, where they study their algebraic and probabilistic properties. On the other hand, these statistics come about naturally in the representation theory of finite unipotent groups. Viewed in this context, it is natural to consider a wider family of unipotent groups whose representation theory is governed by the integer lattice points inside a family of polytopes (called transportation polytopes). This talk develops these ideas, and raises some questions about the geometry of set partition statistics suggested by this connection. The geometry of set partition statistics?
Sep. 08, 2015 3pm (Math 350)	Matias del Hoyo (IMPA) X The Linearization Theorem for Lie groupoids provides an organizing framework for classic results on the geometry of fibrations, actions and foliations. It was conjectured by A. Weinstein and solved by N. Zung using analytical methods. In a joint work with R. Fernandes, building on previous works by M. Pflaum et al, we abord the linearization problem from a new perspective, developing a notion of metrics on Lie groupoids, obtaining a simpler proof and a stronger result. I will discuss the linearization problem for groupoids, our solution by metrics, and if time permits, future lines of research. Lie groupoids, linearization and metrics Sponsored by the Meyer Fund
Sep. 09, 2015 4pm (MATH 350)	Grad Student Seminar Mason Pelfrey (CU-Boulder) X An exterior differential system (EDS) is a system of equations of defined on a manifold involving exterior differentials forms. In this talk, we'll introduce differential forms and differential ideals and describe how to construct an EDS. We'll see a couple of theorems (probably without proof) on the existence of solutions to EDS. One reason that EDS are useful is that every PDE can be rephrased as an EDS and the tools of exterior algebra give a coordinate-free way to analyze the PDE/EDS Exterior Differential Systems
Sep. 15, 2015 10am (Math350)	Ryan Rosenbaum (Colorado) More Representation Theory
Sep. 15, 2015 1pm (Math350)	Stephen Preston X I will continue the survey of the aspects of Riemannian geometry from last time. In particular I will discuss normal and isothermal coordinates, the basic constant curvature spaces, and the uniformization theorem for surfaces. Riemannian geometry overview, part 2 of 3
Sep. 15, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The simplest polynomial time algorithm for CSPs: checking local consistency, Part 1
Sep. 15, 2015 2pm (MATH 220)	Keith Kearnes (CU) X Continuation. Tame Congruence Theory
Sep. 15, 2015 2pm (MATH 350)	Lie Theory Shawn Burkett (CU) X Every finite group has two trivial supercharacter theories: the usual character theory and the one coming from "clumping" all nonprincipal characters. If the group has order greater than two, then these supercharacter theories are distinct. Recently, Lewis and Wynn showed that there are only two solvable groups and possibly only one nonsolvable group that have exactly two supercharacter theories. In this talk we discuss this result and an algorithm which was employed to finish the above classification. Groups with No Nontrivial Supercharacter Theories
Sep. 15, 2015 3pm (Math 350)	Markus Pflaum (CU Boulder) Introduction to Poisson geometry and deformation quantization (part 2)
Sep. 16, 2015 4pm (MATH 350)	Grad Student Seminar Sarah Salmon & Katherine Adamyk (CU-Boulder) X After briefly introducing some terminology, we will explore how colored, directed graphs can be used to construct interesting examples of C-algebras. No prior knowledge of C-algebras required! Constructing C*-algebras from k-graphs
Sep. 17, 2015 3pm (Webber 20…	Algebraic Geometry Valentijn Karemaker (Utrecht) X TBA The Inverse Galois problem for symplectic groups
Sep. 22, 2015 10am (Math350)	Ryan Rosenbaum (Colorado) X TBD Lie groups?
Sep. 22, 2015 11am (MATH 350)	Number Theory Jayadev Athreya (University of Washington) X Given an Apollonian Circle Packing and a circle in , color the set of disks in tangent to red. What proportion of the concentric circle is red, and what is the behavior of this quantity as ? Using equidistribution of closed horocycles on the modular surface , we show that the answer is We also describe an observation due to Alex Kontorovich connecting the rate of this convergence in the Farey-Ford packing to the Riemann Hypothesis. For the analogous problem for Soddy Sphere packings, we find that the limiting radial density is , where denotes the volume of an ideal hyperbolic tetrahedron with dihedral angles . Radial Density in Apollonian Packings
Sep. 22, 2015 12:10pm (MATH …	Kempner Piotr Hajac (Polish Academy of Sciences and University of New Brunswick) X In terms of multipullback C-algebras, we construct a noncommutative deformation of odd-dimensional spheres that preserves the natural partition of the (2n+1)-dimensional sphere into (n+1)-many solid tori. The aim of this talk is to explain in an elementary way basic ideas proving that the noncommutative line bundles associated to the multipullback quantum (2n+1)-dimensional sphere are pairwise stably non-isomorphic. In particular, we conclude that the tautological line bundles over the multipullback quantum complex projective spaces are not stably trivial. First, we use the technology of higher-rank graph C-algebras to prove that our multipullback C*-algebras are universal for commuting isometries satisfying a sphere equation. Furthermore, by finding a strong connection, we show that the natural U(1)-action on our quantum (2n+1)-dimensional sphere is free. This puts us in the framework of Chern-Galois theory which, combined with the aforementioned universal presentation, reduces the pairwise non-isomorphism problem from dimension 2n+1 to dimension 3. The latter case is handled by an index pairing computation thus completing the proof. By very ample references to the standard geometry of odd-dimensional spheres thought of as U(1)-principal bundles over complex projective spaces, the talk will be accessible to non-experts. (Based on joint work with David Pask, Aidan Sims and Bartosz Zielinski.) Multidimensional line bundles associated to multipullback quantum odd spheres
Sep. 22, 2015 1pm (MATH 220)	Grad Algebra/Logic Peter Mayr (CU Boulder) X The subpower membership problem (SMP) for a fixed finite algebra A has as input tuples a_1,...a_k and b in A^n. The question is whether b belongs to the subalgebra of A^n that is generated by a_1,...a_k. The SMP arises from the question whether relations (subalgebras of powers) can be efficiently represented by generators. We consider the complexity of the problem for various algebras. Introduction to the Subpower Membership Problem
Sep. 22, 2015 1pm (Math350)	Stephen Preston Riemannian geometry overview, part 3 of 3
Sep. 22, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Sep. 22, 2015 2pm (MATH 350)	Lie Theory Jon Lamar (CU) X Let G be a group and let SCT(G) be the set of all supercharacter theories of G. We can endow SCT(G) with a natural partial order, which in fact gives this set the structure of a lattice. From this jumping-off point, we can study the interplay between the combinatorics of SCT(G) and the algebra of G. In this talk, I will summarize what is already known about the lattice of supercharacter theories of a group, as well as present some new results and open problems along these directions. Poset Theory of Supercharacters
Sep. 22, 2015 3pm (Math 350)	Markus Pflaum (CU Boulder) Foundations of Deformation Quantization (continued)
Sep. 22, 2015 4pm (Math 350)	Alexander Nita (CU Boulder) Fedosov's Deformation Quantization
Sep. 23, 2015 4pm (MATH 350)	Grad Student Seminar Cliff Blakestad (CU-Boulder) X We will see how writing integers in their base p expansion can lead to entirely new number systems. We will then explore some of the basic properties of these systems. On p-Adic Numbers
Sep. 24, 2015 3pm (MATH 350)	Probability Wilfried Huss (Cornell) X A rotor router walk is a deterministic walk on a graph, where the exits from each vertex follow a fixed cyclic order. We give a necessary and sufficient condition for recurrence of rotor router walks on supercritical Galton-Watson trees, in the case where the first exit of each vertex is chosen at random. Joint work with Sebastian Müller and Ecaterina Sava-Huss Rotor router walks on Galton-Watson trees
Sep. 29, 2015 10am (Math350)	Erica Shannon (Colorado) X TBD Hopf Algebras
Sep. 29, 2015 1pm (MATH 220)	Grad Algebra/Logic Markus Steindl (Johannes Kepler Universitat Linz) X Fix a finite semigroup , and let be tuples in a direct power . The subpower membership problem (SMP) for asks whether can be generated by . For certain semigroups we will show that SMP() is NP-hard by reducing the Boolean satisfiability problem (SAT) to SMP(). Subpower Membership Problem for semigroups, Part 1
Sep. 29, 2015 1pm (Math350)	Sebastian Casalaina-Martin Complex geometry overview, part 1 of 3
Sep. 29, 2015 2pm (MATH 350)	Lie Theory Joseph Timmer (CU) X With a group factorization of a finite group and a field one may construct the bismash product Hopf algebra . The connections between the representations of and have many similar qualities, especially when one looks at the Frobenius-Schur indicator. In this talk, we will review (almost) all the background necessary for understanding the constructions of these Hopf algebras in question, the concept of Indicators and also consider the case of factorizing the symmetric group . Group Factorizations and Hopf Algebras
Sep. 29, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Sep. 29, 2015 3pm (Math 350)	Alexander Nita (CU Boulder) Fedosov's Deformation Quantization (Part II)
Sep. 30, 2015 4pm (MATH 350)	Grad Student Seminar Jae Min Lee (CU-Boulder) X The Calculus of Variations is one of the classical branches of mathematics, which concerns with maximizing or minimizing a functional. We will start with the isoperimetric problem, which is one of the oldest problems in mathematics. Then we will formulate a general minimization problem and a direct method to solve the problem. After introducing the Sobolev Space and some Functional Analysis, we will prove the existence and uniqueness of the Dirichlet problem. If time permits, we will discuss the regularity of the solution. An Introduction to the Calculus of Variations

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