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Events for November 2015 – March 2016

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Nov. 03, 2015 10am (Math350)	Sarah Salmon (Colorado) X TBD A slow introduction to the Temperley--Lieb diagram algebra
Nov. 03, 2015 1pm (MATH 220)	Grad Algebra/Logic Ross Willard (University of Waterloo) X In congruence modular varieties, subdirectly irreducible algebras with abelian monolith are conveniently classified into `similarity' classes. For each class there is a unique simple module which can, in a certain sense, be identified with each monolith block of each member of the class. All of this has been known since the 1980s. In this lecture I will summarize part of this theory. Similarity and coordinatization in congruence modular varieties Sponsored by the Meyer Fund
Nov. 03, 2015 2pm (MATH 350)	Lie Theory Ed Green (Virginia Tech) X I will present a brief introduction to the theory of quivers, path algebras and theirquotients. The talk is designed for anyone having had a course in graduatealgebra. I will survey the basic theorems and ideas underlying current research in the representation theory of finite dimensional algebras. My next talk willdescribe some of my current research. An Introduction to the Representation Theory of Quivers with Relations
Nov. 03, 2015 2pm (MATH 220)	Ross Willard (University of Waterloo) X Dalmau’s algorithm solving CSPs over templates with a Maltsev polymorphism (generalized to templates with a cube polymorphism) is both beautiful (because it works) and terrible (because it cannot be further generalized). My current work aims to discover a new, radically different algorithm for CSPs over templates with a Maltsev polymorphism. So far all I’ve discovered is obstacles. In this lecture I will describe one intriguing obstacle which (I hope) coordinatization will resolve. Coordinatization in constraint networks over Maltsev templates Sponsored by the Meyer Fund
Nov. 03, 2015 3pm (Math 350)	Jordan Watts (CU Boulder) X Given a mechanical system, a technique often used to simplify calculations is to reduce the number of degrees of freedom of the system by removing symmetry, thereby creating a new system with lower dimension. More geometrically, given a Lie group and a Poisson manifold on which acts properly and via Poisson diffeomorphisms, the orbit space inherits a natural Poisson structure. We will prove this, and also see how the natural stratification of by orbit-type descends to the natural stratification of , but as a Poisson stratification; that is, the strata are Poisson submanifolds. This is not immediately obvious, since the strata upstairs on generally are not Poisson submanifolds. Poisson Reduction
Nov. 04, 2015 4pm (MATH 350)	Grad Student Seminar Leo Herr (CU-Boulder) X A primer. Spec, Sheaves, and Bezout
Nov. 10, 2015 10am (Math350)	Erica Shannon (Colorado) X TBD Heaps
Nov. 10, 2015 1pm (MATH 220)	Grad Algebra/Logic Jakub Bulin (CU Boulder) The Bounded Width Theorem, Part 1
Nov. 10, 2015 2pm (MATH 350)	Lie Theory Ed Green (Virginia Tech) X Brauer tress were introduced in 1970s in the study of finite group rings over fields of characteristic p. In the 1980s they were generalized to Brauer graphs. Brauer graph algebras are biserial and tame (terms I will define in my talk). Together with Sybille Schroll of Univ. of Leicester, England, we have been able to generalize such algebras to Brauer configuration algebras, which are mostly wild. I will describe these symmetric algebras and their relationship to multiserial algebras and some properties of their modules. Brauer configuration algebras
Nov. 10, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Nov. 10, 2015 3pm (Math 350)	Jordan Watts (CU Boulder) X We will continue last week's discussion, beginning by developing the language of vector fields on subcartesian spaces. Using this language, we will outline the proof that the orbit-type stratification on the orbit space coming from a Lie group action that is proper and Poisson is in fact a Poisson stratification; that is, the strata are Poisson submanifolds. We then specialise to the case of a Hamiltonian group action, and define symplectic reduction. Here, the symplectic quotient is a quotient space of a level set of the momentum map. We will show that in this case, the orbit-type stratification on the symplectic quotient is a symplectic stratification; that is, the strata are symplectic submanifolds. Symplectic Reduction
Nov. 11, 2015 4pm (MATH 350)	Grad Student Seminar Paul Lessard (CU-Boulder) X Assuming nothing, we'll use our intuition about functions from calculus to motivate a notion of looking at the behavior of functions close to a point sufficiently broad to discover algebraic topology where we hoped to, but dared not presume to find it. From Taylor Series to Etale Morphisms
Nov. 17, 2015 10am (Math350)	Jonathan Lamar (Colorado) X Combinatorial Hopf algebras (CHAs) are part of a nascent field, and as such have no accepted definition; rather several attempts to classify a growing set of algebras that we all agree to be examples of CHAs. In this talk, I will "define" a CHA and provide a few examples, including my favorite object in all of mathematics. If I manage to get through that in less than 50 minutes, then I will talk about recent work (Pang et al, 2014ff) using bases of CHAs as the state spaces of random walks with the increment distribution induced by the Hopf-square. In particular, this approach admits analysis of the Gilbert--Shannon--Reeds model of riffle shuffling by Hopf-algebraic techniques. Combinatorial Hopf Algebras (and Markov chains)
Nov. 17, 2015 11am (MATH 350)	Number Theory Hao Chen (University of Washington) X We start by defining fully homomorphic encryption and the Ring Learning-With-Errors (RLWE) problem. Then we introduce an attack to RLWE based on the chi-square statistical test, and give examples of Galois RLWE instances vulnerable to our attack. We prove a search-to-decision reduction for Galois fields with unramified modulus. Also, we analyze the vulnerability of cyclotomic fields to our attack, and show that they are safe in general, except when the modulus is totally ramified. We will use algebraic number theory and Fourier analysis on finite fields. In particular, no cryptographic background is necessary for the talk. Attacks on Search-RLWE
Nov. 17, 2015 1pm (MATH 220)	Grad Algebra/Logic Jakub Bulin (CU Boulder) The Bounded Width Theorem, Part 2
Nov. 17, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Nov. 17, 2015 3pm (Math 350)	Jordan Watts (CU Boulder) X This week, we look at a different problem on orbit spaces of proper Lie group actions, as well as symplectic quotients. We first recall two facts: 1) If a proper action is free, the de Rham complex on the orbit space matches the de Rham complex of basic forms upstairs on the original manifold. 2) It is a result of Koszul and Palais that even in the non-free case, the singular cohomology of the orbit space matches the cohomology of the basic forms upstairs. Question: is there a de Rham complex of differential forms on the orbit space in the non-free case that yields a cohomology matching the singular cohomology? (The orbit space is not a manifold, typically.) The answer is yes, but we will not use the language of Sikorski differential spaces to answer this question (for which the answer seems to be false). Instead, we will introduce a "dual" smooth structure called diffeology, give an idea of the proof, and then consider a similar question for the symplectic quotient. The de Rham Complex on Orbit Spaces and Symplectic Quotients
Nov. 30, 2015 3pm (Math 350)	Functional Analysis Piotr Hajac (IMPAN) X For any finite-dimensional representation V of a compact quantum group acting freely on a unital C-algebra A, we can form an associated finitely-generated projective module A_V over the fixed-point subalgebra B of this action. The module A_V is the section module of the associated noncommutative vector bundle. Given an equvariant C-homomorphism f from A to A', we get an induced K-theory map f* from K_0(B) to K_0(B'), where B' is the fixed-point subalgebra of A'. Using Chern-Galois theory or applying coflatness and faithful-flatness arguments, we show that f([A_V])=[A'_V]. This result allows us to move index pairing calculations from K_0(B) to K_0(B'). As an application, we show that any finite equivariant join SUq(2)...*SUq(2) is not trivializable as an SUq(2)compact quantum principal bundle. (Based on joint work with Tomasz Maszczyk.) THE EQUIVARIANT-PULLBACK INVARIANCE OF ASSOCIATING NONCOMMUTATIVE VECTOR BUNDLES Sponsored by the Meyer Fund
Dec. 01, 2015 10am (Math 350)	Jonathan Lamar (Colorado) X The set of all supercharacter theories of a finite group has a natural partial order, under which it forms a lattice. I will talk about some of the interactions between the algebra of the group and the combinatorics of the lattice. The Lattice of all Supercharacter Theories
Dec. 01, 2015 11am (Math 350)	Functional Analysis Palle Jorgensen (University of Iowa) X The talk will have two sides, one tilted towards applications, and the other representation theory. The applications are from symbolic dynamics, fractals, and computational harmonic analysis, e.g., discrete wavelet algorithms; both standard wavelets and wavelets on fractals. The representation theory part: The representations considered in the talk are representations of classes of certain non-abelian algebras (one in particular, the Cuntz algebra); and families of associated unitary representations of groups. We will show that a number of questions which arise naturally from the point of representation theory (equivalence classes of irreducibles, restriction, induction, decompositions etc) are at the same time key to solving questions in the applied areas mentioned. Atomic and non-atomic representations: algebras in analysis and in symbolic dynamics Sponsored by the Meyer Fund
Dec. 01, 2015 1pm (MATH 220)	Grad Algebra/Logic Jakub Bulin (CU Boulder) The Bounded Width Theorem, Part 3
Dec. 01, 2015 2pm (MATH 220)	Peter Mayr (CU) Generation and residual finiteness in products
Dec. 01, 2015 3pm (Math 350)	Algebraic Geometry Mattia Talpo (UBC) X I will talk about a comparison result between two objects that one can associate to a fine saturated log scheme over the complex numbers, namely the Kato-Nakayama space and the infinite root stack (joint work with D. Carchedi, S. Scherotzke and N. Sibilla). I will start by giving an introduction to log geometry through motivations and examples, then I will briefly introduce these two objects, that are different incarnations of the "log part" of the geometry of a log scheme. Towards the end I will state our result, and (time permitting) give an idea of what it boils down to. Kato-Nakayama spaces vs infinite root stacks Sponsored by the Meyer Fund
Dec. 02, 2015 12:10pm (MATH …	Kempner Palle Jorgensen (University of Iowa) X It has been known for some time that complex Hadamard matrices are important in quantum physics, where they appear as a recurrent theme in diverse contexts; especially in measurements, and in uncertainty-considerations. In fractal analysis, seemingly unrelated to quantum physics, complex Hadamard matrices appear as follows: For every complex Hadamard matrix there are associated (typically) singular probability measures \mu , with self-similarities dictated by the complex Hadamard matrix. The family of measures \mu has a dual pair of symmetries in time-frequency, also dictated by the given complex Hadamard matrix. The study of spectral duality for singular measures started with a joint paper [JoPe98] between a former student of mine S. Pedersen and myself. When the specified complex Hadamard matrix further satisfies an additional symmetry; then the L^2 space of \mu will have an orthogonal Fourier basis; in other words we get an associated fractal Fourier transform; a fact that surprised classical harmonic analysts at the time. In order to appreciate the nature of the spectral duality, [JoPe98] showed that spectral duality holds for the middle-1/4 Cantor measure, but not for the middle-1/3 cousin. Typically the distribution of the associated Fourier frequencies satisfies very definite lacunar properties, in the form of geometric almost gaps; the size of the gaps grows exponentially, with sparsity between partitions. Folks in harmonic analysis have fun with them; for example R. Strichartz showed (shortly after [JoPe98] ) that these lacunar Fourier series has better convergence properties than the classical counterparts; one reason is that they are better localized. Fractal Fourier analysis
Dec. 04, 2015 3pm (ECCR 245)	Kempner Paul Constantine (Colorado School of Mines) X Scientists and engineers use computer simulations to study relationships between a physical model's input parameters and its outputs. However, thorough parameter studies---e.g., constructing response surfaces, optimizing, or averaging---are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are a set of dimension reduction tools that identify important directions in the parameter space. I will describe methods for discovering a model's active subspace and propose strategies for exploiting the reduced dimension to enable otherwise infeasible parameter studies. For more info, see www.activesubspaces.org Active subspaces: Emerging ideas for dimension reduction in parameter studies
Dec. 08, 2015 12:10pm (MATH …	Kempner Hoi Nguyen (Ohio State University and IAS) X I will survey recent characterization results on inhomogeneous random walks which stick to a small region unusually long. In applications, among other things we demonstrate a repulsion behavior of the eigenvalues of random Wigner matrices of general type. Anti concentration of random walks and eigenvalue repulsion of random matrices
Dec. 08, 2015 1pm (MATH 220)	Grad Algebra/Logic Andrew Moorhead (CU Boulder) X Abstract: This is an appendix to previous seminar talks on the bounded width theorem, but is of independent interest. The absorption theorem classifies those finite algebras which we can expect to have a so called 'linked' subdirect product that is not the full product, when working in an idempotent, locally finite Taylor variety. The Absorption Theorem
Dec. 08, 2015 2pm (MATH 220)	Steve Weinell (CU) Embeddings, Quantifier Elimination and Elementary Embeddings
Dec. 09, 2015 12am (Math245)	Jeff Taylor Test - Please ignore!
Dec. 11, 2015 4pm (ECCR 150)	Kempner Matthew Kahle (Ohio State University) X Hard spheres are routinely studied as model particles in statistical mechanics. However, the underlying phase space or energy landscape seems to not be very well understood, even for systems of a small number of particles. On the other hand, understanding the topology and geometry of such spaces, including basic questions such as connectivity, is of intrinsic interest in mathematics and physics. I will report on some recent progress in understanding topology of such spaces, both theoretically and computationally. The talk will survey work from a few papers, including joint work with several people: Yuliy Baryshnikov, Peter Bubenik, Gunnar Carlsson, Jackson Gorham, Robert MacPherson, and Jeremy Mason. Topology of configuration spaces of hard spheres
Jan. 12, 2016 11am (MATH 350)	Number Theory Chong Gyu (Joey) Lee (University of Illinois at Chicago) X Dyamical systems defined by self maps commuting each other are closely related. In othe owrds, maps defining dynamical system with some specific property should have strict condition. For example, we only have three kinds of polynomials commtuning each others; power maps, Chebychev polynomials and iterates of the same polynomial. In this talk, we examine properties of dynamical systems defined by commuting maps and conclude that the number of commuting endomorphisms of bounded degree is finite. It is a joint work with Hexi Ye. Finiteness of commuting maps of bounded degree
Jan. 12, 2016 12:10pm (MATH …	Kempner Erica Flapan (Pomona College) X Chemists have defined the point group of a molecule as the group of rigid symmetries of its molecular graph in R^3. While this group is useful for analyzing the symmetries of rigid molecules, it does not include all of the symmetries of molecules which are flexible or can rotate around one or more bonds. To study the symmetries of such molecules, we define the topological symmetry group of a graph embedded in R^3 to be the subgroup of the automorphism group of the abstract graph that is induced by homeomorphisms of R^3. This group gives us a way to understand not only the symmetries of non-rigid molecular graphs, but the symmetries of any graph embedded in R^3. The study of such symmetries is a natural extension of the study of symmetries of knots. In this talk we will present a survey of results about the topological symmetry group and how it can play a role in analyzing the symmetries of non-rigid molecules. Topological symmetry groups
Jan. 14, 2016 3pm (MATH 350)	Probability Nikolai Krylov (University of Minnesota) X I will describe the history of constructing diffusion processes related to partial differential operators starting from oprators with H\"older continuous coefficients and ending with operators with VMO coefficients and partly VMO coefficients. At least one open problem will be stated. Some old and relatively new results on diffusion processes and their connection to PDEs
Jan. 19, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The ultimate generalization of Gaussian elimination to solve CSPs, Part 1
Jan. 19, 2016 2pm (MATH 220)	Peter Mayr (CU) Finitely generated varieties 1
Jan. 19, 2016 4pm (Math 220)	Ryan Rosenbaum (CU Boulder) X We will define the ring of symmetric functions, Symm, in a few useful ways, and investigate its algebraic structure. We will also introduce some important bases for Symm. Introduction to Symm
Jan. 26, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Algebras with few subpowers, Part 1
Jan. 26, 2016 2pm (MATH 220)	Peter Mayr (CU) Finitely generated varieties 2
Jan. 26, 2016 4pm (Math 220)	Jonathan Lamar (CU Boulder) X I will pick up where Ryan left off last week and define the Schur function basis of the Hopf algebra of symmetric functions (Sym). I will also discuss the representation-theoretic interpretation of Sym and how its concrete construction can be used for computations in the representation theory of symmetric groups. Schur functions, their structure coefficients, and the symmetric groups
Feb. 02, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Algebras with few subpowers, Part 2 --- cancelled due to snow
Feb. 02, 2016 1pm (Math 350)	Functional Analysis Organizational Meeting (University of Colorado) X We will have an organizational meeting for this seminar on Tuesday, Feb. 2 at 1 p.m. in Math 350. All are welcome!! Organizational Meeting Sponsored by the Meyer Fund
Feb. 02, 2016 2pm (MATH 220)	Peter Mayr Finitely generated varieties 3 -- canceled due to snow!
Feb. 03, 2016 10am (MATH 350…	Lauren Grimley (Texas A&M) X Hochschild cohomology of an associative algebra has a graded ring structure and a compatible graded Lie algebra structure, making it a Gerstenhaber algebra. The structures on Hochschild cohomology reveal information about the algebra and its deformations. One class of algebras with interesting Hochschild cohomology is quantum complete intersections which are a non-commutative analog of truncated polynomial rings. The behavior of Hochschild cohomology of this class of algebras has been shown to vary greatly based on the choice of quantum coefficients, exhibiting behaviors unseen with commutative algebras. In this talk, we explore the behavior of Hochschild cohomology of group extensions of quantum complete intersections. Hochschild cohomology of group extensions of quantum complete intersections Sponsored by the Meyer Fund
Feb. 03, 2016 11am (MATH 350…	Timo de Wolff (Texas A&M) X Deciding nonnegativity of real polynomials is a key question in real algebraic geometry with crucial importance in polynomial optimization. Since this problem is NP-hard, one is interested in finding sufficient conditions (certificates) for nonnegativity, which are easier to check. Since the 19th century the standard certificates are sums of squares (SOS); see particularly Hilbert's 17th problem. In this talk we introduce polynomials supported on circuits. For this class, nonnegativity is characterized by an invariant, which can be derived immediately from the initial polynomial. In consequence, we obtain an entirely new class of nonnegativity certificates, which are independent of SOS certificates. Our certificates crucially extend geometric programming approaches for the computation of lower bounds in polynomial optimization. Particularly, for polynomials with simplex Newton polytope our approach is significantly faster and often yields better than bounds than semidefinite programming, which is the standard method for polynomial optimization. These results generalize earlier works by Fidalgo, Ghasemi, Kovacec, Marshall, and Reznick. The talk is based on joint work with Sadik Iliman. New Certificates for Nonnegativity via Circuit Polynomials and Geometric Programming Sponsored by the Meyer Fund
Feb. 09, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Algebras with few subpowers, Part 2
Feb. 09, 2016 1pm (Math 350)	Functional Analysis Konrad Aguilar (University of Denver) X AF algebras are inductive limits of finite-dimensional C*-algebras. We will present that certain classes of unital AF algebras can be described as metric limits with respect to the quantum propinquity metric. To achieve this, we provide a quasi-Leibniz quantum compact metric space structure for unital AF algebras with faithful tracial state. With this structure available, we show that certain classes of AF algebras form continuous images of maps from suitable metric spaces to the topology induced by the quantum propinquity metric. These classes include UHF algebras, Effros-Shen AF algebras, and the Cantor AF algebra. Joint work with Dr. Frederic Latremoliere. Quantum propinquity convergence of AF algebras Sponsored by the Meyer Fund
Feb. 09, 2016 2pm (MATH 220)	Peter Mayr (CU) Finitely generated varieties 3
Feb. 09, 2016 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X Combinatorial representation theory seeks to associate the representations of groups and algebras to combinatorial gadgets. For many groups, we know how to find combinatorics in dimensions of irreducible modules, index sets, and branching rules. However, a seemingly far more difficult problem seeks to construct an explicit basis for the irreducible modules that have nice formulas for the action of the group. This talk gives an overview of approaches, some examples of success, and some long-standing mysteries. Combinatorial module constructions
Feb. 09, 2016 3pm (Math 350)	Markus Pflaum (CU Boulder) Introduction to Stratified Spaces
Feb. 09, 2016 4pm (Math 220)	Jonathan Lamar (CU Boulder) X I will define a polynomial representation of GL(n,C) and show that there is an equivalence of categories between polynomial representations of GL(n,C) and finite-dimensional representations of the Symmetric group on n letters. Polynomial Representations of GL(n,C)
Feb. 10, 2016 4pm (MATH 350)	Grad Student Seminar Noah Williams X Traditional classroom formats, dominated by lecture and at the whims of content-cramming tempos, often stifle what we love most about mathematics and the skills mathematicians value. On the other hand, Inquiry-Based Learning (IBL) approaches introduce mathematics to students as a living, breathing organism, where success is measured by struggle, creativity, and hard work. Teachers and students act as facilitators and apprentices rather than dispensers and consumers, and in-class activities are student-centered, involving group-work and presentations. In this interactive session, we'll discuss IBL, and I'll share my experience from the IBL workshop I attended last summer. Participants will leave with a basic understanding of IBL and some ideas for implementing IBL practices in their classrooms. How do IBLong? An introduction to teaching mathematics with IBL methods
Feb. 16, 2016 12:10pm (MATH …	Kempner Patricio Gallardo (University of Georgia) X We will describe new and old ways to understand the moduli space of points and lines in the plane. Depending on our choice of the allowed degenerations, we can obtain a moduli space that is arbitrarily singular or a configuration space that is smooth with well behaved boundary. For the most part, this talk will be expository, though if time allows we will describe a connection to my recent work with Noah Giansiracusa and Kenny Ascher. Point and line to plane
Feb. 16, 2016 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The ultimate generalization of Gaussian elimination to solve CSPs, Part 2
Feb. 16, 2016 2pm (MATH 350)	Lie Theory Shawn Burkett (CU) X Under certain conditions, the action of a finite group on a finite group induces an action of on the set of supercharacter theories of . In particular, this is possible when acts via automorphisms. The two trivial supercharacter theories must be fixed under these actions, but it is not so clear if any other fixed points exist. In this talk, such actions will be discussed, with particular focus on determining groups in which no nontrivial supercharacter theories of are fixed by and those in which all supercharacter theories are fixed by . Actions on the set of supercharacter theories of a finite group
Feb. 16, 2016 3pm (Math 350)	Algebraic Geometry Patricio Gallardo (UGA) X TBA TBA Sponsored by the Meyer Fund
Feb. 16, 2016 4pm (Math 220)	Megan Ly (CU Boulder) X I will introduce classical Schur-Weyl duality and discuss other situations where Schur-Weyl duality arises. Schur-Weyl duality
Feb. 17, 2016 4pm (MATH 350)	Grad Student Seminar Sebastian Bozlee X A Galois connection is a relationship between posets following the same pattern as that between fixed fields and Galois groups in Galois theory. This talk will be an introduction to Galois connections via examples you've probably seen before, but didn't realize were Galois connections. Missed Connections
Feb. 23, 2016 1pm (Math 350)	Functional Analysis Sooran Kang (University of Colorado, Boulder) X Quantum Heisenberg manifolds (QHMs) are noncommutative manifolds constructed by Marc Rieffel as a strict deformation quantization of Heisenberg manifolds (in the direction of the Poisson bracket). They are the fibers of a continuous field of noncommutative -algebras , where are parameters of the Poisson bracket, is a positive integer and is the deformation parameter. The QHM is in fact a generalized fixed point algebra of a certain crossed product -algebra by construction and it can be also realized as a crossed product by a Hilbert -bimodule, Cuntz-Pimsner algebra and twisted groupoid -algebra. The goal of this series of lectures is to introduce various types of -algebras and to discuss the structure of the QHM in some details. In the first lecture, we briefly discuss the history and the motivation of deformation quantization, and introduce the QHMs as a strict deformation quantization of Heisenberg manifolds. Quantum Heisenberg Manifolds
Feb. 23, 2016 1pm (MATH 220)	Grad Algebra/Logic Julie Linman (CU Boulder) Minimal functions on the random permutation, Part 1
Feb. 23, 2016 2pm (MATH 350)	Lie Theory Erica Shannon (CU) Some stuff about invariant forms
Feb. 23, 2016 3pm (Math 350)	Markus Pflaum (CU Boulder) Introduction to Stratified Spaces (Part II)
Feb. 23, 2016 4pm (Math 220)	Megan Ly (CU Boulder) X We will explore the rich combinatorial structure based on set partitions that arises from the supercharacter theory of unipotent upper triangular matrix groups. Supercharacters and Set Partition Combinatorics
Feb. 24, 2016 4pm (MATH 350)	Grad Student Seminar Robert Hines X Have any of your students approached you and said something to the effect of, "I saw this guy on youtube say 1+2+3+4+...=-1/12..."? Perhaps this talk will prepare you for the next time (no guarantees). The plan is to present one or two proofs of the functional equation relating \zeta(s) and \zeta(1-s). As a byproduct, we obtain special values of the zeta function, including \zeta(-1)=-1/12. We'll start with the definition of the zeta function (and a word or two about why it's interesting), the concept of analytic continuation, and (time permitting) we'll touch upon the gamma function, Poisson summation, theta functions, crazy contour integrals, Bernoulli numbers, and so on. Some knowledge of complex analysis is presupposed. The functional equation of the Riemann zeta function
Feb. 25, 2016 12:10pm (MATH …	Kempner Antoine Julien (Norwegian University of Science and Technology) X In this talk, my goal is to give an introduction to some of the mathematics behind quasicrystals. Quasicrystals were discovered in 1982, when Dan Schechtmann observed a material which produced a diffraction pattern made of sharp peaks, but with a 10-fold rotational symmetry. This indicated that the material was highly ordered, but the atoms were nevertheless arranged in a non-periodic way. These quasicrystals can be modeled by certain aperiodic tilings, amongst which the famous Penrose tiling. What makes aperiodic tilings so interesting--besides their aesthetic appeal--is that they can be studied using tools from many areas of mathematics: combinatorics, topology, dynamics, operator algebras... While the study of tilings borrows from various areas of mathematics, it doesn't go just one way: tiling techniques were used by Giordano, Matui, Putnam and Skau to prove a purely dynamical statement: any Z^d free minimal action on a Cantor set is orbit equivalent to an action of Z. Quasiperiodic tilings and orbit equivalence of dynamical systems
Mar. 01, 2016 11am (MATH 350)	Number Theory Anna Haensch (Duquesne University) X There is a well known correspondence between lattices and codes via the classical “construction A.” With this, the weight enumerator for codes corresponds to the theta series for lattices, where one counts the number of codewords by composition, and the other counts the number of vectors in a lattice of a certain length. In this talk, we will explore how some of the attendant machinery of theta series are born out in this correspondence. In particular, we will consider the Kneser-Hecke operator, a code theoretic analogue of the classical Hecke operator. Kneser-Hecke operators for codes over finite chain rings
Mar. 01, 2016 1pm (MATH 220)	Grad Algebra/Logic Julie Linman (CU Boulder) Minimal functions on the random permutation, Part 2
Mar. 01, 2016 2pm (MATH 350)	Lie Theory Jay Taylor (University of Padova) X The classical groups , , , have long been of interest in group theory; often because of their close relationship to finite simple groups. These groups are all examples of finite reductive groups. Such a group is obtained as the fixed point subgroup of a connected reductive algebraic group under a Frobenius endomorphism . Assuming the characteristic of the field defining is not too small (greater than 5 suffices) then Kawanaka has defined a family of complex representations of the finite group called Generalised Gelfand—Graev Representations (GGGRs). Using these representations Kawanaka conjectured that one could associate to every irreducible character of a well-defined -stable unipotent conjugacy class of which he called the wave front set. Under certain assumptions on the underlying characteristic Lusztig proved Kawanaka’s conjecture, asserting the existence of the wave front set. In this talk we will give an introduction to these ideas an present our result that Kawanaka’s conjecture holds whenever the GGGRs are defined. Generalised Gelfand—Graev Representations and Wave Front Sets Sponsored by the Meyer Fund
Mar. 01, 2016 3pm (** Math 2…	Jordan Watts (CU Boulder) X A famous question of Dusa McDuff, often referred to as the "McDuff Conjecture", is whether there exists a non-Hamiltonian symplectic circle action with isolated fixed points on a compact symplectic manifold. Susan Tolman recently answered this question in the affirmative, constructing a -dimensional such space with exactly fixed points. A crucial ingredient to this construction involves Hamiltonian circle actions on complex manifolds and orbifolds in which the interaction between the complex structure and the symplectic form is fairly weak. Specifically, versions of Sjamaar's holomorphic slice theorem, the birational equivalence theorem of Guillemin and Sternberg, as well as reduction, cutting, and blow-up (all of which work in the Kaehler world) are required in this weaker setting. All of these theorems and constructions are extended to this weaker setting in joint work by Tolman and myself. In particular, by weak, we mean that if is the vector field induced by the circle action, the symplectic form, and the complex structure, then on the complement of the fixed point set. This condition is sufficient for all of the theorems and constructions above except for the blow-up (which also requires tameness at the point to be blown-up). In this talk, I will focus on the holomorphic slice theorem about a fixed point, reduction, and (time-permitting) the birational equivalence theorem proven in the joint paper. Tame Circle Actions
Mar. 08, 2016 11am (MATH 350)	Number Theory Joseph H. Silverman (Brown University) X A divisibilty sequence is a sequence of integers W_1,W_2,... with the property that if m divides n, then W_m divides W_n. Classical divisibility sequences include a^n-b^n, Fibonacci and Lucas sequences, and elliptic divisibility sequences. These tend to grow rapidly, and their behavior modulo p is quite interesting. After surveying these sequences, I will move on to higher dimensional analogues such as gcd(a^n-1,b^n-1), which tend to grow slowly, and faster growing Divisor Divisibility Sequences that Katherine Stange, Patrick Ingram, and I have recently been studying. Despite their elementary-seeming nature, divisibility sequences arise in many areas of mathematics due to their intrinsic definition in terms of arithmetic intersections on arithmetic groups. Along the way I will describe many open questions whose easy statements belie their depth. Divisibility Sequences
Mar. 08, 2016 12:10pm (MATH …	Kempner Paul Horn (University of Denver) X Graphs are a mathematical abstraction of networks, which on their most basic level capture objects and their relationships. Although graphs are discrete objects, there turns out to be many striking analogies between them and Riemannian manifolds. Most famous of these are the relationships between the spectra of the Laplace operator on graphs and the spectra of the Laplace-Beltrami operator on a manifold. Recent work, however, has attempted to bring other ideas from the world of geometry into the graph setting – notably by trying to introduce notions of curvature on graphs. In this talk, I will describe some of my work in this area and how it reflects a rich interplay between the local structure of a graph, the behavior of random walks on graphs, and more global geometric properties of a graph. The Geometry of Graphs
Mar. 08, 2016 1pm (MATH 220)	Grad Algebra/Logic Andrew Maurer (University of Georgia) X Lie superalgebras can be defined abstractly as an associative ZZ/(2)-graded algebra with the usual commutator operation. It turns out the bracket structure respects the grading. When studying the representation theory of Lie superalgebras, we may use the tools provided by support varieties. This involves taking Spec of the cohomology ring modulo its nilradical. As in the theory of Lie algebras, our study begins with complex Lie superalgebras. Quickly, we encounter a problem in that the cohomology ring is finite dimensional as a complex vector space, and thus support varieties are points. This may be remedied by using Hochschild's relative cohomology, which have much more interesting, and much more elusive, support varieties. In this talk I will speak about some results concerning so-called classical Lie superalgebras, with particular emphasis on cohomology relative to its even Lie subsuperalgebra. (Relative) Cohomology and Support Varieties and Lie Superalgebras
Mar. 08, 2016 2pm (MATH 350)	Lie Theory Marcelo Aguiar (Cornell) X Consider an arrangement of linear hyperplanes integral with respect to a given lattice. The lattice gives rise to a torus and the arrangement to a subdivision of the torus. We are interested in the combinatorics of this subdivision. We will describe questions and results for particular lattices associated to root systems and arrangements associated to graphs. This is joint work in progress with Swee Hong Chan. Integral hyperplane arrangements Sponsored by the Meyer Fund
Mar. 08, 2016 4pm (Math 220)	Shawn Burkett (CU Boulder) X A central idea in group theory is to study a group by studying homomorphic images into families of groups in which a lot of information is already known. For example, given a group action, one gets a homomorphism of the acting group into the symmetric group on the elements of the set being acted on. The permutation representation so acquired may contain significant information about the acting group. Extending this idea, if a group G acts on a k-vector space V, one gets a homomorphism of G into GL(V), called a linear representation. That is, each element of G acts as an invertible linear transformation on V. Linear transformations have many invariants, one being the trace. If we compose the linear representation with the trace map, one obtains a map from G to k, called a k-character. In this talk, we will discuss the basics of linear representation theory and character theory in great detail, providing all necessary information to introduce supercharacter theories of finite groups. Character Theory of Finite Groups
Mar. 09, 2016 3pm (Math 350)	João Nuno Mestre (Utrecht University) X We explain how an extension of Haefliger's approach to transverse measures for foliations allows us to define and study measures and geometric measures (densities) on differentiable stacks. The abstract theory works for any differentiable stack, but it becomes very concrete for proper stacks - for example, when computing the volume associated with a density, we recover the explicit formulas that are taken as definition by Weinstein. This talk is based on joint work with Marius Crainic. Measures and densities on differentiable stacks Sponsored by the Meyer Fund
Mar. 09, 2016 4:15pm (MATH 3…	Grad Student Seminar Natalie Coston X The fifteen puzzle consists of a 4x4 puzzle board grid on which there are 15 tiles and one blank. The goal of the puzzle it to slide the tiles around until the numbers appearing on the board are ordered 1 to 15. If we started with an ordered board and were mixing the tiles back up to give to a friend, as curious mathematicians we might wonder "How do I know if my board is really mixed?" or, "How long should I mix these tiles?" In this talk, which is based off the paper "The Mixing Time of the Fifteen Puzzle" by Morris and Raymer, I will introduce Markov Chains and demonstrate how they can be used to bound the time it takes to mix the 15 puzzle. The Math Behind the Mixing of the 15 Puzzle
Mar. 10, 2016 3pm (Weber 201…	Algebraic Geometry Joe Silverman (Brown) X TBA TBA
Mar. 11, 2016 4pm (MATH 350)	Grad Student Seminar Sarah Salmon X This atypical time for Slow Pitch is part of Welcome Weekend! Come learn some neat stuff and meet some prospective students. We will explore some connections between simple graphs and polynomial rings. Generally speaking, finding monomial prime decompositions of ideals or minimal generating sets of ideals in polynomial rings can be rather unpleasant. If you start with a simple graph, we can construct some interesting ideals using vertices (called the cover ideal) or edges (called the edge ideal). Using properties of the graph, finding minimal generating sets of cover ideals or minimal monomial prime decompositions of the edge ideal is not so bad! The short version: We're going to build some ideals, find some nice generating sets, and draw some pictures (as always)! Simple Graphs and Monomial Ideals: How I Spent Summer 2014
Mar. 15, 2016 1pm (Math 350)	Functional Analysis Sooran Kang (University of Colorado, Boulder) X Abstract: As mentioned in the first lecture, the quantum Heisenberg manifold can be realized as a crossed product by a Hilbert -bimodule which is the special case of Cuntz-Pimsner algebras. In this lecture (and the next lecture), we introduce Cuntz-Pimsnef algebras and crossed products by Hilbert -modules, and discuss how we realize the quantum Heisenberg manifold as those algebras using the classical Picard groups. Cuntz-Pimsner algebras and crossed products by -bimodules. Sponsored by the Meyer Fund
Mar. 15, 2016 1pm (MATH 220)	Grad Algebra/Logic Dmitriy Zhuk (Moscow State Unuversity) X The standard way to parameterize interesting subclasses of the constraint satisfaction problem (CSP) is via finite relational structures. The main problem is to classify those subclasses that are tractable (solvable in polynomial time) and those that are NP-complete. It was conjectured that if a core of a relational structure has a weak near-unanimity polymorphism then the corresponding constraint satisfaction problem is tractable, otherwise it is NP-complete. This conjecture was proved by Andrei Bulatov for 3-element domain, by Petar Markovic for 4-element domain. We present the proof of this conjecture for 5-element domain. Precisely, we prove the remaining part of this conjecture showing that a CSP instance can be solved in polynomial time if the relational structure has a weak near-unanimity polymorphism. The proof of CSP Dichotomy Conjecture for 5-element domain Sponsored by the Meyer Fund
Mar. 15, 2016 2pm (MATH 220)	Dmitriy Zhuk (Moscow State University) X The main problem in clone theory is to get a description of all clones. In 1941 Emil Post obtained an amazing description of all clones on 2 elements, but in 1959 it was proved that there exists a continuum of clones on k elements if k > 2. The first part of my talk is devoted to the efforts to describe uncountable lattices of clones, in particular, I show how uncountable lattice of all clones of self-dual operations on 3 elements can be described. However, obtaining such description for other maximal clones seems to be too cumbersome and complicated. This motivated me to focus on the following questions: how to check properties of a clone and how to find finite sublattices. Despite the fact that clone theory has been studied for many years, we still don't know how to check simple properties of clones. For example we don't know how to check whether a clone defined by a relation is finitely generated, or how to decide how many clones contain a given operation. In the second part of the talk I try to collect such open problems and present some partial results. Open problems in clone theory Sponsored by the Meyer Fund
Mar. 15, 2016 3pm (Math 350)	Christopher Seaton (Rhodes College) X Let be a compact Lie group and a unitary representation of . Treating as a real symplectic manifold and choosing the homogeneous quadratic moment map, we can form the symplectic quotient, the quotient where is the zero fiber of the moment map. The space has a variety of structures, including that of a symplectic stratified space and a semialgabraic set, and its algebra of smooth functions has a graded subalgebra of regular functions defined as a quotient of the real polynomial invariants of the -action on . In this talk, we will discuss the use of the polynomial invariants of the -representation to construct symplectomorphisms and distinguish between symplectic quotients. In particular, we will study the problem of which symplectic quotients are symplectomorphic or diffeomorphic to symplectic orbifolds. We demonstrate that in some cases, has many of the nice properties of a ring of orbifold invariants and describe explicit computations of invariants of . Along the way, we will see some recent results in computational invariant theory that are relevant in other contexts. (Joint work with Joshua Cape, Carla Farsi, Hans-Christian Herbig, Daniel Herden, Ethan Lawler, and Gerald Schwarz) Constructing symplectomorphisms between singular linear symplectic quotients Sponsored by the Meyer Fund
Mar. 15, 2016 4pm (Math 220)	Shawn Burkett (CU Boulder) X Supercharacter theory was originally developed to describe the representation theory of algebra groups, a family of groups in which unimodular groups belong. Essentially, supercharacter theories are certain types of central subalgebras which approximate the usual character theory of a finite group. In this talk, we will introduce supercharacter theories from multiple persepectives and discuss a few ways to use the structure of a given finite group to construct nontrivial supercharacter theories. Time permitting, I will discuss some recent work of myself and Jonathan Lamar (CU Boulder) on induced actions on the set of supercharacter theories of a finite group. Random talk on a supercharacter theory
Mar. 17, 2016 12:10pm (MATH …	Kempner Guoliang Yu (Texas A&M) X I will explain how certain geometric properties of groups can be used to study rigidity and non-rigidity of manifolds. In particular, I will discuss how a certain secondary invariants of elliptic operators can be used to estimate the degree of non-rigidity of manifolds. Parts of the work are joint with Erik Guentner, Romain Tessera, Shmuel Weinberger, and Zhizhang Xie. This talk will be accessible to graduate students. Geometry of groups and rigidity of manifolds
Mar. 17, 2016 3pm (MATH 350)	Probability Asad Lodhia (MIT) X We provide an overview of results on the Central Limit Theorem for Linear Statistics of Eigenvalues. We will discuss how the central limit theorem depends on the scale at which the eigenvalues are analyzed and mention various results. We discuss how universality of the behavior of the Law of Large Numbers (e.g. local semicircle law) relates to universality of the Central Limit Theorem for these statistics. CLTs for Random Matrix Eigenvalues
Mar. 28, 2016 4pm (Math 350)	Functional Analysis Daniel Goncalves (Universidade Federal de Santa Catarina) X In this talk we show how to obtain representations of graph algebras from branching systems and show how these representations connect to the Perron-Frobenius operator from Ergodic Theory. We also describe a sufficient condition that guarantees faithfulness of our representations and show how to use these representations to give a new proof to the converse of the Cuntz-Krieger Uniqueness Theorem for graph algebras (including Leavitt path algebras). Representations of graph algebras via branching systems Sponsored by the Meyer Fund
Mar. 29, 2016 11am (MATH 350)	Number Theory Pedro Berrizbeitia (Ulam Visitor from Universidad Simon Bolivar) X Let an odd prime and a non quadratic residue mod . Let be the ring of integers of . If is coprime to , then has order in the multiplicative group , hence must be congruent mod to (why?). Using properties of the classical biquadratic residue symbol including the Biquadratic Reciprocity Law we present two different methods to compute the sign, which leads to what we call the "Norm Relation Theorem". As an application we prove the following rather curious property of Mersenne primes that we believe had not been noticed: Let be prime. Let be prime (i.e. a Mersenne prime). It is known that has integer solutions . Moreover, is unique with . We prove that !! Examples: ; and ; and The Biquadratic Symbol in . A new property of the Mersenne Primes
Mar. 29, 2016 1:10pm (MATH 3…	Kempner Daniel Goncalves (Universidade Federal de Santa Caterina) X Symbolic dynamics is a fundamental area of dynamical systems, and is typically concerned with a finite alphabet , spaces of infinite sequences or , and subspaces of or which are closed under the shift map (shift spaces). Over the years many approaches have been proposed to generalize shift spaces to the infinite alphabet case, one of the hurdles to overcome is the fact that the countable product of an infinite discrete space is not locally compact. In this talk I will describe a recent approach to infinite shift spaces introduced by Ott, Tomforde and Willis. I intend to show that, while many of the finite alphabet symbolic dynamics results still hold for these infinite alphabet shifts (as for example the connection of conjugacy of edge shifts of graphs with isomorphism of the associated C*-algebras), some surprising results appear (for example there are (M+1)-step shifts not conjugate to an M-step shift). One sided shift spaces over infinite alphabets
Mar. 29, 2016 4pm (Math 220)	Sarah Salmon (CU Boulder) TBD
Mar. 30, 2016 4pm (Math 220)	Functional Analysis Piotr Hajac (IMPAN) X Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum 3-sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces. Then we use this representation of Z/NZ to construct an associated complex line bundle. The main result is the stable non-triviality of these line bundles over any of the quantum lens spaces we consider. We use the pullback structure of the C*-algebra of the lens space to compute its K-theory via the Mayer-Vietoris six-term exact sequence. Then we combine an explicit form of the odd-to-even connecting homomorphism (Milnor idempotent) with Chern-Galois theory (strong connections) to prove the stable non-triviality of the bundles. (Joint work with Adam Rennie and Bartosz Zielinski.) THE K-THEORY OF HEEGAARD QUANTUM LENS SPACES Sponsored by the Meyer Fund
CANCELED Mar. 31, 2016	Probability Hakima Bessaih (University of Wyoming at Laramie) X We study Brinkman's equations with microscale properties that ar ehighly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by an SDE. Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic. We use the asymptotic properties of the SDE and the periodicity of the Brinkman's coefficient in the space variable to prove the convergence result. The SDE has a unique invariant measure that is ergodic and strongly mixing. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics) and also by averaging the Brinkman's coefficient with respect to the space variable. Our results can be extended to more general nonlinear diffusion equations with heterogeneous coefficients. This is a joint work with Yalchin Efendiev and Florian Maris. HOMOGENIZATION OF BRINKMAN FLOWS IN HETEROGENEOUS DYNAMIC MEDIA

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