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Events for September 2015 – January 2016

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Oct. 13, 2015 5pm
Sep. 01, 2015 10am (Math350)	Jonathan Lamar (Colorado) X TBD Intro to algebraic combinatorics: A personal voyage
Sep. 01, 2015 1pm (Math350)	Stephen Preston Riemannian geometry overview, part 1 of 3
Sep. 01, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Algebra and Computation: Some Open Problems
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 (Math350)	Sebastian Casalaina-Martin Complex geometry overview, part 1 of 3
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 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
Oct. 01, 2015 3pm (MATH 350)	Probability Philip Matchett Wood (University of Wisconsin-Madison) X Random noise can be modeled by a non-Hermitian random matrix with iid mean zero variance one entries. When scaled by 1/sqrt(n), the eigenvalues of such a matrix follow the circular law, and when scaled by a smaller function, for example 1/n, the eigenvalues collapse to the origin. This talk will discuss what happens to the eigenvalues of a fixed matrix when you add small noise in the form of an iid matrix scaled by something smaller than 1/sqrt(n). There are interesting cases where the eigenvalue distribution is known to change dramatically when small Gaussian random noise is added, and this talk will focus on what happens when the noise is not Gaussian. The eigenvalues of a fixed matrix plus small random noise
Oct. 06, 2015 10am (Math350)	Megan Ly (Colorado) X Since the irreducible representations of algebra groups are impractical to work with, we define a coarser approximation of the usual character theory known as a supercharacter theory. We then find a nice way to "induce" supercharacters by modifying the definition of induction to the concept of superinduction. Supercharacters and superinduction for algebra groups
Oct. 06, 2015 11am (MATH 350)	Number Theory Chris Hall (University of Wyoming) X Let G be a finite undirected graph and C-->G be a "random cover". One interesting object one can associate to C are the characteristic polynomial of its adjacency matrix. One can ask how it is distributed as C varies in a "nice" family of covers. We'll sharpen this and other variational questions and describe some recent work with D. Puder and W. Sawin. Arithmetic and Graphs
Oct. 06, 2015 1pm (MATH 220)	Grad Algebra/Logic Markus Steindl (Johannes Kepler Universitat Linz) Subpower Membership Problem for semigroups, Part 2
Oct. 06, 2015 1pm (Math350)	Sebastian Casalaina-Martin Complex geometry overview, part 2 of 3
Oct. 06, 2015 2pm (Math 220)	Keith Kearnes (CU) Tame Congruence Theory
Oct. 06, 2015 2pm (MATH 350)	Lie Theory Mandi Schaeffer-Fry (Metro State) X Given a finite group with size n, the Galois group Gal(Q(omega)/Q), where omega is an nth root of unity, acts naturally on the irreducible characters of G. We discuss some parametrizations for characters of groups of Lie type and the problem (and its motivation) of describing this Galois action in terms of these parametrizations. On the Action of Galois Automorphisms on Characters of Groups of Lie Type
Oct. 06, 2015 3pm (Math 350)	Alexander Nita (CU Boulder) Fedesov's Deformation Quantization (Part III)
Oct. 07, 2015 4pm (MATH 350)	Grad Student Seminar Peter Mayr (CU-Boulder) X It is well known that the direct product of two groups is finitely generated if and only if both factors are finitely generated. But is this a result about groups, classical structures with a group operation (e.g., rings, associative algebras,...), semigroups, algebras with neutral element, or true for all algebraic structures? We use universal algebra to investigate this question and corresponding results for finite presentability and residual finiteness of algebras. The Unbearable Lightness of Direct Products
Oct. 08, 2015 3pm (MATH 350)	Probability Ecaterina Sava-Huss (Cornell) X After a short introduction on deterministic random walks (called also rotor walks) and some related cluster growth models, I will introduce a family of stochastic processes on the integers, depending on a parameter p. These processes interpolate between the deterministic rotor walk (for p=0) and the simple random walk (for p=1/2), and they are not Markovian. For such processes, I will prove that the scaling limit is a one-sided perturbed Brownian motion, which is a linear combination of a Brownian motion and its running maximum. Interpolating between rotor walk and random walk
Oct. 13, 2015 10am (Math350)	Fred Goodman (Iowa) X TBD Introduction to Cellular Algebras
Oct. 13, 2015 11am (MATH 350)	Number Theory Lillian Pierce (Duke University) X Fifty years ago Birch proved a landmark result on how many variables are required by the circle method in order to produce an asymptotic for the number of (simultaneous) representations of a fixed tuple of integers by a fixed system of forms of the same degree. While this result has not budged much since, some progress can be made in lowering the number of variables in certain cases. This talk will introduce new work for systems of 2 quadratic forms, joint with Roger Heath-Brown, and for systems of 3 quadratic forms, joint with Damaris Schindler and Melanie Wood, that brings the number of variables down if we relax our requirement to representing “almost every” tuple of integers. The key innovation is a multi-dimensional version of Kloosterman’s circle method, which allows us to harvest more cancellation from exponential sums on the minor arcs. This talk will discuss the advantages and difficulties of obtaining cancellation in oscillatory integrals and exponential sums, and will not assume extensive prior knowledge of the circle method. Integers represented by systems of quadratic forms
Oct. 13, 2015 12:10pm (MATH …	Kempner Lillian Pierce (Duke University) X Each number field (finite extension of the rationals) has an integer associated to it called the class number (the cardinality of the class group of the field). Class numbers are important objects that naturally occur in number theory, but many open questions remain about the growth and divisibility properties of class numbers of fields varying over an appropriate infinite family. We will survey some key conjectures and results since the pioneering work of Gauss, and then turn to new work on averages and moments for p-torsion in class groups of fields of degree 2, 3, 4 and 5. This includes joint work with Ellenberg, Heath-Brown, Thorne, and Wood. This talk will be accessible to a general math audience. Averages and moments associated to class numbers
Oct. 13, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The simplest polynomial time algorithm for CSPs: checking local consistency, Part 2
Oct. 13, 2015 1pm (Math350)	Sebastian Casalaina-Martin Complex geometry overview, part 3 of 3
Oct. 13, 2015 2pm (MATH 350)	Lie Theory Fred Goodman (Iowa) X I will discuss the construction of cellular bases for the Brauer algebras, BMW algebras, etc. which share many properties of the Murphy bases of the Hecke algebras of the symmetric groups. Murphy bases for algebras with a Jones basic construction
Oct. 13, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Oct. 13, 2015 3pm (Math 350)	Jonathan Wise (CU Boulder) X We'll revisit the idea of linear approximation in a way that allows us to talk about first-order approximations of quite general mathematical objects. We'll see in a few examples how first-order deformations can be classified using cohomology. Differentiation and linear approximation
Oct. 14, 2015 4pm (MATH 350)	Grad Student Seminar Taylor "TK" Klotz (CU-Boulder) X One of the snazziest results in differential geometry/topology is the Gauss-Bonnet theorem. In this talk we'll informally discuss all the needed concepts (mostly Gaussian curvature) to present the statement of the theorem and if time permits we'll explore some fun consequences. No differential geometry knowledge needed!....just a bit of calc. 3. Something, something, Gauss-Bonnet theorem?
Oct. 20, 2015 11am (Math 350)	Functional Analysis Jean Renault (University of Orleans, France) X The study of semigroup C-algebras presents new challenges. Among various C-algebras associated to a semigroup, the reduced C-algebra is one of the most tractable. I will show, extending A. Nica's work on quasi-lattice ordered semigroups, how it can be expressed as a groupoid C-algebra. The same techniques can be applied to study C-algebras associated to semigroup actions and to -graphs, where is an arbitrary semigroup. In particular, they give under suitable assumptions the nuclearity of these C-algebras and their ideal structure. Semigroups, inverse semigroups and higher rank graphs Sponsored by the Meyer Fund
Oct. 20, 2015 12:10pm (MATH …	Kempner Jean Renault (Université d'Orléans) X Let be the path space of a Bratteli diagram. The Markov measures are the measures on which are quasi-invariant under the tail equivalence relation and which admit a quasi-product cocycle as Radon-Nikodym derivative. This observation provides a classical identification of the ergodic decomposition of . This will be applied to the study of random walks on groups or on groupoids. This study is a joint ongoing project with T. Giordano. Random walks on Bratteli diagrams
Oct. 20, 2015 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) The simplest polynomial time algorithm for CSPs: checking local consistency, Part 3
Oct. 20, 2015 2pm (MATH 220)	Keith Kearnes (CU) Tame Congruence Theory
Oct. 20, 2015 2pm (MATH 350)	Lie Theory Richard Green (CU) X Generalized nil-Temperley–Lieb algebras are certain associative algebras defined by generators and relations. The defining relations resemble those of the generalized Temperley–Lieb algebras, but with certain products of generators set equal to zero. I will explain how to use the combinatorics of heaps to define representations of the nil versions of the algebras, and describe some of their properties. Representations of generalized nil-Temperley–Lieb algebras
Oct. 20, 2015 3pm (Math 350)	Jonathan Wise (CU Boulder) X We'll study the general problem of classifying all deformations (of arbitrary orders) of a mathematical object by a commutative ring (and maybe also by a differential graded Lie algebra), culminating in the representability theorems of Artin and Schlessinger. Higher order derivatives and representability
Oct. 27, 2015 10am (Math350)	Sarah Salmon (Colorado) X TBD Coxeter Groups
Oct. 27, 2015 1pm (MATH 220)	Grad Algebra/Logic Nik Ruskuc (University of St Andrews) X In an inverse semigroup it is well known that the set of idempotents carries a strong algebraic/order-theoretic structure itself, namely it forms a semilattice. To elucidate the relevant structure for an arbitrary semigroup is harder, and it turns out that the relevant notion is that of a biorder. This in turn gives rise to a free object, namely the free idempotent generated semigroup over a given biorder. Since this object is built on the framework of idempotents, general semigroup theory guarantees that it is replete with subgroups, and it is natural to expect they somehow control the behaviour of the semigroup. In this talk I will discuss some recent results on this topic, including the description of subgroups that can arise in free idempotent generated semigroups, and to what extent they control the word problem of the semigroup. Free idempotent generated semigroups Sponsored by the Meyer Fund
Oct. 27, 2015 2pm (MATH 220)	Nik Ruskuc (University of St Andrews) X A partially ordered set (or more generally a quasi-ordered set) is said to be well quasi-ordered if it has no infinite descending chains and no infinite antichains. It has been investigated a fair bit in different areas of combinatorics, where it often represents a demarcation line between tractable and intractable down sets of combinatorial structures. The key technical result on well quasi-orders is the so-called Higman's Lemma. In its best known incarnation it establishes a direct and strong link between well quasi-order and regular languages. Recently, I (together with various collaborators) have been deploying this link to investigate well quasi-ordered classes of permutations, and possible enumerative, computational and decidability consequences. Well quasi-order: words and permutations Sponsored by the Meyer Fund
Oct. 27, 2015 3pm (Math 350)	Jonathan Wise (CU Boulder) X (Continuing last time's discussion.) Higher order deformations
Oct. 28, 2015 4pm (MATH 350)	Grad Student Seminar Mark Pullins (CU-Boulder) X Model theory is a fierce branch of logic primarily concerned with studying classes of mathematical structures. It has been described as "universal algebra + logic" and "algebraic geometry - fields". In this talk, we'll start slowly by introducing models and ultraproducts with the goal of proving the compactness theorem. Then we'll conclude with a potpourri of consequences. No background in model theory or logic is required. An Introduction to America's Next Top Model (Theory)
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 220)	Keith Kearnes (CU) Tame Congruence Theory
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 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

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