Algebraic Geometry Algebra/Logic DeLong Diversity Functional Analysis Geometry/Analysis Init Conditions Kempner Lie Theory MathClub Math Phys Noncomm Geometry Number Theory Probability Rep Theory Grad Student Seminar Thesis Defenses Topology Ulam Math Edu

Events for June – October 2020

Return to this week

Jul. 08, 2020 3pm (Zoom room…	Thesis Defenses Taylor Klotz (TK) X In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to the existence of a cascade feedback linearization for a given invariant control system. These theorems are presented in Chapter 4, where truncated versions of operators from the calculus of variations are introduced and explored to prove these new results. This connection reveals new geometry behind cascade feedback linearization and establishes a foundation for future exciting work on the subject with important consequences for dynamic feedback linearization. Geometry of Cascade Feedback Linearizable Control Systems
Sep. 10, 2020 1pm (Zoom (vir…	Rep Theory Andrew Linshaw (Denver University) Trialities of W-algebras
Sep. 17, 2020 2pm (Zoom)	Functional Analysis Andrew Stocker (CU Boulder) Hilbert C*-modules - Modules and Maps
Sep. 17, 2020 4pm (Zoom)	Grad Student Seminar Howie Jordan (CU Boulder) X We’ve all heard the hype: all you have to do is forget about “excluded middle” and then BOOM, your logic is constructive (in a certain sense). But like… why would you do that? And in what sense is it more constructive? If you aren’t aware, the Law (ha!) of Excluded Middle is the assertion that, for any particular sentence, either that sentence or its negation holds in your logic. In this talk we’ll look at what kind of logic you get when you drop excluded middle and discuss various motivations and interpretations of this, from the philosophical hooey of Brouwer to the structural interpretations arising from Gentzen’s methods. We will also look at a sample of some of the differences in practice and theory that arise when you don’t allow yourself the luxury of excluded middle in your proofs, in particular the interesting effects this has on the theory of real analysis! Noo don’t exclude the middle you’re so constructive aha
Sep. 24, 2020 1pm (Zoom (vir…	Rep Theory Jinwei Yang (University of Alberta) X Tensor categories of vertex operator algebras play an important role in the study of vertex operator algebras and conformal field theories. A central problem of tensor category theory of Huang-Lepowsky-Zhang is the existence of the vertex tensor category structure. We develop a few general methods to establish the existence of tensor structure on module categories for vertex operator algebras, especially for non-rational and non-C_2 cofinite vertex operator algebras. As applications, we obtain the tensor structure of affine Lie algebras at various levels, affine Lie superalgebra gl(1\|1), the Virasoro algebra at all central charges as well as the singlet algebras. We also study important properties, including constructions of projective covers, fusion rules and rigidities of these tensor categories. This talk is based on joint work with T. Creutzig, Y.-Z. Huang, F. Orosz Hunziker, C. Jiang, R. McRae and D. Ridout. Recent progress on tensor categories of vertex operator algebras
Sep. 24, 2020 2pm (Zoom)	Functional Analysis Shen Lu (CU Boulder) Hilbert C*-modules - Multipliers and morphisms
Sep. 24, 2020 4pm (Zoom)	Grad Student Seminar Chase Meadors (CU Boulder) X Coxeter groups are groups with a certain kind of presentation. Associated to each such group is an R-algebra called the Hecke algebra, and, in some cases, quotients of these algebras are isomorphic to a class of diagram algebras called Generalized Temperley-Lieb algebras. A diagram algebra is an algebra whose basis can be represented as pretty pictures, where multiplication is performed by "pasting pictures together" and following certain rules. Were this talk in person, I would undoubtedly bring construction paper, crayons, and Elmer's glue so we could all do calculations in these algebras together; alas, we will have to settle for looking at pretty pictures on my screen instead. At any rate, we will explore the connection between Coxeter groups and these diagram algebras and discuss some results and open conjectures. Coxeter groups and diagram algebras (pretty pictures included)
Sep. 29, 2020 10:30am (zoom)	MathClub Yano Casalaina-Martin (CU-Boulder) X I will discuss what it means for the zero set of a polynomial in several variables to be rational, as well as an open problem regarding cubic polynomials. Rationality of cubic hypersurfaces
Sep. 29, 2020 1pm (Zoom)	Peter Mayr (Boulder) X We review properties of varieties generated by finite simple algebras, their subvarieties and free objects. In particular we show that every congruence modular variety that is generated by a finite nonabelian simple algebra has a unique maximal subvariety. Varieties generated by finite simple algebras
Sep. 29, 2020 1pm (Zoom)	Peter Mayr (CU) X We review properties of varieties generated by finite simple algebras, their subvarieties and free objects. In particular we show that every congruence modular variety that is generated by a finite nonabelian simple algebra has a unique maximal subvariety. Varieties generated by finite simple algebras
Oct. 01, 2020 2pm (Zoom)	Functional Analysis Rachel Chaiser (CU Boulder) Hilbert C*-modules - Projections and Unitaries
Oct. 01, 2020 3pm (Zoom (vir…	Rep Theory Reimundo Heluani (IMPA, Brazil) X We prove a new Fermionic quasiparticle sum expression for the character of the Ising model vertex algebra, related to the Jackson-Slater q-series identity of Rogers-Ramanujan type. We find, as consequences, an explicit monomial basis for the Ising model, and a description of its singular support. We find that the ideal sheaf of the latter, defining it as a subscheme of the arc space of its associated scheme, is finitely generated as a differential ideal. We prove three new q-series identities of the Rogers-Ramanujan-Slater type associated with the three irreducible modules of the Virasoro Lie algebra of central charge 1/2. This is joint work with G. E. Andrews and J. van Ekeren and is based on arxiv.org:2005.10769 The singular support of the Ising model.
Oct. 01, 2020 4pm (Zoom)	Grad Student Seminar Andrew Campbell (CU Boulder) X Assume you attend one Fall 2020 Grad Student Seminar at random. Somehow you know there is at least a 1/20 chance the random talk is on the probabilistic method with examples in combinatorics and geometric functional analysis. This would imply there is at least one talk this semester with the above property, otherwise how could there possibly be any chance of such a thing happening? You now understand how the probabilistic method is used to prove the existence of mathematical objects. Since you are now an expert you know the probabilistic method is nonconstructive and the only way to find this talk is to show up every week. The Probabilistic Method
Oct. 06, 2020 1pm (Zoom)	Keith Kearnes (Boulder) X I will explain why any minimal strongly abelian variety with bounded essential arity is categorically equivalent to a minimal unary variety. Minimal strongly abelian varieties
Oct. 08, 2020 1pm (Zoom (vir…	Rep Theory Jethro Van Ekeren (UFF, Brazil) X (joint work with Lam, Moeller and Shimakura) If V is a holomorphic vertex algebra of central charge 24 then its weight one space V_1 is known to be a reductive Lie algebra which is either trivial, abelian of dimension 24 (in which case V is the Leech lattice vertex algebra) or else one of 69 semisimple Lie algebras first determined by Schellekens in 1993. Until now the only known proof of Schelekens result was a heavily computational one involving case analysis and difficult integer programming problems. Recently Moeller and Scheithauer have established a bound on the dimension of the weight one space of a holomorphic orbifold vertex algebra, using the Deligne bound on the growth of coefficients of weight 2 cusp forms. In this talk I will describe how the dimension bound together with Kac's very strange formula implies that all holomorphic vertex algebras of central charge 24 and nontrivial weight one space are orbifolds of the Leech lattice algebra. Since the automorphism group of the latter algebra is known one can, with a little more work, recover Schellekens result in this way. Schellekens list, the Leech lattice and the very strange Formula
Oct. 08, 2020 2pm (Zoom)	Functional Analysis Andrew Stocker (CU Boulder) Tensor products
Oct. 08, 2020 4pm (Zoom)	Grad Student Seminar Michael Wheeler (CU Boulder) X We all know the story of how Calculus started as a non-rigorous confusion of intuitive notions of the infinitely small and infinitely big and how eventually the field was put on rigorous footing with the invention of the limit. This story leaves out an interesting question: If the foundation using infinitesimal numbers was so treacherous, why is it that so many of the results obtained using this faulty foundation continued to be true when using the limit formulation, a formulation where all the proofs look different? In this talk, we will explore a modification of the Cauchy construction of the reals that results in an ordered field very closely resembling the real numbers except that it has infinitesimal and infinite elements (and so is not Archimedean). If time permits, we will talk about how some of the basics of Calculus can be formulated in this larger field. Reviving the Ghosts of Departed Quantities
Oct. 13, 2020 10:30am (zoom)	MathClub Kate Stange (CU-Boulder) X We'll take a little tour of some famous and less famous integer recurrence sequences, including the Fibonacci numbers and elliptic divisibility sequences, viewing them as shadows of geometric group laws on curves, which connects these sequences to current topics in research. Along the way, we'll use software to visually explore some of their properties. The integer shadows of curves
Oct. 13, 2020 1pm (Zoom)	Stefano Fiovaranti (JKU Linz, Austria) X We investigate finitary functions from Z_n to Z_n for a squarefree number n. We show that for squarefree n the lattice of all clones on Z_n which contain the addition of Z_n is finite and we provide an upper bound for the cardinality of this lattice. Furthermore, we prove that these clones can be generated by functions of arity at most the greatest prime factor of n. Expansions of squarefree abelian groups
Oct. 14, 2020 3pm (Zoom)	Math Phys Daniel Spiegel (CU Boulder Physics Department) X We aim to shed light on the description of topological charges and particle exchange statistics in the framework of algebraic quantum mechanics. The notions of observable, state and pure state, superselection sector, and locality are defined in terms of C*-algebras and form the basis of our discussion. We show how physically relevant superselection sectors may be obtained from localized, transportable endomorphisms of a quasi-local algebra. These endomorphisms act as charge creation operators and are endowed with a tensor product from which particle exchange statistics may be analyzed. We briefly discuss Kitaev’s toric code as an example of these ideas. Superselection Sectors and Braid Statistics in Algebraic Quantum Mechanics
Oct. 15, 2020 11am (Zoom)	Noncomm Geometry Zhengfang Wang (University of Stuttgart) X Analgous to Hochschild cohomology, we define the singular Hochschild cohomology of an algebra as the Yoneda algebra of the identity bimodule in the singularity category of bimodules. The singularity category was introduced by Buchweitz in 1986 and then rediscovered by Orlov in 2003. In this talk, we construct a natural complex to compute the singular Hochschild cohomology. We prove that this complex carries a natural B-infinity algebra structure. In particular, the singular Hochschild cohomology is a Gerstenhaber algebra. We will also talk about Keller’s recent theorem and conjecture for singular Hochschild cohomology. B-infinity algebra structure on singular Hochschild cohomology
Oct. 15, 2020 1pm (Zoom (vir…	Rep Theory Naoki Genra (University of Alberta) X Screening operators are useful tools to characterize free field realizations of vertex algebras, and give new perspectives in the structures of them. We explain screening operators of the beta-gamma system, affine vertex (super)algebras and W-(super)algebras. We also explain the applications to the coset constructions, representations and trialities of W-algebras. Screenings and applications
Oct. 15, 2020 2pm (Zoom)	Functional Analysis Shen Lu (CU Boulder) Induced representations
Oct. 20, 2020 10:30am (zoom)	Geometry/Analysis Braden Balentine (CU Boulder) X We discuss mild solutions to the Navier-Stokes equation on the $n$ -dimensional hyperbolic space $ℍ^{n}$ , $n ≥ 2$ . Substantial results have already been obtained by Pierfelice. In this talk, we discuss how to extend the Fujita-Kato theory of mild solutions from Euclidean space to the hyperbolic space and also examine the ways in which the theory can be improved in this setting. More precisely, due to the additional exponential time decay offered on $ℍ^{n}$ for dispersive and smoothing estimates of the heat kernel, we are able to significantly simplify the proofs of the $L^{n}$ and $L^{p}$ norm decay results as compared to the Euclidean setting. Additionally, we are able to show that the $L^{n}$ norm of a global solution decays to zero as $t$ goes to infinity on $ℍ^{n}$ , and does so at a much faster rate than is known in the Euclidean setting. The proof does not rely on dimension or the energy inequality in any way. As a necessary part of our work, we extend to $ℍ^{n}$ known facts in Euclidean space concerning the strong continuity and contractivity of the semigroup generated by the Laplacian. This work, together with Pierfelice's, contributes to providing a full Fujita-Kato theory on $ℍ^{n}$ . Global Time Behavior of $L^{p}$ -Mild Solutions to the Navier-Stokes Equation on the Hyperbolic Space
Oct. 20, 2020 1pm (Zoom)	Branimir Seselja (University of Novi Sad, Serbia) X By several postulates we introduce a new class of algebraic lattices, in which a main role play so called normal elements. A model of these lattices are weak-congruence lattices of groups, so that normal elements correspond to normal subgroups of subgroups. We prove that in this framework many basic structural properties of groups turn out to be lattice-theoretic. Consequently, we give necessary and sufficient conditions under which a group is Hamiltonian, Dedekind, Abelian, solvable, perfect, supersolvable, finite nilpotent. These conditions are given as lattice theoretic properties of a lattice with normal elements. Joint research with Andreja Tepavcevic and Jelena Jovanovic. Lattices with normal elements
Oct. 21, 2020 4pm (Zoom)	Topology Howie Jordan (CU Boulder) X This talk will be a gentle introduction to sheaves. Join Zoom Meeting https://cuboulder.zoom.us/j/98979344859 Meeting ID: 989 7934 4859 Passcode: 787231 Sheaves
Oct. 22, 2020 1pm (Zoom (vir…	Rep Theory Darlayne Addabbo (University of Arizona) X I will discuss the level two Zhu algebra for the Heisenberg vertex operator algebra and techniques used in determining its structure. I will also discuss more general results helpful in determining generators and relations for higher level Zhu algebras, and in particular, will provide an example to clarify the necessity of an extra condition required in the definition of higher level Zhu algebras. (Joint with Katrina Barron.) Higher level Zhu algebras for vertex operator algebras
Oct. 27, 2020 10:30am (zoom)	MathClub Judy Packer (CU-Boulder) X A brief history of the Heisenberg Uncertainty Principle will be given, with an eye towards introducing the (Weyl)-Heisenberg group. This group (which can be viewed as a subgroup of the group of invertible 3 x 3 real matrices, has many interesting applications, and a few will be discussed. The Heisenberg Uncertainty Principle and the Heisenberg group
Oct. 27, 2020 1pm (Zoom)	H. Peter Gumm (Philipps University Marburg, Germany) X Motivating our investigation, we begin by demonstrating how all sorts of transition systems studied in Computer Science - automata (deterministic, nondeterministic, probabilistic), Kripke structures, neighbourhood systems (including topological spaces) and many more - can be naturally modeled as instances of the concept of "universal coalgebra". Each of the mentioned cases requires an appropriate Set-functor replacing what we know in universal algebra as "signature". Various preservation properties of the signature functor F determine the structure theory of the class of all F-coalgebras. In our talk we concentrate on functors parameterized by some universal algebras, be it a complete lattice or a commutative monoid, and mainly on the functor $F_{Σ}$ given by constructing for a set X the free $Σ$ -Algebra $FΣ(X)$ . $F_{Σ}$ preserves preimages if and only if each $Σ$ -term which is weakly independent at a variable position x is (strongly) independent of x, (in short: $Σ$ implies its own 'derivative' $\Sigma'$). For every permutable variety V(\Sigma) the free algebra functor weakly preserves kernel pairs. For the converse we exhibit a syntactic condition stating that an equation p(x,x,y) = q(x,y,y) holds if and only both p(x,y,z) and q(x,y,z) arise as substitution instances of a common term s(x,y,z,u). We give a geometrical interpretation of this fact and use it to show that if $V(Σ)$ is n-permutable then $F_{Σ}$ weakly preserves kernel pairs iff $V(Σ)$ is Mal'cev. Free algebra functors as coalgebraic signatures
Oct. 28, 2020 4pm (zoom)	Topology Agnes Beaudry (CU Boulder) X This is the second talk in a sequence of introductory lectures whose goal is to discuss the notions of gerbes, bundle gerbes and their classification. Last week, we discussed sheaves of sets and sheaves of groups. In this talk, we will discuss sheaves of categories, also known as stacks. Topic: CU Topology Seminar Time: This is a recurring meeting Meet anytime Join Zoom Meeting https://cuboulder.zoom.us/j/98979344859 Meeting ID: 989 7934 4859 Passcode: 787231 Stacks & Gerbes - Part I
Oct. 29, 2020 1pm (Zoom (vir…	Rep Theory Ryo Sato (Academia Sinica,Taipei, Taiwan) X The Kazama-Suzuki coset vertex operator superalgebra associated with a simple Lie algebra g and its Cartan subalgebra h is a ``super-analog'' of the parafermion vertex operator algebra associated with g. At positive integer levels, the coset superalgebra turns out to be C_2-cofinite and rational by the general theory of orbifolds (Miyamoto) and Heisenberg cosets (Creutzig-Kanade-Linshaw-Ridout), respectively. On the other hand, at Kac-Wakimoto admissible levels, the coset superalgebra is not C_2-cofinite nor rational. In this talk we discuss a relationship between the category of weight modules for the admissible affine vertex algebra associated with g and that for the corresponding Kazama-Suzuki coset vertex superalgebra. In our discussion the inverse Kazama-Suzuki coset construction, which is originally due to Feigin-Semikhatov-Tipunin in the g=sl_2 case, plays an important role. As an application, for g=sl_2 at level -1/2, we determine all the fusion rules between simple weight modules of the Kazama-Suzuki coset vertex superalgebra and verify the conjectural Verlinde formula in this case (corresponding to Creutzig-Ridout's result in the affine side). The last part is based on the joint work with Shinji Koshida. Kazama-Suzuki coset vertex superalgebras at admissible levels.
Oct. 29, 2020 2pm (Zoom)	Functional Analysis Shen Lu (CU Boulder) Imprimitivity Bimodules

Main menu

Search

Other ways to search:

Events for June – October 2020

Thesis Defenses

Rep Theory

Functional Analysis

Grad Student Seminar

Rep Theory

Functional Analysis

Grad Student Seminar

MathClub

Functional Analysis

Rep Theory

Grad Student Seminar

Rep Theory

Functional Analysis

Grad Student Seminar

MathClub

Math Phys

Noncomm Geometry

Rep Theory

Functional Analysis

Geometry/Analysis

Topology

Rep Theory

MathClub

Topology

Rep Theory

Functional Analysis