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Events for April – August 2021

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Apr. 27, 2021 5pm (zoom)	Diversity Diversity Committee and Tea X This is a special collaboration between Diversity Committee and Tea - FaculTea Day! Don’t have an advisor? Don’t know which research group to join? The FaculTea Day will be a chance for you to come talk with faculty and get to know what they do. Already have an advisor or research group? Come anyway! You can help provide information to your potential future academic siblings. https://cuboulder.zoom.us/s/95892147111 Passcode : 864963 FaculTea
Apr. 15, 2021 5pm (Zoom (vir…	Rep Theory Ana Kontrec (University of Zagreb) X One of the simplest examples of $𝒲$ -algebras is the Bershadsky-Polyakov vertex algebra $Wk(g, fmin)$ , associated to $g = sl(3)$ and the minimal nilpotent element $f_{m i n}$ . We study the simple Bershadsky-Polyakov algebra $𝒲_{k}$ at positive integer levels and obtain a classification of their irreducible modules. In the case $k=1$ , we show that this vertex algebra has a Kazama-Suzuki-type dual isomorphic to the simple affine vertex superalgebra $L_{k'} (osp(1 \vert 2))$ for $k'=-5/4$. This is joint work with D. Adamovic. Bershadsky-Polyakov vertex algebras at positive integer levels and duality
Apr. 01, 2021 9:10am (Zoom 9…	Ulam Patrick Wynne (CU Boulder) X Let A be a finite first-order structure and Phi a set of first-order formulas in its language with certain closure properties. We use a result about clonoids to show that the finitary relations on A definable by formulas in Phi are uniquely determined by the definable subsets of arity A^2. This gives new proofs of some finiteness results in Universal Algebraic Geometry. This talk is based on work of Erhard Aichinger and Bernardo Rossi. Some Finiteness Results in Universal Algebraic Geometry via Clonoids
Apr. 06, 2021 10am (zoom: 98…	Thesis Defenses Albany Thompson (CU Boulder) X In this talk, we study the stationary linear and nonlinear Navier-Stokes equations on the hyperbolic space. This study includes discussing the existence of weak solutions to the linear stationary equation in two and three dimensions, proving the uniqueness of the weak solutions to the linear stationary problem in three dimensions, and examining the nonuniqueness in two dimensions. We also prove the existence of weak solutions to the nonlinear stationary equation. We then outline the construction of a coercive estimate for the linear stationary Navier-Stokes equation in two dimensions. Finally, we show how using the Hodge Laplacian in two dimensions requires us to look for weak solutions in a different function space, and we discuss an exterior domain problem in this case. This is a thesis defense. Foundations of the steady Navier-Stokes equation on the hyperbolic space
Apr. 06, 2021 1pm (Zoom)	Nick Galatos (University of Denver) X Residuated lattices were introduced by Ward and Dilworth as tools in the study of ideal lattices of rings. Residuated lattices have a monoid and a lattice reduct, as well as division-like operations; examples include Boolean algebras, lattice-ordered groups and relation algebras. Also, they form algebraic semantics for substructural logics and are connected to mathematical linguistics and computer science (for example pointer management and memory allocation). We focus on a class of residuated lattices that have an idempotent multiplication and all elements are comparable to the monoid identity; these are related to algebraic models of relevance logic. After establishing a decomposition result for this class, we show that it has the strong amalgamation property, and extend the result to the variety generated by this class; this implies that the corresponding logic has the interpolation property and Beth definability. Amalgamation for certain conic idempotent residuated lattices
Apr. 06, 2021 4pm (zoom: 994…	Thesis Defenses Carlos E. Pinilla (CU Boulder) X The Hodge decomposition is well-known for compact manifolds. The result has been extended by Kodaira to non-compact complete manifolds in the space of $L2$ forms. We showed this decomposition with Chan and Czubak in the Sobolev space $H1$ on a space form of a nonpositive sectional curvature. In this thesis we extend the decomposition to the Sobolev space $Hℓ(λk( Hn))$ for integers $n≥ 2, ℓ≥ 0, n≥ k≥ 0.$ We also prove that this decomposition holds in the strong sense, depending on the dimension of the space and the degree of the differential form. This is a thesis defense. Hodge decomposition for the Sobolev space $Hℓ(λk)$ on a space form of nonpositive sectional curvature
Apr. 07, 2021 4pm (via zoom)	Math Phys Marcelo Disconzi (Vanderbilt University) X We consider the relativistic Euler equations with a physical vacuum boundary and an equation of state $p()=γ$ , $γ > 1$ . We establish the following results. (i) local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and continuous dependence on the data; (ii) low regularity solutions: our uniqueness result holds at the level of Lipschitz velocity and density, while our rough solutions, obtained as unique limits of smooth solutions, have regularity only a half derivative above scaling; (iii) stability: our uniqueness in fact follows from a more general result, namely, we show that a certain nonlinear functional that tracks the distance between two solutions (in part by measuring the distance between their respective boundaries) is propagated by the flow; (iv) we establish sharp, essentially scale invariant energy estimates for solutions; (v) we establish a sharp continuation criterion, at the level of scaling, showing that solutions can be continued as long as the velocity is in $L1t Lipx$ and a suitable weighted version of the density is at the same regularity level. This is joint work with Mihaela Ifrim and Daniel Tataru. Meeting ID: 940 0255 3301 Passcode: 790356 The relativistic Euler equations with a physical vacuum boundary.
Apr. 08, 2021 9:10am (Zoom 9…	Ulam Vladimir Kolmogorov (IST Austria) X A series of recent works have established the dichotomy of general-valued constraint satisfaction problems (VCSPs): every VCSP language can either be solved in polynomial time or is NP-hard. I will describe the algorithmic part of this dichotomy. As a key subroutine, we use a polynomial-time algorithm for ordinary CSPs satisfying a certain algebraic condition, whose existence was proved by Bulatov and by Zhuk in 2017. Joint work with Andrei Krokhin and Michal Rolinek (http://pub.ist.ac.at/~vnk/papers/VCSP.html ). The Complexity of General-Valued CSPs
Apr. 08, 2021 5pm (Zoom (vir…	Rep Theory Shunsuke Tsuchioka (Tokyo Institute of Technology) X We generalize the theory of linked partition ideals due to Andrews using finite automata in formal language theory and apply it to prove three Rogers-Ramanujan type identities of modulo 14 that were posed by Nandi through vertex operator theoretic construction of the level 4 standard modules of the affine Lie algebra $A(2)2$ . This is a joint work with Motoki Takigiku. A proof of conjectured partition identities of Nandi.
Apr. 13, 2021 10:30am (zoom)	MathClub Carla Farsi (CU-Boulder) X In recent years there has been some spectacular advances in the field of prime numbers. In particular, striking progress has been made on the prime numbers gap conjectures. Classically, the conjecture posits that there are infinitely many pairs of twin prime numbers (i.e., pairs of prime numbers that differs by 2; one such twin pair is 17 and 19). More generally one can ask if there are infinitely many pairs of primes within a fixed gap x. https://www.quantamagazine.org/mathematicians-prove-conjecture-on-big-prime-number-gaps-20141210/ Inspired by these recent breakthroughs, we review some fascinating properties of prime numbers and of Bungus numbers that can be introduced in mathematics classrooms at almost any level. To make the learning of these notions fun and playful, we introduce three student games. The first one is suitable for most grades, while the other two are suitable for higher grades. We also suggest topics for additional classroom workshops. Reference: Bridges 2014 http://archive.bridgesmathart.org/2014/bridges2014-365.html The magic of prime numbers (and their twin pairs)
Apr. 13, 2021 1pm (Zoom)	Marcos Mazari-Armida (Carnegie Mellon University) X Abstract elementary classes (AECs for short) were introduced by Shelah in the seventies to study those classes of structures that can not be axiomatized by a first-order theory. In this talk, we will introduce the basic notions of AECs and showcase them in classes of modules. In particular, we will explore if every AEC of modules with pure embeddings is stable. Using that the class of p-groups with pure embeddings is a stable AEC, we will present a solution to a problem of László Fuchs. For those at CU Boulder, I am assigned to teach Topics in Logic next semester so the talk will also be a preview of the material I am planning to cover in that course. Stability in abstract elementary classes of modules
Apr. 15, 2021 9:10am (Zoom 9…	Ulam Dmitriy Zhuk (Moscow State University) X The Quantified Constraint Satisfaction Problem (QCSP) is the problem to evaluate a sentence of the form "for all x1 exists y1 ... forall xn exists yn (R1(...) and ... and Rs(...))", where R1, ..., Rs are relations from a constraint language Gamma. It is known that the complexity of the QCSP depends only on the algebra of polymorphisms of the constraint language. If all constraints are allowed then the QCSP is PSpace-complete. We will discuss what properties of the algebra place the problem in the class NP, what properties place it in the class co-NP, and how PSpace-hardness can be proved if the algebra has no such properties. Algebraic approach to the Quantified Constraint Satisfaction Problem
Apr. 20, 2021 10am (via Zoom)	Geometry/Analysis Teemu Saksala (North Carolina Stat University) X Consider the geometric inverse problem: There is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov--Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense. This talk is based on a joint work with Maarten V. de Hoop, Joonas Ilmavirta and Matti Lassas Stable reconstruction of simple Riemannian manifolds from unknown interior sources
Apr. 20, 2021 1pm (Zoom)	Ross Willard (University of Waterloo) X This is a progress report on an exploration of Isaev's algebras and their cousins. Isaev's algebras were the first, and remain the only, known examples of inherently nonfinitely based finite algebras in Maltsev varieties. In this talk I will describe a class of finite algebras containing Isaev's algebras, and explain some basic tools that we have developed to help determine which of these algebras are inherently nonfinitely based. At the moment we are only able to apply these tools to Isaev's algebras themselves, but that won’t stop me from filling the 50-minute time slot which I have been offered! This is joint work with Emily Carlson, Mehul Gupta and George McNulty. Inherently nonfinitely based nonassociative algebras
Apr. 20, 2021 1:30pm (https:…	Diversity Ysatiz M. Piñero (Center for Inclusion and Social Change) X Co-facilitated by CISC staff and the peer education team, this interactive 90-minute training is designed for students on the CU Boulder campus. During the training, participants will engage in small and large group discussions to help identify examples of sexism in their lives or in an institution they participate in. They will also learn strategies for interrupting sexism. https://cuboulder.zoom.us/j/99247389611 Recognizing & Interrupting Sexism
Apr. 20, 2021 2pm (MATH 350)	Lie Theory Riccardo Biagioli (University of Bologna) X The Temperley-Lieb algebra is a well studied finite dimensional associative algebra : it can be realized as a diagram algebra and it has a basis indexed by the fully commutative elements in the Coxeter group of type A. A few years ago, Dana Ernst introduced an elegant generalization of such diagrammatic representation for the generalized Temperley-Lieb algebra of type affine C. The proof that such representation is faithful is quite involved and the same author wonders if an easier proof exists. In this talk, we present a new combinatorial way to describe Ernst’s algebra homomorphism, from which injectivity and subjectivity follow more easily. Our results are based on a recent classification of fully commutative elements of type affine C in terms of heaps of pieces, and on certain operations that we define on such heaps. This is a joint work with Giuliana Fatabbi and Gabriele Calussi. Temperley-Lieb algebra and fully commutative elements in type affine C
Apr. 22, 2021 9:10am (Zoom 9…	Ulam Zarathustra (Zeb) Brady X Barto and Kozik have introduced several weak consistency notions for CSPs, such as ``Prague instances'', ``weak Prague instances'', and ``pq-consistency'', and have shown that any CSP template which can be solved by a local consistency algorithm can also be solved using one of these weak consistency notions. Their definition of ``weak Prague instance'' breaks up into three natural conditions on the directed graph of implications between single-variable restrictions, which they call (P1), (P2), and (P3). (P1) is the standard generalization of arc-consistency to CSPs with relations of higher arity, (P2) is a condition which is closely related to the basic linear programming relaxation of the instance, and (P3) is a condition which is closely related to the basic semidefinite relaxation of the instance. Barto and Kozik have raised the question of whether any instance of a bounded-width CSP which satisfies just (P1) and (P3) has a solution - this is a weaker consistency notion than all other consistency notions which are known to guarantee solvability. In this talk, I'll introduce an even weaker type of consistency than (P1) and (P3), and explain how we can use algebraic results about finite affine-free idempotent Taylor algebras in a purely black-box way to prove that this weaker consistency is strong enough to guarantee the existence of a solution. The algebraic input needed is a new type of subalgebra which I call a ``stable subalgebra'', which satisfies some amazingly strong axiomatic rules. Stable subalgebras and weaker consistency for bounded width CSPs
Apr. 22, 2021 1pm (Zoom (vir…	Rep Theory Fei Qi (University of Manitoba) X Meromorphic open-string vertex algebras (abbre. MOSVAs) is a noncommutative generalization of the usual vertex algebra defined by Yi-Zhi Huang in 2012. Vertex operators still satisfy the associativity but do not necessarily satisfy commutativity. In this talk I will illustrate nontrivial examples of MOSVAs and modules we know so far, including the universal bosonic construction, the universal fermionic construction, and the example from the geometry over constant curvature manifolds. Bosonic and fermionic constructions of meromorphic open-string vertex algebras.
Apr. 27, 2021 1pm (Zoom)	Alexander Hulpke (Colorado State) X The first examples of groups in a textbook are often as words in generators, subject to some easy rules. This seems nice and natural, but gets quickly abandoned once the groups involved become more complicated. A similar disappointment happens when introducing group extensions: Examples in textbooks never go beyond easy cases such as cyclic groups or split extensions. But this is not intended to whine about textbooks. Instead I want to show how a systematic approach to normal form words (namely confluent rewriting systems) can be used to describe group extension (and explicitly compute 2-cohomology), resulting in practically useful (and implemented!) algorithms. Rewriting systems and group extensions
Apr. 28, 2021 5pm (via zoom)	Math Phys Mayuko Yamashita (RIMS, Kyoto, Japan) X Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. Two of the main difficulty of this problem are the following. First, we do not have the axioms for QFT’s. Second, The Anderson dual is defined in an abstract way. In this talk, I will explain the ongoing work to give a new approach to this conjecture, in particular to overcome the second difficulty above. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT’s which physicists believe to hold in general. I will start from basic motivations for the classification problem, report the progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Kyushu, physics). Meeting ID: 940 0255 3301 Passcode: 790356 The classification problem of non-topological invertible QFT’s and a physically motivated model for the Anderson duals
Apr. 29, 2021 9:10am (Zoom 9…	Ulam Manuel Bodirsky (TU Dresden) X Post completely described clones on a 2-element set; there are only countably many. Yanov and Muchnik proved that already on 3 elements, there are uncountably many clones. These results may also be viewed as results about 2-element and 3-element structures considered up to primitive positive interdefinability. Motivated by research in constraint satisfaction, a coarser equivalence relation on finite structures has been introduced recently, based on primitive positive (pp) constructions instead of primitive positive definitions. On the algebraic side, this amounts to studying idempotent linear strong Maltsev conditions for clones on finite sets. We do not know how many finite structures that are up to pp interconstructability; all uncountable families of structures on finite domains known to the speaker collapse down to countably many with respect to pp interconstructability. I will present some recent results about the special case of finite directed graphs, where at least we know the largest finite digraphs with respect to pp constructability. Joint work with Florian Starke, Albert Vucaj, and Dmitriy Zhuk Finite structures ordered by pp constructability
Apr. 29, 2021 1pm (Zoom (vir…	Rep Theory Gaywalee Yamskulna (Illinois State University) X In this talk, I will discuss an impact of Leibniz algebras on the algebraic structure of $ℕ$ -graded vertex algebras. Along the way, I will provide easy ways to characterize several types of $ℕ$ -graded vertex algebras. A remark on $\mathbb{N}$-graded vertex algebras
May. 04, 2021 1:30pm	Diversity Levi Lorenzo and Gabriel Lopez with the Diversity Committee X CHAT(+)s are discussion sessions for graduate students and faculty of the Department of Mathematics organized by the Diversity Committee. They are structured conversations about key issues, including discussions of issues relating to diversity, for graduate students (CHATs) and between graduate students and faculty (CHAT+s). The goal of the CHAT+ organized for May 4th is to discuss our experiences with sexism in advanced mathematics and how we can each play an active role in addressing and dismantling that sexism. The discussion will be guided by the following short readings: https://www.womendomath.org/research/ (this is a graphic) http://www.theliberatedmathematician.com/2015/12/why-i-do-not-talk-about-math/ Faculty and students are asked to take a look at the above readings before the CHAT+. If you are unable to do the readings, however, please do not be deterred from participating. If you can only attend for part of the discussion, please join us when you are able to. https://cuboulder.zoom.us/j/93615800408 Meeting ID: 936 1580 0408 Passcode: CUMath CHAT+ : Interrupting Sexism in Advanced Mathematics
May. 06, 2021 9:10am (Zoom 9…	Ulam Petar Markovic (University of Novi Sad) X We investigate the semilattices of Mal'cev blocks ("SMB algebras"), a quasivariety of Taylor algebras invented by R. McKenzie and the speaker in 2009. The Constraint Satisfaction Problem over SMB algebras was proved to be tractable by A. Bulatov in 2017, and he used this case as a template for his proof of the Dichotomy Conjecture. In Bulatov's terminology of edge-colored graphs of algebras, SMB algebras are the prime example of as-connected algebras. Any simplification of the tractability proof for SMB algebras gives hope that one can, using Bulatov's theory of edge colored graphs of algebras, generalize to a simplification of the proof of the Dichotomy Theorem, motivating our investigation. We were trying to prove D. Zhuk's reduction of "irreducible instances", which are consistent enough, to binary absorbing subuniverses ("Zhuk's Reduction Theorem") for the case of SMB algebras. We prove two results: One is a special case of Zhuk's Reduction Theorem, but assuming only 1-consistency, i.e. when all constraint relations are subdirect subuniverses of the product. The second result states that Zhuk irreducible instances, which are also Maroti reduced and consistent enough, must have a solution. Constraint Satisfaction Problem over semilattices of Mal'cev blocks (joint work with A. Prokic)
May. 06, 2021 4pm (Zoom (vir…	Rep Theory David Ridout (University of Melbourne) X Minimal models are simple vertex operator algebras (VOAs) for which the structure of the associated universal VOA is somehow maximally degenerate. Some minimal models are rational and $C2$ -cofinite, eg those for Virasoro or $N=1$ , and some are not. I will look at some examples which are not, specifically the admissible-level affine minimal models associated with $sl3$ . The novelty here is the fact that the rank of the associated algebra is not $1$ . Weight modules for $\mathfrak{sl}_3$ minimal models
May. 13, 2021 1pm (Zoom (vir…	Rep Theory Cris Negron (University of North Carolina) X I will discuss joint work with Terry Gannon in which we provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp(pi i/p), and the representation category of the triplet vertex operator algebra at integral parameter p>1. We provide similar quantum group equivalences for representation categories associated to the Virasoro, and singlet vertex operator algebras at central charge c=1-6(p-1)^2/p. Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge
May. 18, 2021 2pm (zoom)	Topology Erik Knutsen (CU Boulder) X This talk is based on the paper "The Picard Group of Equivariant Stable Homotopy Theory” by Fausk, Lewis, Jr., and May. I plan to go through the highlights of the paper and give an idea for the proof of the paper’s main theorem. Join Zoom Meeting https://cuboulder.zoom.us/j/98979344859?pwd=K3ZrTWt4Wkk1cllOQ1pkcW4vZ1FCZz09 Meeting ID: 989 7934 4859 Passcode: 787231 The Picard Group of Equivariant Stable Homotopy Theory
May. 20, 2021 4pm (Zoom (vir…	Rep Theory Zachary Fehily (University of Melbourne) X While regular W-algebras have enjoyed many years of study and attention, recent developments in physics have the less popular subregular W-algebras playing an important role. Moreover, these subregular W-algebras appear at levels where the corresponding conformal field theory is likely non-rational. This necessitates a deeper understanding of the representation theory of such vertex operator algebras at non-rational levels. In type A_n, only the n=1 (sl_2) and n=2 (Bershadsky-Polyakov algebra) cases are particularly well-understood. In both cases an 'inverse reduction-by-stages' approach, first described for sl_2 in vertex operator algebra language by D. Adamovic, relates much of the representation theory to that of the corresponding regular W-algebra. In this talk, I will describe how to generalise this approach to all type A_n subregular W-algebras using screening operators developed by N. Genra. Subregular W-algebras
May. 28, 2021 9am (online vi…	Math Phys Agnes Beaudry (University of Colorado Boulder) X Phases of matter are classes of quantum systems that may look different microscopically but share certain common macroscopic properties. An active problem in condensed matter physics is to classify phases of matter. In certain cases, the tools of homotopy theory provide a useful mathematical framework. Specifically, certain classes of phases of matter are expected to form a generalized cohomology theory, a point of view introduced by Kitaev. This can be accessed via quantum field theories as in the work of Freed-Hopkins. Another problem is to get at this connection directly from the point of view of lattice models, which are idealizations of materials commonly used by condensed matter physicists. In this mostly expository talk, I will discuss the latter perspective, with some results on this topic which are part of joint work with Hermele, Moreno, Pflaum, Qi, Spiegel, Vishwanath and Wen. Meeting ID: 940 0255 3301 Passcode: 790356 Homotopy theory and phases of matter
Aug. 25, 2021 5pm (MATH 350)	Grad Student Seminar Howie Jordan (CU Boulder) X Ask a working mathematician what it is they are \emph{REALLY} talking about, and the 1st most common answer is to point at Sets. The 0th most common answer is "Oh f#&! you, why are you even at this analysis seminar?!" There are only so many Kinds of things that a mathematician is interested in, and they need a langauge to tell each other, and to remind themselves, which Sorts of objects are which. But what makes Sets the Type of Stuff that a mathematician might be using? We are going to take an intuitive overview tour of the mathematical multiverse and make a few landmark stops. Worlds where all functions R->R are continuous, worlds where every set is constantly changing, and worlds where everything is pointless. We'll construct universes to make a noncommutative thing become commutative, and universes with a (multi)universal group or ring. And even if we don't find ourselves drawn to a mathematical home, we'll at least leave with a better appreciation for the one we have. Mathematical MultiVerses
Aug. 31, 2021 10am (https://…	Geometry/Analysis Monique Chyba (University of Hawaii) X Abstract: SARS-CoV-2 (COVID-19) has impacted not only health, but the economy and how we live daily life. On January 30, 2020 the World Health Organization (WHO) declared a global health emergency. COVID-19 was officially named on February 11, as it continued to spread across Asia and Europe. Mathematicians have found themselves at the front seat of this race against COVID-19. However, there is still a lot of unanswered questions and challenges regarding the outcome of several models as well as their limitations. It is unclear at this time if there is a "better" model, and while most of the challenges in epidemiological forecasting come from incomplete data and impossibility to model people's behavior, there is still the question of what model to use when and for what purpose. Throughout the current COVID-19 pandemic, most results and forecasting come from one model but not a combination. We consider what can be learned from running both compartment and agent based models side-by-side; taking and applying the best of each model using the measured data. We will also discuss the Hawaiian Islands are providing a unique opportunity to study heterogeneity and demographics in a controlled environment due to the geographically closed borders and mostly uniform pandemic-induced governmental controls and restrictions. Epidemiological modeling, and COVID-19 Heterogeneity in Islands Chain Environment

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