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Events for May – September 2021

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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
Sep. 01, 2021 5pm (MATH 350)	Grad Student Seminar Levi Lorzenzo (CU Boulder) X Join me on a journey through the land of Operator Algebras. Walk with me as I read from the gospel according to Gelfand. Enjoy vistas of von Neumann as we discuss Connes' embedding problem. Experience the interconnectedness of math as we see equivalent formulations of this problem show up in surprising places. But wait!! Stay tuned for a twist ending thanks to a recent result in quantum complexity theory. Connes' Embedding Problem, Kirchberg's conjecture, and MIP*= RE
Sep. 07, 2021 1:50pm (Zoom)	Math Edu April Ström (Chandler-Gilbert Community College) X The MAA Instructional Practices (IP) Guide addresses the call to action put forth to improve post-secondary mathematics instruction and increase student engagement. In this session, we will learn about the development of the IP Guide, explore ideas promoted in the guide, and discuss classroom strategies that increase student engagement. Leveraging the MAA Instructional Practices Guide: A Roadmap for Increasing Student Engagement
Sep. 16, 2021 5pm (MATH 350)	Grad Student Seminar Peter Rock (CU Boulder) X Come find out what it is on this week's episode of GSS! (Or if you don't mind spoilers...) There is a single theorem of Gauss which he felt was worthy of being called his masterpiece, his Theorema Egregium. However, in its original formulation, the beauty of this theorem is hidden beneath a web of tensors and some creative algebra. Certainly, the statement of the theorem is simple "Gauss curvature is an intrinsic property of a surface," but what does that even mean? Why is this so surprising that Gauss saw fit to call it his greatest accomplishment? To answer these questions more clearly, we need an approach that is dramatically different from the standard: Cartan's method of moving frames. Come witness the power of moving frames as we try to cram an audacious amount of Riemannian Geometry into a 50-minute talk. Gauss's Greatest Hit (or Another look at Gauss's Theorema Egregium)
Sep. 21, 2021 1:50pm (Zoom)	Math Edu Emily Braley (Johns Hopkins University) X In this interactive session we will look back at some of the tools and techniques introduced earlier in the seminar from the MAA's Instructional Practices Guide. Participants will work together on problems in small groups and we will debrief on small group facilitation for the undergraduate classroom. Then, we will think about transforming traditional problems into more open ended questions that make space for exploration and discussion! Along the way we will highlight various teaching techniques that elicit student thinking and use student contributions. Activating the Classroom Practices
Sep. 22, 2021 4pm (Math 350)	MathClub Divya E. Vernerey (CU-Boulder) X We'll discuss some mental "tricks" like multiplying two-digit numbers in your head. In fact, there are simple mathematical principles behind these tricks. Of course, one can potentially use these math tricks to annoy siblings, family, and friends (warning: this might also lead to loss of friends). Magic of Mental Math: ways to annoy your siblings
Sep. 22, 2021 5pm (MATH 350)	Grad Student Seminar Andrew Campbell (CU Boulder) X There are three analysis courses every graduate student in our department has to take. In Real Analysis 1 and 2 we study measures, Lebesgue integration, L^p-spaces, Hilbert spaces, Fourier series, and differentiation. In Complex Analysis 1 we study holomorphic functions, complex integration, the Cauchy-Riemann equations, Cauchy's integral formula, and all of its wonderful consequences/applications. It is easy for a graduate student to go through these courses and never really consider that besides several integral symbols and the word analysis these two tracks do not actually have much overlap. In this talk we will go through a brief review/introduction to some of the topics above, discuss why the study of holomorphic functions appears so different from other areas of analysis, and describe some of the many connections between the two subjects. Party Hardy Spaces: An Introduction to Complex and Real Analysis
Sep. 23, 2021 3pm (virtual)	Probability Jonas Jalowy X The Circular Law states that the empirical eigenvalue distribution of non-Hermitian random matrices with independent entries will converge to the uniform distribution on the complex disk as the size of the matrix tends to infinity. In this talk, I will address the rate of convergence to the Circular Law in terms of a uniform Kolmogorov-like distance. The optimal rate of convergence is determined by matrices with Gaussian entries and is given by $n-1/2$ . Secondly, I will present that also matrices with non-Gaussian entries nearly attain this optimal rate. The method of proof involves a smoothing inequality for logarithmic polynomials. In a similar fashion, we will also discuss related models such as products of independent matrices and the empirical distribution of the roots of certain random polynomials with independent coefficients. The talk will contain numerous illustrations and numerical simulations supporting some open problems. Rate of convergence to the Circular Law and its powers
Sep. 28, 2021 1pm (Zoom)	Peter Mayr (CU) X For relational structures A, B, the Promise Constraint Satisfaction Problem PCSP(A, B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases. Note that if there exists C with homomorphisms A ? C ? B, then PCSP(A, B) reduces to CSP(C). All known tractable PCSPs seem to reduce to tractable CSPs in this way. However Barto (2019) showed that some PCSPs over finite structures require solving CSPs over infinite C. We provide examples showing that even when a reduction to finite C is possible, this structure may become arbitrarily large. This is joint work with Alexandr Kazda and Dmitriy Zhuk. Solving small PCSPs via large CSPs
Sep. 28, 2021 2pm (MATH 350)	Lie Theory Robert Muth (Washington & Jefferson College) X Khovanov-Lauda-Rouquier (KLR) algebras arise in the categorification theory of quantum groups. In affine type A, KLR representations can be studied through the lens of cuspidal modules, which categorify root vectors in PBW bases of the associated quantum group, or through the lens of Specht modules, associated with the cellular structure of cyclotomic KLR algebras. Cuspidal ribbons provide a sort of combinatorial bridge between these approaches. I will describe the combinatorics of cuspidal ribbon tableaux, as well as some implications they have in the world of KLR representation theory, such as providing bounding information on simple factors of Specht modules, as well as presentations of cuspidal modules. Cuspidal ribbon tableaux and representations of KLR algebras Sponsored by the Meyer Fund
Sep. 30, 2021 3pm (Zoom)	Probability Rodrigo Ribeiro (CU Boulder) X In this talk, we will discuss the dichotomy recurrence/transience and ballisticity in the context of a class of random walks that build their on domain. At each step of the walker on its domain, a random number of new vertices is attached to the walker's position. We will present distributional conditions over this random number of new vertices for which we observe distinct sharp behavior on the walker. We also discuss structural results, that is, when this process is seen as a random graph model, the walker is capable of generating tree whose degree distribution approaches a power-law. On random walks that build their on domains

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