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Events for June – October 2021

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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
Oct. 05, 2021 1pm (Zoom)	Philipp Rothmaler (CUNY) X A partition of the set of unary positive primitive (pp) formulas for modules over an associative ring into four regions will be presented. These four types of formula have a bearing on various structural properties of modules, a few instances of which will be discussed in the talk. Domains, specifically Ore domains, turn out to play a prominent role. One of the four types of formula are called high. These are used to define Ulm submodules and Ulm length of modules over an arbitrary associative ring. Pure injective modules turn out to have Ulm length at most 1 (just as in abelian groups). As a consequence, pure injective modules over RD domains (in particular, pure injective modules over the first Weyl algebra over a field of characteristic 0) decompose into a largest injective and a reduced submodule. High and low formulas
CANCELED Oct. 05, 2021	Math Edu Jess Ellis Hagman (Colorado State University) X In this talk I will share my current research that addresses student success in STEM from a critical perspective. A critical perspective on student success means locating student challenges in STEM not within the students' themselves but within the systems at play, and that these systems are failing students not because they are broken but because they are functioning perfectly well based on their design. I will share my research teams' current work focused on student experiences in college precalculus and calculus from a critical perspective, discussing both recent qualitative research and quantitative research studies. I care about these courses personally because I think the content is fun, but more importantly because of the role they play in STEM students' college experiences. This talk is intended for a broad audience to gain a new perspective on student success in STEM and learn a bit about research coming from this perspective. Speaker bio: Jess Ellis Hagman is an Associate Professor in the Department of Mathematics at CSU. She completed her PhD in Mathematics Education from the joint program between San Diego State University and the University of California, San Diego. Her area of research is undergraduate mathematics education. Her work is focused on dramatically increasing the number and diversity of people who succeed in undergraduate mathematics-especially introductory mathematics courses that often function as a roadblock for STEM intending students. Her current research includes studying characteristics of successful precalculus and calculus programs, focusing on investigating ways departments can create diverse, equitable, and inclusive introductory mathematics programs. Talking Critically about Student Success in STEM
Oct. 06, 2021 4pm (Math 350)	MathClub Markus Pflaum (CU-Boulder) X The question "Can one hear the shape of a drum?" was posed by Marc Kac in 1966 in an article in the American Mathematical Monthly. This question has become a central one in geometric spectral theory, a particular discipline within modern analysis, and could be solved only 30 years later by Carolyn Gordon and David Webb. In the talk the mathematics underlying this famous question will be explained together some modern aspects and developments. And not to forget, the answer will be given at the end of the talk together with a video of a short performance of a famous scientist and bongo player who lectured on the same question. Can one hear the shape of a drum?
Oct. 06, 2021 5pm (MATH 350)	Grad Student Seminar Chase Meadors (CU Boulder) X Some of you may know of Hilbert's famous hotel, but how do you get there from the airport? You take the transfinite subway, which has stations at every ordinal number up to the first uncountable cardinal \aleph_1, the stop at which Hilbert's hotel is located. At each station, only 1 passenger gets off the train, while a countable infinity of passengers get on. How many passengers will arrive at Hilbert's hotel? This talk will introduce basic set-theoretic concepts of ordinals and cardinals, their theory, and a key theorem that will help us get a handle on this situation, hopefully convincing you that \aleph_1 is much weirder than you may or may not have previously thought. Time permitting we will explore how this weirdness also leads to some counterexamples in other fields like topology. The transfinite subway to Hilbert's Hotel
Oct. 07, 2021 11am (Zoom)	Geometry/Analysis Padi Fuster Aguilera (CU Boulder) X We study a particular PDE model for chemotaxis with logarithmic sensitivity and logistic growth. We obtain existence and uniqueness of solutions as well as results for the zero-diffusion limit of the solutions with Neumann boundary conditions. We also show the formation of a boundary layer for the problem with dynamic boundary conditions, as well as some stability results. Numerical simulations will bring some light about the time-scale parameters as well as possible extensions on the problem. This is joint work with Kyle Zhao, Vincent Martinez and Ricardo Cortez. https://cuboulder.zoom.us/j/96510976623 A PDE model for chemotaxis with logarithmic sensitivity and logistic growth
Oct. 07, 2021 3pm (Zoom)	Probability Evgeni S. Dimitrov (Columbia University) X Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability. Gibbsian line ensembles can be thought of as collections of finite or countably infinite independent random walkers whose distribution is reweighed by the sum of local interactions between the walkers. I will discuss some recent progress in the asymptotic study of Gibbsian line ensembles, summarizing some joint works with Barraquand, Corwin, Matetski, Wu and others. Beta-corners processes are Gibbs measures on triangular arrays of interacting particles and can be thought of as analogues/extensions of multi-level spectral measures of random matrices. I will discuss some recent progress on establishing the global asymptotic behavior of beta-corners processes, summarizing some joint works with Das and Knizel. Gibbsian line ensembles and beta-corners processes
Oct. 12, 2021 1pm (Zoom)	Anna Zamojska-Dzienio (Warsaw University of Technology, Poland) X The Yang-Baxter equation is a fundamental equation occurring in integrable models in statistical mechanics and quantum field theory. Description of all possible solutions seems to be extremely difficult and therefore there were some simplifications introduced (V.G. Drinfeld 1992). Biracks are algebras studied in low-dimensional topology which are in a one-to-one correspondence with set-theoretical, non-degenerate solutions to the Yang-Baxter equation. The use of the language of biracks allows us to apply universal algebra tools. In this talk, we describe the generalized retraction relation on a birack which gives new classes of solutions. This is joint work with Premysl Jedlicka and Agata Pilitowska. Biracks and solutions of the Yang-Baxter equation
Oct. 13, 2021 5pm (MATH 350)	Grad Student Seminar Emily Montelius (CU Boulder) X Join us for an interactive talk exploring the wonderful world of tiling. Rather than spending an hour thinking about complex and abstract ideas, come and play with dominoes as we discover the fun properties they have. Together we will work to find or disprove the existence of fault free tilings on rectangles, cylinders, tori, and Möbius strips. Fault Free Tileability of Rectangles, Cylinders, Tori, and Möbius Strips with Dominoes
Oct. 14, 2021 2pm (MATH 350)	Functional Analysis Frederic Latremoliere (University of Denver) X Spectral triples, introduced by A. Connes in 1985, have emerged as the preferred generalization of Riemannian geometry to the noncommutative realm, and provide a new formalism for the study of problems form quantum physics to fractal geometry. Many problems in physics and geometry suggests that a quantification on "how close" spectral triples can be from each others would prove very helpful; however, only heuristics can be found in the literature. Examples of problems where such a notion could prove useful include the convergence of matrix models in mathematical physics, or the geometry of fractal sets constructed, in a natural manner, as limits of simpler spaces. In this talk, we will survey our construction of an actual metric, up to unitary equivalence, on a large class of spectral triples, which indeed provides a framework to discuss such problems . Our construction starts with our work in noncommutative metric geometry, spurred by the work of Rieffel, and our construction of a noncommutative analogue of the Gromov-Hausdorff distance on the class of quantum compact metric spaces. From this initial step, we will see how to enhance our construction to define convergence for Hilbert modules over quantum compact metric spaces, convergence of certain dynamics over quantum compact metric spaces and their modules, and, as a synthesis of these various tools, how to define our metric on spectral triples. A geometry for the space of metric spectral triples Sponsored by the Simons Foundation
Oct. 19, 2021 1pm (Zoom)	Marcel Jackson (La Trobe University, Melbourne) X It is well-known and easy to prove that the variety of groups abstractly captures algebras of permutations under composition and inverse, that the variety of inverse semigroups capture algebras of partial injective functions under composition and inverse, and that the variety of semigroups abstractly capture the algebras of any of total functions, partial functions or binary relations under the operation of composition. In contrast to this, a landmark result of Hirsch and Hodkinson showing the undecidability of determining when a finite algebra is isomorphic to an algebra of binary relations under Tarski’s signature: the usual set theoretic Boolean operations, composition, converse and identity. This is a very rich signature, and it has subsequently been discovered that undecidability of representability begins in weaker signatures. This talk will survey some of the very extensive literature in this area, and an overview of the approaches to undecidability, possibly touching on some new results for one of the weakest known algebraic signature to experience undecidability of representability as binary relations. Undecidability of representability as binary relations
Oct. 19, 2021 2pm (Math 350)	Lie Theory Aram Bingham (Centro de Ciencias Matemáticas, UNAM) X Borel subgroup orbits of classical symmetric spaces are parametrized by families of signed involutions called clans, which provide a combinatorial model for studying questions related to Schubert calculus on symmetric spaces. For symmetric spaces of Hermitian type, clans are grouped into “sects” corresponding to Schubert cells of an associated Grassmannian variety, yielding a cell decomposition of the symmetric space and facilitating a combinatorial description of the closure (Bruhat) order on the orbits. This decomposition reveals coincidences of clans in the largest sect with other well-studied posets of matrix Schubert varieties. We further describe explicit bijections between clans for Hermitian type symmetric spaces and several other combinatorial families of objects, including certain rook placements, set partitions, and weighted Delannoy paths. (Based on joint work with Mahir Can and Ozlem Ugurlu.) The Bruhat order on symmetric spaces
Oct. 19, 2021 4pm (Zoom)	Math Edu Jess Ellis Hagman (Colorado State University) X In this talk I will share my current research that addresses student success in STEM from a critical perspective. A critical perspective on student success means locating student challenges in STEM not within the students' themselves but within the systems at play, and that these systems are failing students not because they are broken but because they are functioning perfectly well based on their design. I will share my research teams' current work focused on student experiences in college precalculus and calculus from a critical perspective, discussing both recent qualitative research and quantitative research studies. I care about these courses personally because I think the content is fun, but more importantly because of the role they play in STEM students' college experiences. This talk is intended for a broad audience to gain a new perspective on student success in STEM and learn a bit about research coming from this perspective. Speaker bio: Jess Ellis Hagman is an Associate Professor in the Department of Mathematics at CSU. She completed her PhD in Mathematics Education from the joint program between San Diego State University and the University of California, San Diego. Her area of research is undergraduate mathematics education. Her work is focused on dramatically increasing the number and diversity of people who succeed in undergraduate mathematics-especially introductory mathematics courses that often function as a roadblock for STEM intending students. Her current research includes studying characteristics of successful precalculus and calculus programs, focusing on investigating ways departments can create diverse, equitable, and inclusive introductory mathematics programs. Talking Critically about Student Success in STEM
Oct. 20, 2021 4pm (Math 350)	MathClub Robin Deeley (CU-Boulder) X Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can consider a function mapping a space to itself. For example, f(x)=x^2 defined on the set of real numbers. Using this formulation, time is represented by iterating the function. In the example f(x)=x^2, if the initial value is 2, then after one unit of time, the value is f(2)=4, after two units of time, the value is f(f(2))=f(4)=16 and so on. We will discuss a number of explicit examples of dynamical systems and the precise mathematical formulation of chaos. We will also learn the answer to the question: why is my dad's favorite number 6174? Dynamical systems, chaos, and my dad's favorite number
Oct. 21, 2021 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X Scarparo has constructed counterexamples to Matui's HK-conjecture. These counterexamples are essentially principal but not principal. For group actions the difference between essentially principal and principal is related to the difference between the action being topologically free and free. I will discuss a counterexample to the HK-conjecture that is principal. Like Scarparo's original counterexample, this counterexample is the transformation groupoid associated to a particular odometer. However, the relevant group is the fundamental group of a flat manifold (and hence is torsion-free) and the associated odometer action is free. A counterexample to the HK-conjecture that is principal
Oct. 26, 2021 1pm (Zoom)	Michael Pinsker (Technical University Vienna, Austria) X Many mathematical objects are naturally equipped with both an algebraic and a topological structure. For example, the automorphism group of any first-order structure is, of course, a group, and in fact a topological group when equipped with the topology of pointwise convergence. While in some cases, e.g. the additive group of the reals, the algebraic structure of the object alone carries strictly less information than together with the topological structure, in other cases its algebraic structure is so rich that it actually determines the topology (under some requirements for the topology): by a result of Kechris and Solecki, the pointwise convergence topology is the only compatible separable topology on the full symmetric group on a countable set. Which topologies are compatible with a given algebraic object has intrigued mathematicians for decades: for example, Ulam asked whether there exists a compatible locally compact Polish topology on the full symmetric group on a countable set (by the above, the answer is negative). In the case of automorphism groups of first-order structures, the question of the relationship between the algebraic and the topological structure has been pursued actively over the past 40 years, and numerous results have been obtained: many of the most popular automorphism groups, including that of the order of the rationals and of the random graph, do have unique Polish topologies. The endomorphism monoid of a first-order structure is algebraically not as rich as its automorphism group, and often allows many different compatible topologies. We show, however, that there is a unique compatible Polish topology on the endomorphism monoids of the random graph, the weak linear order of the rational numbers, the random poset, and many more. This is joint work with L. Elliott, J. Jonušas, J. D. Mitchell, Y. Péresse, and C. Schindler. Uniqueness of Polish topologies on endomorphism monoids of countable structures
Oct. 26, 2021 3pm (MATH 350)	Topology Ezzeddine El Sai (CU Boulder) X Machine learning methods aimed at learning the underlying geometry of data predominantly assume that the underlying geometry is a smooth embedded manifold. This assumption fails for many physical models where the underlying geometry contains singularities. In this talk, we discuss learning the underlying geometry of data within the scope of algebraic geometry and we use this to detect singularities in data. Detecting Singularities in Data
Oct. 28, 2021 2pm (MATH 350)	Functional Analysis Andrew Stocker (CU Boulder) X Expansive systems are a class of topological dynamical systems which exhibit sensitivity to initial conditions. Following work by Klaus Thomsen, we will construct a C-algebra from an asymptotic equivalence relation on the points in a given expansive system. This generalizes the C-algebraic construction made by Ian Putnam for Smale Spaces, which are themselves an important special case of expansive systems. We will then present some results obtained for a type of expansive system called synchronizing systems, and we will compute this C-algebra for some specific examples. No knowledge of dynamical systems will be assumed for this talk. Expansive Systems and their C-Algebras

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