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Events for July – November 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
Nov. 02, 2021 1pm (Zoom)	Laszlo Zadori (University of Szeged, Hungary) X In the talk, I sketch a semantical proof of the conjecture of Garcia and Taylor that congruence permutability is a prime Maltsev condition in the lattice of interpretability types of varieties. The proof was obtained jointly with Gyenizse and Maróti, and it is based on a combinatorial property of certain digraph powers. I also discuss how the present proof is related to the proof of our earlier result on the non-primeness of n-permutability when n>4 and some other result that we obtained for 3-permutability. On the primeness of 2-permutability
Nov. 02, 2021 1:50pm (Zoom)	Math Edu Karina Uhing (University of Nebraska at Omaha) X This talk will highlight students’ learning experiences with active learning in Precalculus, Calculus 1 and Calculus 2 courses using data from Phase 1 of the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) project. Specifically, I will share how students perceive five elements involved with active learning: interactions with their peers during group work, relationships with instructors, formats of courses, assessment, and their affective experiences while learning. Finally, we will discuss how investigating students’ experiences with active learning can help us better design our courses to engage and motivate students to learn. Speaker Bio: Dr. Karina Uhing is an Assistant Professor of Mathematics at the University of Nebraska at Omaha. She has worked on the SEMINAL project for the last 4 years. Currently, Dr. Uhing is part of a large-scale effort to improve Quantitative Reasoning courses at UNO. This semester, she is helping to investigate the transition from an emporium to an active learning model in College and Intermediate Algebra and students’ mathematical and emotional experiences in these courses. Student Experiences with Active Learning in Precalculus Through Calculus 2
Nov. 02, 2021 3pm (On Zoom)	Topology Cherry Ng (CU Boulder) X Bredon homology (and its expanded cousin RO(G)-graded homology) are homology theories suitable for computing homotopical invariants of $G$ -spaces. Such equivariant homology theories have proved useful and powerful, and they played a role in landmark results such has Hill, Hopkins, and Ravenel's work on manifolds of the Kervaire invariant. In this talk, we will discuss both geometric and algebraic methods used to compute Bredon homology, in particular when $G$ is the nonabelian group of order 21. Join Zoom Meeting https://cuboulder.zoom.us/j/98979344859?pwd=K3ZrTWt4Wkk1cllOQ1pkcW4vZ1FCZz09 Meeting ID: 989 7934 4859 Passcode: 787231 Bredon homology of the nonabelian group of order 21
Nov. 03, 2021 4pm (Zoom)	Grad Student Seminar Boris Hanin (Princeton) X Abstract: Deep neural networks are a centerpiece of modern machine learning. They are also fascinating mathematical objects, about which much remains unclear. In this talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical questions in mathematics, ranging from random matrix theory, to optimal transport, and combinatorics of hyperplane arrangements. Join Zoom Meeting https://cuboulder.zoom.us/j/92773933686?pwd=S1pSMWtORmRGUjNQTEtFbFdFRlFSUT09 Meeting ID: 927 7393 3686 Passcode: 146970 What is a Neural Network?
Nov. 03, 2021 4pm (Math 350)	MathClub Magdalena Czubak (CU-Boulder) X The nonlinear Schrodinger equation (NLS) appears in a wide range of physical phenomena. For example, it is a leading order approximation of the slowly varying envelope of waves in optics, and it also the mean field limit in many-body quantum systems. In this talk, we focus solely on the mathematical analysis of NLS, and discuss what it means to solve the equation, and how using simple Calculus, we can establish a formation of a singularity in finite time. The nonlinear Schrodinger equation: wellposedness and blowup
Nov. 04, 2021 11am (Zoom)	Noncomm Geometry Yining Zhang (CU Boulder) X In this talk, I will discuss the curved Koszul duality for associative algebras presented by quadratic-linear-constant (QLC) relations. Let A be a QLC algebra, the Koszul dual coalgebra of the associated quadratic algebra qA is a curved DG coalgebra. Moreover, this curved DG coalgebra gives rise to resolutions of A which can be used to compute the Hochschild and cyclic homology of A. I will describe the cyclic (co)homology of a QLC algebra and its Koszul dual curved DG algebra, and extend a result due to Feigin and Tsygan. Curved Koszul duality and cyclic (co)homology
Nov. 04, 2021 3pm (Zoom)	Probability Konstantin Matetski (Columbia University) X The KPZ universality class includes random growing interfaces, which, after rescaling, are conjectured to converge to the KPZ fixed point. The latter is a Markov process, which has been characterized through the exact solution of TASEP, a particular model in the class. The KPZ equation plays a special role and is conjectured to be the only model connecting the Edwards-Wilkinson (Gaussian) and the KPZ fixed points. In the talk, I will introduce the KPZ fixed point and review recent progress on the KPZ universality. KPZ universality of random growing interfaces
Nov. 05, 2021 3pm (350)	Math Phys Boris Hanin (Princeton University) X Deep neural networks are often considered to be complicated "black boxes," for which a full systematic analysis is not only out of reach but also impossible. In this talk, which is based in part on joint work with Sho Yaida and Daniel Adam Roberts, I will make the opposite claim. Namely, that deep neural networks with random weights and biases (i.e. networks at the start of training) are solvable models. Our approach applies to networks at finite width n and large depth L, the regime in which they are used in practice. A key point will be the emergence of a notion of "criticality," which involves a finetuning of model parameters (weight and bias variances). At criticality, neural networks are particularly well-behaved but still exhibit a tension between large values for n and L, with large values of n tending to make neural networks more like Gaussian processes and large values of L amplifying higher cumulants. Our analysis at initialization has a number of consequences for networks during and after training, which I will discuss if time permits. Random Neural Networks at Finite Width and Large Depth Sponsored by the Meyer Fund
Nov. 09, 2021 1pm (MATH 220)	Miguel Couceiro (Universite de Lorraine, France) X In this presentation we consider aggregation procedures (consensus functions) over median algebras (ternary algebras that subsume several ordered structures such as distributive lattices as well as several combinatorial structures such as median graphs). Our starting point is a recent Arrow type impossibility result that states that any median preserving consensus function over linearly ordered sets is trivial in the sense that it only depends on a single argument. In view of this result, a natural problem is then to identify those median algebras that lead to such impossibility results. In particular, we will show that such impossibility results are inevitable when the codomain contains no cycle, i.e., it is a "tree", and we will provide a surprisingly simple condition that completely describes the latter as median algebras. To broaden the talk, we will also present some recent results that answer the parametrized version of this problem in which dependence is restricted to k arguments. We will conclude by observing that the underlying property to proving such results is that of congruence distributivity, which naturally raises the question whether these results extend to other varieties of algebras, e.g., congruence modular varieties. Impossibility theorems over median algebras and beyond
Nov. 09, 2021 2pm (MATH 350)	Lie Theory Jiayuan Wang (George Washington University) X Fully commutative elements in Coxeter groups $B_{n}$ and $D_{n}$ are completely characterized and counted by Stembridge. Feinberg-Kim-Lee-Oh have extended the study of fully commutative elements from Coxeter groups to the complex setting, giving an enumeration of such elements in complex reflection groups $G(m,1,n)$ . In this talk, we will present a combinatorial connection between fully commutative elements in $B_{n}$ and $G(m,1,n)$ , which allows us to characterize fully commutative elements in $G(m,1,n)$ by pattern avoidance and enumerate them. Further, we will show that fully commutative elements in $G(m,m,n)$ do not have the pattern avoidance property and we will explore full commutativity in $G(m,m,n)$ with different generating sets. Fully commutative elements in complex reflection groups Sponsored by the Meyer Fund
Nov. 09, 2021 3pm (MATH 350)	Topology André Davis (CU Boulder) X In a precise sense, the prime ideals of the stable homotopy category are given by a class of extraordinary co/homology theories called the Morava K-theories K(n). Much like we study rings by localizing at prime ideals, we can study the stable homotopy category by localizing at K(n). Associated to each K(n) is a certain formal group law whose automorphism group G appears on the E_2 page of a spectral sequence that computes the K(n)-local homotopy groups of spheres. In this talk, I hope to provide the necessary background on categorical localization, cohomology theories, and formal group laws to define G (called the Morava stabilizer group) and to describe some related original results. A computation of the action of the Morava stabilizer group on the Lubin-Tate deformation ring
Nov. 10, 2021 4pm (Zoom)	MathClub organized by Padi Fuster (Math For All in Boulder) X Are you interested on learning how to make a scientific poster? Not sure how to get started? Have questions? Join us for an online poster workshop on November 10th from 4pm-5pm organized by Math For All in Boulder! We will cover the following topics: 1. What is a poster presentation? 2. How to pick a topic and find a mentor 3. How to design a poster 4. How to create a poster in LaTeX 5. How to prepare an elevator pitch 6. What to expect at the poster session Registration is not required for this workshop. More info about Math For All in Boulder conference here: https://sites.google.com/view/mathforallnola/satellite-conference/boulder-co Learn how to make a scientific poster!
Nov. 11, 2021 2pm (MATH 350)	Functional Analysis Menevse Eryuzlu (CU Boulder) X We construct a functor that maps C-correspondences to their Cuntz-Pimsner algebras. We then use our functor to investigate the passage of certain C-correspondence relations to the associated Cuntz-Pimsner algebras. If the time permits, we shall discuss other "possible" applications of this functor. A categorical approach to C-algebras arising from C-correspondences
Nov. 11, 2021 3pm (Zoom)	Probability Brian Hall (University of Notre Dame) X The two most basic results in random matrix theory are the circular law and the semicircular law. The circular law says that if N is large and Z is an N x N random matrix with i.i.d. entries of mean zero and variance 1/N, then the eigenvalues of Z will be almost uniformly distributed on the unit disk. The semicircular law says that if N is large and X is a Hermitian random matrix with i.i.d. entries of mean zero and variance 1/N on and above the diagonal, then the (real) eigenvalues of X will have a nearly semicircular distribution on the interval [-2,2]. We now make a simple observation about the relationship between the circular and semicircular laws: twice the real part of the eigenvalues in the circular law has the same limiting distribution as the eigenvalues in the semicircular law. The observation is at one level trivial—if z is uniformly distributed over the unit disk, then 2Re(z) has a semicircular distribution on [-2,2]. But it is, at another level, mysterious: Why should the real parts of the eigenvalues in one random matrix model be related to the eigenvalues in a different random matrix model? In this talk, I will try to persuade you that the relationship between the circular and semicircular laws is not a coincidence but part of a general phenomenon relating the bulk eigenvalue distributions of different random matrix models. For example, if X0 is an arbitrary Hermitian random matrix independent of Z and X, then there is a formula relating the real parts of the eigenvalues of X0+Z to the eigenvalues of X0+X. The talk will be self-contained and have lots of pictures. Relating different random matrix models
Nov. 16, 2021 1:50pm (Zoom)	Math Edu Nancy Kress (CU Boulder) X In this talk I will share results from my dissertation that demonstrate how undergraduate mathematics instructors who are committed to equitable and inclusive instruction can support students' success. I will share results from instructor and student interview data that describes specific instructional practices and the impacts these practices had on students' learning experiences. Areas of particular focus will include community building, use of flexible structures and resources, and student centered instructional strategies. Supporting Student Success in Early Undergraduate Mathematics Courses
Nov. 16, 2021 2pm (Zoom)	Peter Jipsen (Chapman University) X In June 2003 I gave a talk at the Annual Meeting of the Association for Symbolic Logic, University of Illinois at Chicago, on “An online database of classes of algebraic structures”. This list of mathematical structures is still on a website at http://math.chapman.edu/~jipsen/structures, but is mostly just an alphabetical list of links that point to (sometimes incomplete) axiomatic descriptions of about 300 categories of universal algebras. This past summer I started a project with Bianca Newell to recreate this list of (partially-ordered) algebraic structures as a computable LaTeX document that can be checked for consistency and updated more reliably than the previous collection of webpages. In this talk I will describe this project and recent joint work on partially ordered universal algebras with José Gil-Ferez. In this setting, a partially ordered universal algebra is a poset with finitary operations that are order-preserving or order-reversing in each argument, and congruences are replaced by compatible preorders. Our investigations are based on an unpublished paper from 2004 by Don Pigozzi: Partially ordered varieties and quasivarieties, available here [pdf]. A survey of partially ordered algebras
Nov. 16, 2021 2pm (Online)	Lie Theory Peter Tingley (Loyola University Chicago) X We present combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. These come from the realization of the corresponding infinity-crystal using quiver varieties. This results is an expression for the multiplicity as counting words subject to some conditions, somewhat similar to the known Lyndon word combinatorics. As with that framework counting these words is hard, but in our setup error is concentrated, and we obtain a tractable over-count giving a good estimate. The framework is general, but we only work out specifics in rank two and certain rank 3 cases. This includes joint work with Colin Williams and with Patrick Chan. (https://cuboulder.zoom.us/j/94126918788) A quiver variety approach to root multiplicities
Nov. 16, 2021 3pm (zoom)	Topology Martina Rovelli (University of Massachusetts Amherst) X Power's 2-categorical pasting theorem, asserting that any pasting diagram in a 2-category has a unique composite, is at the basis of the 2-categorical graphical calculus, which is used extensively to develop the theory of 2-categories. In this talk we discuss an (\infty,2)-categorical analog of the pasting theorem, asserting that the space of composites of any pasting diagram in an (\infty,2)-category is contractible. This result, which is joint with Hackney—Ozornova—Riehl, rediscovers independent work by Columbus. https://cuboulder.zoom.us/j/98979344859?pwd=K3ZrTWt4Wkk1cllOQ1pkcW4vZ1FCZz09 Meeting ID: 989 7934 4859 Passcode: 787231 An (\infty,2)-categorical pasting theorem
Nov. 17, 2021 4pm (Math 350)	MathClub Menevse Eryuzlu (Postdoc CU-Boulder) X The theory of Hilbert spaces is the building block on which functional analysis is based, and is a crucial tool for quantum mechanics. This talk will provide an introduction to the theory, and a brief discussion on how Hilbert spaces are used in the development of one of the best mathematical formulations of quantum mechanics. Hilbert Space Theory and the Beauty of Infinite Dimensions
Nov. 30, 2021 11am (MATH 350)	Diversity CHAT+ (The Diversity Committee) X We kindly ask you to RSVP at the following link to get a headcount for food: https://forms.gle/DGkd4onizvu2Sby59 Overview What: CHAT+ Who: All math faculty, staff, and graduate students When: Tuesday November 30, 11:00AM-12:00PM + lunch provided after the discussion Where: MATH 350 Why: Promoting the success of first-generation students in our classrooms Moderators: Breeann Wilson and Jennifer Gensler Event description 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 November 30th is to address the challenges faced by first-generation students in higher education and discuss practices we can implement in our classrooms that promote the success of these students. The discussion will be guided by the following short readings: 1) https://all4ed.org/blog/the-challenges-and-privileges-of-being-a-first-generation-college-student/ 2) https://equityalliance.stanford.edu/content/equity-and-intersectionality-serving-first-generation-students-creating-inclusive 3) https://firstgen.naspa.org/files/dmfile/FactSheet-01.pdf (this is a graphic) 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. Here are some additional readings that may prove insightful: 1) https://serc.carleton.edu/sage2yc/firstgen/challenges.html 2) https://www.insidehighered.com/advice/2021/06/01/first-generation-grad-student-laments-lack-career-opportunities-academe-opinion If you have any questions, please reach out. We hope to see you there! Breeann and Jennifer, on behalf of the Diversity Committee Serving First-Generation Students in our Classrooms
Nov. 30, 2021 12pm (Zoom)	Michael Kompatscher (Charles University Prague) X Let $G$ be a permutation group on a $n$ -element set. We then say that an algebra $A$ has a $G$ -term $t(x1,…,xn)$ , if $t$ is invariant under permuting its variables according to $G$ , i.e. $A ⊨ t(x1,…,xn) ≈ t(xπ(1),…,xπ(n))$ for all $π ∈ G$ . Since $G$ -terms appear in the study of constraint satisfaction problems and elsewhere, it is natural to ask for their classification up to interpretability. In the first part of my talk I would like to share a few partial results on this problem. In the second part I am going to discuss the complexity of deciding whether a given finite algebra has a $G$ -term. The most commonly used strategy in showing that deciding a given Maltsev condition is in P, is to show that it suffices to check the condition locally (i.e. on subsets of bounded size). We show that this „local-global“ approach works for all $G$ -terms induced by regular permutation groups $G$ (and direct products of them), but fails for some other „rich enough" permutation groups, such as $Sym(n)$ for $n ≥ 3$ . This is joint work with Alexandr Kazda. $G$ -terms and the local-global property
Nov. 30, 2021 1pm (Zoom)	Jennifer Hyndman (University of Northern British Columbia, Canada) X Birkhoff and Mal'cev independently posed the problem: Describe all subquasivariety lattices. Nurakunov in 2009 showed that there are many unreasonable subquasivariety lattices where unreasonable means there is no algorithm to determine if a particular finite lattice is a sublattice. This sugests refinements of the original question are needed. A subquasvariety lattice has a natural equaclosure operator. Adaricheva and Gorbunov in 1989 defined an equaclosure operator abstractly as having the properties that are known to hold in a natural equaclosure operator. The soon-to-be-published book, A Primer of Quasivariety Lattices by Kira Adaricheva, Jennifer Hyndman, JB Nation, and Joy Nishida, refines the abstract definition of equaclosure operator and provides some answers to the refined question: When is a lattice with an equaclosure operator representable by a subquasivariety lattice and the natural equaclosure operator. This presentation explores some of this new approach. A reader's guide to A Primer of Subquasivariety Lattices
Nov. 30, 2021 3pm (Online)	Lie Theory Jieru Zhu (Okinawa Institute of Science and Technology) X In many settings, the Temperley-Lieb algebra is isomorphic to the endomorphism algebra on the tensor representation for $SL2$ . In characteristic zero, the Jones-Wenzl projectors give descriptions at the morphisms level for tilting modules in characteristic zero. Their characteristic p versions provided by Burrull-Libedinsky-Sentinelli, describe the tilting category for $SL2$ and admit a quiver representation given by Tubbenhauer-Wedrich. Our project extends this result to the mixed case, i.e. a field with characteristic p containing all ?’th roots of unity, gives fusion rules for tensoring with the natural module regarding the objects as well as the morphisms. This is joint work with L. Sutton, D. Tubbenhauer, and P. Wedrich. (Zoom Meeting ID: 941 2691 8788, passcode: algebra) The $SL2$ Tilting Category in Mixed Characteristic
Nov. 30, 2021 3pm (Zoom)	Topology Katharine Adamyk (University of Western Ontarion) X One common application of topological methods to data analysis is the clustering of data sets. Many of the methods for clustering depend on the value of certain parameters, and as these parameters vary, they index what is known as a hierarchical clustering. Jardine introduced the notion of layer points as a condensed description of hierarchical clusterings in 2020, in the context of the 2-parameter clustering defined by path components of degree-Rips complexes. In this talk I will present recent work that develops the theory of multiparameter layer points more generally, as well as a specific application to the original context. A main theme will be stability—under what conditions do similar inputs for a clustering algorithm guarantee similar resulting clusterings? I will focus particularly on the stability problem with respect to subsampling a data set. https://cuboulder.zoom.us/j/98979344859?pwd=K3ZrTWt4Wkk1cllOQ1pkcW4vZ1FCZz09 Meeting ID: 989 7934 4859 Passcode: 787231 Stability for Clustering Methods in Topological Data Analysis

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