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Events for November 2025 – March 2026

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Nov. 04, 2025 1:25pm (MATH 2…	Algebra/Logic Andrea Albano (Universita del Salento, Italy) X The Yang--Baxter equation (YBE) is a fundamental relation in mathematical physics that has its roots in the investigation of many-particle interactions in two-dimensional quantum dynamical systems, where it can be interpreted as governing integrability properties. When a system presents a boundary that interacts with the objects in motion, the Reflection Equation (RE) - as first studied by Cherednik and Sklyanin in 1984 and 1988, respectively - is a condition that ensures the persistence of integrability. To determine a uniform procedure that produces special solutions, in 1990 Drinfel'd suggested studying the set-theoretical YBE, thus paving the way for the introduction of new combinatorial tools in the subject. In recent years, Caudrelier and Zhang initiated the investigation of the set-theoretic formulation of the RE, taking inspiration from the study of soliton collisions on the half-line. The aim of this talk is to provide a self-contained overview of the set-theoretic YBE with a particular attention to the role played by self-distributive structures. Moreover, we study the interplay between bijective non-degenerate set-theoretic solutions of the YBE and their reflections, with a focus on solutions of derived type. Based on a joint work with M. Mazzotta and P. Stefanelli. Set-theoretic solutions of the Yang-Baxter equation and their reflections Sponsored by the Meyer Fund
Nov. 04, 2025 3:30pm (MATH 3…	Topology Ben Knudsen (Colorado State University) X The homology groups of the unordered configuration spaces of a�graph�form a finitely generated module over the polynomial ring generated by its edges; in particular, each Betti number is eventually equal to a polynomial in the number of particles, an analogue of classical homological stability. Wishing to lift this result to an analogue of representation stability, one encounters the unavoidable fact that the corresponding algebraic structure at the level of ordered configuration spaces is non-Noetherian. Thus, finite generation results are likely to be neither useful nor within easy reach. Drawing on ideas from twisted algebra and factorization homology, we circumvent this obstacle to give a complete asymptotic calculation of the Betti numbers of pure graph braid groups over any field and, in characteristic zero, of the multiplicities of many irreducible representations of the symmetric groups. This talk represents joint work with Hainaut and Wawrykow, building on joint work with An and Drummond-Cole. Representation asymptotics in the homology of pure graph braid groups
Nov. 06, 2025 11:15am (MATH …	Algebraic Geometry Lisa Marquand (NYU) X Abstract: Cubic fourfolds have been classically studied up to birational equivalence, with an eye towards rationality problems. We will discuss two other notions of equivalence: Fourier-Mukai equivalence, and `hyperkahler equivalence'. We'll discuss how these equivalences are conjecturely related. We will give new examples of pairs of cubic fourfolds satisfying all three equivalences. In particular, our examples will be pairs of birational cubic fourfolds, with birational Fano varieties of lines, a previously unknown phenomenon. This is joint work with Corey Brooke and Sarah Frei. Cubic fourfolds with birational Fano varieties of lines Sponsored by the Meyer Fund
Nov. 06, 2025 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) X Minimal homeomorphisms of topological spaces provide a source of simple C-algebras whose structure and K-theory can be understood through dynamical systems. I will present results on the existence of minimal homeomorphisms of flat manifolds with positive first Betti number. When the flat manifold has a spin^c structure we will show that the resulting cross product satisfies Poincare Duality for C-algebras. Finally, I will describe ongoing work toward constructing explicit KK-cycle representatives in the presence of minimal flows, in analogy with the classical case of irrational rotation algebras. Flat manifolds, C*-algebras, and duality
Nov. 07, 2025 10:10am (Math …	Math Edu Natalie Snow & JB Shilcutt (New Mexico State University & Utah Tech University) X This workshop will cover student-centered pedagogical practices that can be used in a higher education mathematics setting. We will talk about the pillars of the Activist Approach, discuss how we are employing these methods in both in-person and asynchronous courses at two universities, and share processes we use to build a foundation with our students in order to connect with their interests, motivations, and learning needs. At the end of the session, there will be time for participants to develop their own questions that they would like to ask their students to facilitate their learning. Redefining the Equation: Student-Centered Pedagogies in Mathematics
Nov. 11, 2025 12:10pm (MATH …	Kempner Gregory Berkolaiko (Texas A&M) X Quantum chaos is the study of signatures of chaotic dynamics at the quantum level.� The objects of study include the energy (eigenvalue) or wavefunction (eigenfunction) statistics.� Nodal fluctuations belong to the second class; they express deviations of the number of zeros (or nodal domains) of the eigenfunction from its expected value.� We will discuss the nodal fluctuations in a particular model, discrete Schroedinger operators on graphs.� The conjecture is that the nodal fluctuations are always Gaussian, in the appropriate limit and after appropriate normalization.� While the conjecture has been established in some classes of graphs, it is mostly wide open.� We will review recent progress in this area which combines many different approaches: Morse Theory, Random Matrices, Spectral Graph Theory and Algebraic Geometry. Universality of nodal fluctuations: from quantum chaos to algebraic geometry
Nov. 11, 2025 1:25pm (online)	Algebra/Logic George Metcalfe (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk will be about idempotent semifields, which, from a purely algebraic perspective are just lattice-ordered groups formulated in a restricted language with the group multiplication, neutral element, and lattice-join operation. We will see that although countably infinitely many equational theories of lattice-ordered groups have a finite equational basis, no non-trivial equational theory of idempotent semifields has this property. On the other hand, as in the case of lattice-ordered groups, there are continuum-many equational theories of classes of idempotent semifields. Finally, we will relate the problem of deciding equations in the class of idempotent semifields to the problem of deciding if there exists a right order on a free group satisfying a given finite set of inequalities, and show that these problems are, respectively, co-NP-complete and NP-complete. This is joint work with Simon Santschi. Equational Theories of Idempotent Semifields
Nov. 11, 2025 1:30pm (MATH 3…	Homotopy Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Nov. 11, 2025 1:30pm (MATH 3…	Topology Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Nov. 11, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X We will describe the bounded width portion of the CSP dichotomy theorem. In particular, we will explain what bounded width CSPs are, and present the proof by Barto and Kozik that CSPs whose polymorphism algebras have WNUs for all but finitely many arities, have bounded width.� Bounded width CSPs
Nov. 11, 2025 2:30pm (MATH 3…	Lie Theory Peter Brooksbank (Bucknell University) X Tensors have roughly as many definitions and notations as there are fields that use them. Nevertheless there is some broad agreement on the sort of information one might wish to extract from a tensor given by an array of numbers. One common goal is to change the ambient reference frame in order to reveal some internal structure. For instance, one might wish to know if, by a suitable change of basis, the nonzero entries of the array can be made to cluster in some prescribed manner. In this talk I will discuss clustering techniques whose origins lie in computational algebra and show they can be adapted to tensors that occur in the real world. The algorithms that result from this algebraic perspective have certain advantages�such as provable efficiency and reproducibility�and they can detect cluster patterns that elude existing methods. This is a report on joint work with Martin Kassabov and James Wilson. Clustering algorithms for tensors: an algebraic approach Sponsored by the Meyer Fund
Nov. 12, 2025 4:30pm (MATH 3…	Algebraic Geometry Zhijia Zhang (NYU) X Abstract: The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces. Broadly speaking, a G-variety is a variety X carrying an action of a group G. The group can act via automorphisms of X or via Galois actions if the base field is non-closed. There are close connections, as well as drastic differences between these two types of actions from the perspective of birational geometry. In this talk, I will explore these similarities and differences with a focus on equivariant unirationality of (not only) Fano threefolds. This is joint work with Yuri Tschinkel and Ivan Cheltsov. Title: Equivariant unirationality of Fano threefolds - Note the unusual time and date Sponsored by the Meyer Fund
Nov. 13, 2025 3:35pm (MATH 3…	Grad Student Seminar Jon Kim (CU Boulder) X A moduli space is a parameter space where each point represents some mathematical object. For algebraic geometers, these objects are usually geometric, and moduli spaces help us see how these geometric objects deform and detect their "stability". In this GSS talk, I will give a short survey on the development of moduli spaces in algebraic geometry and provide examples on constructing these moduli spaces. The main result will be showcasing how the moduli space of acute triangles is closely related to the moduli space of elliptic curves. What even is a moduli space?
Nov. 18, 2025 1:25pm (MATH 2…	Algebra/Logic Simon Santschi (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X Lattice-ordered pregroups (l-pregroups) are exactly the involutive residuated lattices where addition and multiplication coincide. Among them, for every positive integer n, the n-periodic l-pregroup F_n(Z) of n-periodic order-preserving functions on the integers plays an important role in understanding distributive l-pregroups and also n-periodic ones. We give a finite axiomatization of the variety generated by F_n(Z). On the way we also obtain some more general results about periodic l-pregroups and we characterize the finitely subdirectly irreducibles of the variety generated by F_n(Z). Joint work with Nick Galatos. Axiomatizing small varieties of periodic l-pregroups
Nov. 18, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X Continuation of last week's talk. Bounded width CSPs, 2
Nov. 18, 2025 2:30pm (MATH 3…	Lie Theory Mandi Schaeffer-Fry (DU) X The McKay Conjecture (now a theorem due to Cabanes--Sp�th) says that there is a bijection between irreducible characters of a finite group G with degree not divisible by p and the corresponding set for the normalizer of a Sylow p-subgroup. Several Galois refinements of this Conjecture exist, positing that the bijection should be compatible with fields of values. I'll discuss joint work with Lucas Ruhstorfer, in which we complete the proof of the original of these Galois refinements, proposed by Isaacs--Navarro in 2002. I'll also discuss several consequences, giving additional local-global properties in the character theory of finite groups. The Isaacs--Navarro Galois Conjecture
Nov. 18, 2025 3:30pm (MATH 3…	Topology Rick TBD
Nov. 19, 2025 4:40pm (MATH 3…	Grad Student Seminar Wei Wu Lu X I'd like to give an overview on some of the basics of automorphic forms, how they arise and avenues of open research regarding them. Automorphic Forms and Other Ellusive Functions
Nov. 20, 2025 11:15am (MATH …	Algebraic Geometry Jon Kim X In 2024, Schock constructed several KSBA compactifications of the moduli space of cubic surfaces. More precisely, he considered pairs consisting of a cubic surface and a boundary divisor given by the sum of the 27 lines, all with the same weight value in the interval (1/9, 1] and provided a finite wall-and-chamber decomposition and described the weighted stable pairs parameterized by the moduli spaces in each chamber. In this talk, I will describe recent work where I provide a similar finite wall-and-chamber decomposition for KSBA compactifications where we weight one �heavy� line with weight b, and the other 26 lines uniformly with weight c. Moduli of (b,c)-weighted stable marked cubic surfaces
Nov. 20, 2025 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X Orbit-breaking in topological dynamical systems was introduced by Ian Putnam in his study of the C-algebras associated to Cantor minimal systems. By breaking an orbit at a single point, Putnam was able to construct all simple unital AF algebras as subalgebras by way of a Cantor minimal system. Since then, orbit-breaking algebras have been used to construct dynamical models for many stably finite �classifiable� C-algebras, most notably the Jiang�Su algebra. In this talk I will highlight these results and also discuss recent work-in-progress with Robin Deeley and Ian Putnam, where we generalize orbit-breaking for a homeomorphism to the setting of a continuous, surjective, local homeomorphism, allowing for purely infinite constructions. Orbit breaking and C*-algebras Sponsored by the National Science Foundation
Dec. 02, 2025 1:25pm (online)	Algebra/Logic Andrea Montoli (Universita degli Studi di Milano) View Online:https://cuboulder.zoom.us/j/96896272260 X We will describe some categorical properties of preordered and right-preordered groups, giving an explicit description of limits and colimits in these categories, studying some exactness properties, and showing that both structures give rise to quasivarieties. We will show that, from an algebraic point of view, the categories of preordered groups and of right-preordered groups share several properties with the one of monoids. Joint work with Maria Manuel Clementino and Nelson Martins-Ferreira. (Right-)preordered groups from a categorical perspective
Dec. 03, 2025 4:40pm (MATH 3…	Grad Student Seminar Stephanie Oh (CU Boulder) X Spectral sequences are fundamental computational tools in algebraic topology/geometry and homotopy theory. In this talk, I will give an example-driven introduction to spectral sequences. Some familiarity with homological algebra and/or Top 2 will be helpful. What even is a spectral sequence?
Dec. 12, 2025 1:30pm (Math 2…	Noncomm Geometry Vladimir Baranovsky (University of California, Irvine) X Let (M, w) be a complex manifold with an holomorphic symplectic form, or an algebraic version of such a pair. Consider also a pair (X, E) consisting of a coisotropic submanifold X in M and a vector bundle E on X. Then (local) sections of E form a module over the ring O of (local) functions on M. Given a deformation quantization O_h of functions, one can ask whether E admits a similar deformation quantization E_h as a module over O_h. For Lagrangian X this is equivalent to existence of a projectively flat connection on E with specific properties. For general coisotropic X only necessary conditions on some characteristic classes are known. The plan is to present some results and conjectures related to the problem, based on recent work of Bogdanova-Vologodsky and a Harish-Chandra bundle approach to quantizations and their Deligne classes, introduced earlier by Bezrukavnikov-Kaledin. Quantization of symplectic manifolds and vector bundles on coisotropic submanifolds.
Dec. 16, 2025 3:30pm (MATH 3…	Topology Bowen Yang (Harvard Center of Mathematical Sciences and Applications) X I will outline a classification framework for quantum phases within the setting of stabilizer states and quantum cellular automata (QCA).� Both admit a precise algebraic formulation�stabilizer codes as modules over Laurent polynomial rings, and QCA as locality-preserving automorphisms of operator algebras�through which topological invariants such as Witt classes and boundary charge modules arise.� I will review my recent work classifying Clifford QCA and Pauli stabilizer codes, which fit naturally into the same mathematical framework. A Case Study in the Classification of Quantum Phase Sponsored by the Meyer Fund
Jan. 14, 2026 4:40pm (MATH 3…	Grad Student Seminar Basia Klos (CU Boulder) X Does that question keep you up at night? If yes, you're in luck - in this talk, we'll define these algebraic objects, which are ubiquitous in the representation theory of infinite-dimensional Lie algebras and also appear in number theory and physics. We'll give a friendly example of a VOA and might even mention why you should care. What even is a vertex operator algebra?
Thu, Jan. 15 11:15am (MATH …	Algebraic Geometry AG Group Organizational meeting
Thu, Jan. 22 2:30pm (MATH 3…	Functional Analysis Dorin Dumitrascu (Adrian College) X I will discuss some aspects of the bivariant K-theory developed by Le Gall. (P. Y. LeGall, Th\'eorie de Kasparov \'equivariante et groupo\"{\i}des. I, K-Theory 16 (1999), 361--390.) Equivariant KK-theory for groupoids acting on C*-algebras (after Le Gall)
Tue, Jan. 27 1:25pm (online)	Algebra/Logic David Stanovsky (Charles University) View Online:https://cuboulder.zoom.us/j/96896272260 X How many groups of order n are there, up to isomorphism? And what about quasigroups, semigroups, and other types of algebraic structures? Why the combinatorial explosion for quasigroups and semigroups, and not for groups? Or, actually, what is the true asymptotic behavior behind enumeration of groups? I will show some number series. I will briefly discuss enumeration methods. I will start with a brief overview of classical results on groups. In the second half of the talk, I will turn to the class of quandles, which provides an exciting playground for various types of enumeration methods. Enumeration of groups and quandles
Tue, Jan. 27 5pm (Math 350)	Math Club Siddhant Agrawal X The Navier Stokes equation is a partial differential equation that describes the motion of viscous fluids. It arises naturally in engineering and other scientific fields. In this talk, we'll derive the Navier Stokes equation and discuss some of its basic properties. We'll also discuss the famous Millennium Prize Problem concerning the Navier Stokes equation. Note: The recommended prerequisite for this talk is Calculus 3, but all are welcome! What is the Navier Stokes Equation?
Thu, Jan. 29 2:30pm (MATH 3…	Functional Analysis Dorin Dumitrascu (Adrian College) X I will give the definition of Le Gall for the equivariant KK-theory under the action of a Hausdorff groupoid, propose a construction for locally compact locally Hausdorff groupoids, and work out an example coming from foliations. Equivariant KK-theory for groupoids acting on C*-algebras (part 2)
Thu, Jan. 29 11:15pm (MATH …	Algebraic Geometry Bob Kuo (University of Colorado Boulder) X Mustafin varieties are a particular class of degenerations of projective space. Projective space, and their subvarieties, have many nice properties. Thus, one might wonder what aspects of projective geometry transfers over to Mustafin varieties. In this talk, we will explore this question through the use of tropical geometry. In particular, we will discuss the Picard group of Mustafin varieties, then describe an analogue of Bezout's theorem for Mustafin varieties. A degenerate analogue of projective geometry
Fri, Jan. 30 12:20pm (Math …	Math Edu Rebekah Jones X Join us to discuss potential topics and speakers for the Seminar on Undergraduate Math Education (SUME) this semester. We encourage all those interested in attending SUME this semester to attend! We'll also spend some time exploring mathematical autobiography assignments�their purpose, how they can support certain instructional goals, and considerations for implementing these assignments in a math classroom. Following our discussion, participants will have the opportunity to write their own brief mathematical autobiographies and share reflections from the experience. Attendees are encouraged (but not required) to read the recent paper on this topic linked below. https://doi.org/10.1080/10511970.2025.2571610 SUME Open House / Discussion of mathematical autobiography assignments
Tue, Feb. 3 12:10pm (MATH …	Kempner David Renfrew (SUNY Binghamton) X We show for a large class of entire functions, f, that after proper rescaling, on compact sets, the derivatives of f converge to cosine, in particular their roots become evenly spaced. This proves a conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789�3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] for our class of entire functions. A main ingredient of our proof is to show that high derivatives of high degree polynomials behave like Hermite polynomials, which we prove using the techniques from the newly developed field of finite free probability. This is joint work with Andrew Campbell and Sean O'Rourke. Universality for roots of derivatives of entire functions
Tue, Feb. 3 1:25pm (online)	Algebra/Logic Sara Ugolini (IIIA-CSIC Barcelona) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we begin by considering the semiring of the natural numbers with truncated difference, N = (N, +, *, -, 0, 1). Its equational theory is not recursively axiomatizable, due to the fact that one can essentially encode in it the undecidability of Hilbert�s tenth problem. Our aim is to study finitely axiomatizable varieties of semirings with difference which include the one generated by N, and are as close to it as possible. To this end, we introduce the variety of almost natural semirings with difference, AN. We show that the subdirectly irreducible algebras in this variety coincide with the models of PA, a weak form of Peano Arithmetic without induction that is an axiomatic extension of Robinson Arithmetic. Models of PA are known to satisfy all Sigma_1 sentences true in N. This variety can be axiomatized by a few simple equations and enjoys several appealing universal-algebraic properties: it is connected to lattice-ordered rings, it is a discriminator variety, ideal determined and 0-regular; thus it admits an associated 0-assertional logic. Nevertheless, we will see that its connection to arithmetic still yields an undecidable equational theory. This talk is based on ongoing joint work with Guillermo Badia, Xavier Caicedo, and Carles Noguera. Almost natural semirings with difference
Wed, Feb. 4 2:10pm (MATH350)	Math Phys Markus Pflaum (CU Boulder) X The semester theme will be the mathematics of Schr�dinger operators� and applications in quantum many-body theory and quantum chemistry. The meeting will be an introductory and organizational meeting. For more please see the seminar webpage under https://math.colorado.edu/mathphysics/ Intro to Schr�dinger operators and semester theme
Tue, Feb. 10 1:25pm (online)	Algebra/Logic Claudia Muresan (University of Bucharest) View Online:https://cuboulder.zoom.us/j/96896272260 Abstracting congruence extensions through complete join�semilattice morphisms between commutator lattices
Tue, Feb. 10 5pm (Math 350)	Math Club Nat Thiem X Come hear about the math department's summer REU program! REU stands for Research Experiences for Undergrads. Our summer REU program is an opportunity for you to gain experience and see what math research is like. Once available, descriptions of the different projects will be posted at www.colorado.edu/math/undergraduate-program/summer-research-undergraduate. Or come to the info session to hear about the projects and get your questions answered! Summer REU Info Session
Wed, Feb. 11 2:10pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M University) View Online:https://cuboulder.zoom.us/j/97049173677 X As a warm-up for the semester, we will explore the time evolution in a finite-dimensional (d=2 mostly) Schr�dinger equation, its relation to the quadratic form and their visualization on the Bloch sphere. If time permits, we will briefly discuss why a 2-dimensional picture is sometimes appropriate even when working with unbounded Schr�dinger operators. Warm-up: Visualizing Schr�dinger's equation in finite dimensions
Wed, Feb. 11 4:40pm (MATH 3…	Grad Student Seminar Colin Jackson X What makes a function earn the title of a zeta function? We will start by looking at the Riemann zeta function, and then generalizations of it and see that if it walks like a zeta function and quacks like a zeta function, then its a zeta function Zeta Function 101
Thu, Feb. 12 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce a class of dynamical systems called shifts of finite type. There are a number of C-algebras one can construct from a shift of finite type. I will discuss properties of these C-algebras such as rational Poincare duality and rational isomorphism. Rationalizing shifts of finite type - Part I
Thu, Feb. 12 11:15pm (MATH …	Algebraic Geometry Bob Kuo X In this talk, we'll discuss tropical and toric geometry, and a relationship between the two given by Mustafin varieties. A degenerate analogue to projective geometry part II
Fri, Feb. 13 12:20pm (MATH …	Math Edu Shelby Stanhope (US Air Force Academy) View Online:https://cuboulder.zoom.us/j/99367133807 X Students often find the transition from two-dimensional to three-dimensional thinking in multivariable calculus challenging. Computer visualization and tactile models can help bridge this gap and deepen students� spatial understanding of concepts. CalcPlot3D is a free, web-based applet for 3D graphing that is easy for students and instructors to use due to its code-free, menu-driven interface with fillable textboxes, dropdown lists, and checkboxes. In this presentation, I will show demonstrations that instructors can use to illuminate concepts and visualizations that students can easily create themselves. In addition, I will discuss several classroom activities that incorporate 3D-printed models, allowing students to physically explore concepts in small groups. Together, these tools provide engaging ways for instructors to support student learning and help cultivate stronger geometric intuition in multivariable calculus. Supporting conceptual understanding in multivariable calculus using computer visualization and classroom activities with 3D-printed models
Tue, Feb. 17 2:30pm (MATH 3…	Lie Theory Carlos Ortiz (Colorado State University) X A fundamental problem in topology is to determine when two spaces are distinct. For surfaces, classical invariants suffice, but for three-dimensional manifolds the question is considerably harder. The Witten-Reshetikhin-Turaev invariants, originating in quantum field theory, provide one family of tools. For torus bundles, i.e. 3-manifolds built by cutting a torus, applying a mapping class in SL(2,Z), and regluing, the skein algebra embeds into a non-commutative torus at roots of unity, yielding a finite-dimensional representation that makes these invariants concretely computable. Exploiting this structure, we develop a classical dynamic programming algorithm and a quantum algorithm that encodes the computation into logarithmically many qubits, achieving an exponential reduction in space. We further identify a natural coefficient-counting problem that is #P-complete yet admits efficient quantum approximation. The first half of the talk will be expository, requiring only linear algebra and modular arithmetic. The second half will outline the algorithmic results. How to tell shapes apart using quantum computers
Tue, Feb. 17 3:30pm (MATH 3…	Topology Gregory Berkolaiko (Texas A&M) X The Rayleigh-Ritz method approximates the eigenvalues of a large Hermitian matrix B with Ritz values, which are the eigenvalues of B's restriction() to a smaller trial subspace S. We can view the k-th Ritz value as a real-valued function ("Ritz energy landscape") on the manifold of all possible s-dimensional trial subspaces, the Grassmannian $Grs(Cn)$ (or $Grs(Rn)$ for the real symmetric case). Motivated by questions from quantum chemistry and spectral optimization, this talk explores the topology of the Ritz energy landscape. A Morse function is called "perfect" if it describes the topology of its domain in the most efficient way possible, meaning the number of its critical points of each type exactly matches the corresponding Betti number of the space. We demonstrate that for a matrix B with distinct eigenvalues, the Ritz landscape is indeed perfect. While the function itself is not everywhere smooth and its critical points are not isolated --- and not even Morse-Bott --- its critical structure is nevertheless well-defined and ultimately reflects the topology of the Grassmannian in a minimal, perfect way. To be more precise, we show that the filtration of the Grassmannian by the sublevel sets of the k-th Ritz value is homologically perfect. The proof proceeds by introducing a suitable perturbation which ensures that points of non-smoothness are not critical (by a theorem of Zelenko and the presenter) and that the remaining smooth critical points are isolated. Based on a joint work with Mark Goresky (IAS). Footnote (): the term "restriction" is appropriate in the equivalent formulation of eigenvalues of quadratic forms. For an operator B, we apply it to vectors in S and then project the result orthogonally back onto S; this is called a "compression" of B. Ritz energy landscape is perfect (almost) Morse
Tue, Feb. 17 5pm (Math 350)	Math Club Edouard Heitzmann X The legal standard set in Rucho v Common Cause puts the onus on the plaintiffs in a Voting Rights Act (VRA) case to demonstrate that a map is a racial rather than a partisan gerrymander in order for it to be struck down as unlawful. This means plaintiffs have to 'do the homework' of the defendants for them: they must produce a map that is at least as politically gerrymandered as the defendants drew, while achieving better racial representation outcomes. This standard was successfully met by a group of mathematicians in the El Paso redistricting case, winning in federal court before the Supreme Court shadow docket put a hold on the decision, allowing the racial gerrymander to go through. The mathematicians who accomplished this used Monte Carlo Markov Chain (MCMC) methods to draw a so-called 'ensemble' of millions of alternative congressional maps for Texas, and used statistical methods to show that the enacted map was an outlier for racial representation among the maps that had similar partisan outcomes. In this talk I will go over these mathematical details, as well as describe the computational tools currently used in this field. Note: If you have a working Jupyter Notebook installation, you are encouraged to bring it to the talk, as you will have the opportunity to follow along the computational demos included in the talk. The Mathematics of Redistricting�what they did in Texas
Wed, Feb. 18 2:10pm (Math350)	Math Phys Howy Jordan (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 The spectral theorem and projection valued measures I
Thu, Feb. 19 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce a class of dynamical systems called shifts of finite type. There are a number of C-algebras one can construct from a shift of finite type. I will discuss properties of these C-algebras such as rational Poincare duality and rational isomorphism. Rationalizing shifts of finite type - Part II
Fri, Feb. 20 12:20pm (Math …	Math Edu Peter Karanevich X This talk will introduce Lev Vygotsky's learning theory of the zone of proximal development. We will then transition to an application of the theory, the concept of productive struggle. Participants will define productive struggle and learn how to modify questions to encourage students to engage in productive struggle. Productive Struggle in the Zone of Proximal Development
Tue, Feb. 24 12:10pm (MATH …	Kempner Liviu Suciu (The Pennsylvania State University) X I plan to discuss several related arithmetic and analytic dualities governed by the M�bius function and the sawtooth function. While these dualities�whether pointwise (twisted or untwisted), or functional in the L^2 or continuous setting�are formally valid, identifying conditions under which they become genuine identities is a subtle and challenging problem. It draws on deep results in analytic number theory, including Vinogradov-type bounds for exponential sums over primes (Davenport; de la Bret�che�Tenenbaum), as well as Tauberian theory (Wintner; Ingham). Arithmetic and analytic dualities governed by the Mobius and sawtooth functions
Tue, Feb. 24 1:25pm (online)	Algebra/Logic Zoltan Vidnyanszky (ELTE Budapest) View Online:https://cuboulder.zoom.us/j/96896272260 X Descriptive combinatorics is a field concerned with graph theoretic problems on nice (definable) infinite graphs. In this first half of the talk, I will introduce the field of descriptive combinatorics and discuss some of the basic results of the area. Then, I will turn to the descriptive version of complexity problems, in particular, the CSP Dichotomy: it turns out that the finitary complexity landscape is only partially reflected in the descriptive context. CSPs in the descriptive context
Tue, Feb. 24 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X The E8 root system is a highly symmetric configuration of vectors, corresponding to the 240 spheres that touch a given one in the densest possible packing of spheres in 8-dimensional Euclidean space. Despite this eightness, some combinatorial features of the root system are much easier to understand in terms of 9-dimensional coordinates. We will use this point of view to gain insight into a certain tightly structured partially ordered set, by using the combinatorics of perfect matchings and Fano planes. This is based on work in progress with Tianyuan Xu (University of Richmond). The ninefold symmetry of the E8 root system
Wed, Feb. 25 2:10pm (Math350)	Math Phys Howy Jordan (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 X Zoom Password 080619 The spectral theorem and projection valued measures II
Wed, Feb. 25 4:40pm (MATH 3…	Grad Student Seminar Daniel Lyness (CU Boulder) X Tori are cool. Varieties are dope. Fans are� related somehow? Prepare to dive into the world of Toric Varieties, which are varieties with a torus embedded inside. We�ll see how lots of our favourite examples of varieties are actually toric varieties, and also how a Toric Variety can be defined from the combinatorial data of a fan (the type used in the 18th century on a hot day). I�ll define everything, but having taken AG1 or knowing what Spec(R) is for a ring R will be an advantage. What even is a Toric Variety?
Fri, Feb. 27 11:10am (MATH …	Algebraic Geometry Lior Alon (MIT) X Abstract: The Poisson summation formula tells us that a lattice and its dual lattice are related through Fourier transform: the Fourier transform of the counting measure of one is the counting measure of the other. The search for non-periodic analogues of Poisson summation�discrete sets whose Fourier transform is again a discrete measure�has appeared independently across number theory, harmonic analysis, and crystallography. In the physical setting, the Fourier transform of the counting measure of an atomic structure is exactly the diffraction pattern observed experimentally. The term quasicrystal refers to a non-periodic set whose diffraction is a pure point measure, and the discovery of such materials by Dan Shechtman in 1984 profoundly altered crystallography and led to a Nobel Prize. A major mystery that remained unresolved until very recently was whether one could find a quasicrystal whose Fourier transform is supported on a discrete (rather than merely countable) set. These objects are now called Fourier quasicrystals (FQs), and until 2020 only the trivial periodic examples were known. Kurasov and Sarnak constructed the first genuinely non-periodic one-dimensional FQ using Lee�Yang polynomials, multivariate polynomials whose zeroes avoid prescribed regions of the complex plane. In our recent work, we show that every one-dimensional Fourier quasicrystal arises from the Kurasov�Sarnak construction via Lee�Yang polynomials, yielding a complete classification in dimension one. We then extend this framework to all dimensions by introducing Lee�Yang varieties, high-codimension algebraic varieties whose geometric and analytic properties govern the Fourier structure of the associated quasicrystals. The talk will introduce Fourier quasicrystals, Lee�Yang polynomials, and Lee�Yang varieties, and explain the geometric mechanism of generating summation formulas from algebraic varieties and how it is related to real-rootedness of trigonometric equations. No prior background will be assumed. Joint work with Alex Cohen, Cynthia Vinzant, Mario Kummer, and Pavel Kurasov. Fourier Quasicrystals and Lee�Yang Varieties
Fri, Feb. 27 2:30pm (Math 3…	Probability Lior Alon (MIT) X Motivated by Berry�s random wave model for chaotic domains, high-energy eigenfunctions are expected, at the scale of the wavelength, to behave like random waves. Accordingly, the size of nodal sets is determined to first order by the Weyl law, while its second-order fluctuations are expected to be universal. In analogy with spectral statistics, we refer to these fluctuations of the nodal set size as nodal statistics. Beginning with work of Berry, and later of Blum�Gnutzmann�Smilansky and Bogomolny�Schmit, it was conjectured that in chaotic systems nodal statistics are asymptotically Gaussian. While striking mathematical results support this picture on the sphere (Nazarov�Sodin), arithmetic symmetries on the torus prevent chaoticity and lead to a breakdown of universality, as shown by Wigman and collaborators and by Marinucci, Rossi, and Peccati. In this talk I will follow Smilansky�s insight and focus on nodal statistics in graph-based models. For quantum graphs and discrete operators on graphs, Berkolaiko�s nodal magnetic theorem relates nodal statistics to the stability of eigenvalues under magnetic perturbations. This connection yields Gaussian limiting statistics for quantum graphs with disjoint cycles (Alon�Band�Berkolaiko), and, combined with Morse inequalities, extends to random discrete operators on finite graphs with disjoint cycles and to complete graphs with strong on-site disorder (Alon�Goresky). I will conclude with recent joint work on nodal statistics for random matrices (Alon�Mikulincer�Urschel), showing that nodal statistics for GOE matrices obey a semicircle law rather than the conjectured Gaussian behaviour. If time permits, I will briefly discuss ongoing work on the Rosenzweig�Porter model, where adding a random on-site potential to a GOE matrix leads to nodal statistics interpolating from semicircle behaviour at low disorder to Gaussian behaviour at strong disorder, suggesting a phase transition between universality classes and a connection to localization�delocalization phenomena. Nodal statistics from quantum graphs to random matrices: universality and phase transitions
Fri, Feb. 27 11:10pm (MATH …	Math Phys Lior Alon (MIT) X The Poisson summation formula tells us that a lattice and its dual lattice are related through Fourier transform: the Fourier transform of the counting measure of one is the counting measure of the other. The search for non-periodic analogues of Poisson summation � discrete sets whose Fourier transform is again a discrete measure � has appeared independently across number theory, harmonic analysis, and crystallography. In the physical setting, the Fourier transform of the counting measure of an atomic structure is exactly the diffraction pattern observed experimentally. The term quasicrystal refers to a non-periodic set whose diffraction is a pure point measure, and the discovery of such materials by Dan Shechtman in 1984 profoundly altered crystallography and led to a Nobel Prize. A major mystery that remained unresolved until very recently was whether one could find a quasicrystal whose Fourier transform is supported on a discrete (rather than merely countable) set. These objects are now called Fourier quasicrystals (FQs), and until 2020 only the trivial periodic examples were known. Kurasov and Sarnak constructed the first genuinely non-periodic one-dimensional FQ using Lee�Yang polynomials, multivariate polynomials whose zeroes avoid prescribed regions of the complex plane. In our recent work, we show that every one-dimensional Fourier quasicrystal arises from the Kurasov�Sarnak construction via Lee�Yang polynomials, yielding a complete classification in dimension one. We then extend this framework to all dimensions by introducing Lee�Yang varieties, high-codimension algebraic varieties whose geometric and analytic properties govern the Fourier structure of the associated quasicrystals. The talk will introduce Fourier quasicrystals, Lee�Yang polynomials, and Lee�Yang varieties, and explain the geometric mechanism of generating summation formulas from algebraic varieties and how it is related to real-rootedness of trigonometric equations. No prior background will be assumed. Joint work with Alex Cohen, Cynthia Vinzant, Mario Kummer, and Pavel Kurasov. Fourier Quasicrystals and Lee�Yang Varieties
Tue, Mar. 3 2pm (online)	Algebra/Logic Ana Belen Avilez Garcia (Chapman University) View Online:https://cuboulder.zoom.us/j/96896272260 X Cozero elements of a frame play an important role in point-free topology. The set of cozero elements, Coz L, of a frame L is a sub $σ$ -frame of L (that is, a sublattice closed under countable suprema and finite infima). Moreover, the lattice Coz L join-generates the frame L if and only if L is completely regular (a result analogous to the classical one for completely regular topological spaces). Within the setting of completely regular frames, we consider the Dedekind�MacNeille completion of the lattice of cozero elements, which in this context coincides with the Bruns�Lakser construction. The frame obtained through this process turns out to be a sublocale of the original frame, specifically, the smallest sublocale containing Coz L. A central aim of the talk is to compare this sublocale with the original frame and to present results and examples showing when the two coincide and when they differ. Viewing Coz L both as a join-generating sublattice and through its completion leads naturally to two related but distinct classes of frames: cozero frames and perfectly regular frames. We will examine the relationship between these notions and provide illustrative examples. This is an ongoing joint work with Guram Bezhanishvili and Joanne Walters-Wayland. Cozero frames and perfectly regular frames
Wed, Mar. 4 2:10pm (Math350)	Math Phys Markus J. Pflaum (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 The theory of Heitler-London
Wed, Mar. 4 3:30pm (MATH 1…	Diversity Siddhant Agrawal, Robin Deeley, Sarah Petersen, Joseph Timmer (CU Boulder) X From adjunct positions to postdocs to faculty, there are a variety of academic jobs, and the application process for those jobs can be daunting. Join our panelists, Professors Siddhant Agrawal and Robin Deeley, Teaching Professor Joseph Timmer, and Postdoctoral Scholar Sarah Petersen, who will share their insights into navigating the academic job market. Designed for those entering the job market in the near future, this session aims to replace uncertainty with strategy and actionable guidance. Pizza will be served! Academic Job Panel
Tue, Mar. 10 1:20pm (MATH 3…	Homotopy Shauly Ragimov (University of Chicago) X I will discuss higher semi-additive character theory, a framework for (n-t)-fold characters that unifies the classical monoidal character and the transchromatic character. Roughly speaking, the goal is to study character maps from R-valued functions on a pi-finite space A to S-valued functions on the (n-t)-fold p-typical free loop space of A, in a way that is functorial not only for restriction maps but also for transfers along pi-finite spaces. A central point is that every infinity-commutative monoid admits a universal character. I will describe key structural properties of this universal character, including chromatic blue shift and higher cyclotomic descent, and I will briefly indicate how it interacts with other higher semi-additive constructions such as the semi-additive Fourier transform. For K(n)-local objects, I will describe an explicit formula for the universal character and explain how it recovers the transchromatic character for Morava E-theory. I will also discuss the natural action of GL_{n-t}(Zp) on the universal character, whose fixed points agree with rationalization when t=0. Higher semi-additive character theory
Tue, Mar. 10 1:25pm (online)	Algebra/Logic Riley Thornton (Carnegie Mellon) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk is a sequel to Zoltan Vidyanszky's talk a couple weeks ago. I will explain some of the questions descriptive set theorists ask about homomorphisms between relational structures, and I will indicate the subtleties involved in adapting the algebraic approach to homomorphism problems in this context. I will also pose some purely algebraic questions that arise from this project. More on CSPs and descriptive set theory
Tue, Mar. 10 2:30pm (MATH 3…	Lie Theory Spencer Daugherty (CU Boulder) X Gessel and Zhuang introduced the concept of shuffle-compatibility of statistics on permutations of subsets of \N to describe statistics whose multiset of values on the shuffles of two disjoint permutations is determined exactly by the size and statistic values of the two permutations being shuffled. Shuffle-compatibility implies the existence of an algebraic structure on the equivalence classes induced by the statistic. For example, the descent set statistic is shuffle-compatible, and the algebra on the equivalence classes it induces is isomorphic to the Hopf algebra of quasisymmetric functions. In this talk, we generalize shuffle-compatibility to objects such as words, parking functions, and set partitions using the Hopf monoids associated with these objects. We cover a variety of well-known statistics on each object. We define various algebraic structures on the equivalence classes formed by these statistics that are, in many cases, quotients of (or isomorphic to) well-known combinatorial Hopf algebras such as FQSym, WQSym, PQSym, and NCSym. Generalizing shuffle-compatibility using Hopf monoids
Tue, Mar. 10 5pm (Math 350)	Math Club Harrison Stalvey (CU Boulder) X Take notes, outline textbooks, work out a lot of problems, visit instructor office hours�These are among answers to the question, "How do we study?" But what about the question, "How do we learn?" Specifically, what happens in our mind developmentally as we study mathematics? In this talk, we will discuss one particular learning theory that describes the learning of advanced mathematical concepts. Then we will apply the learning theory to make a cognitive model of a construction of the integers, which is a topic covered in MATH 2002, Number Systems, at CU Boulder. How Do We Learn Mathematics?
Wed, Mar. 11 4:40pm (MATH 3…	Grad Student Seminar Edouard Heitzmann X The legal standard set in Rucho v Common Cause puts the onus on the plaintiffs in a Voting Rights Act (VRA) case to demonstrate that a map is a racial rather than a partisan gerrymander in order for it to be struck down as unlawful. This means plaintiffs have to 'do the homework' of the defendants for them: they must produce a map that is at least as politically gerrymandered as the defendants drew, while achieving better racial representation outcomes. In this talk I will describe how Markov Chain Monte Carlo (MCMC) methods are typically used to solve these problems, and use this opportunity to describe the underlying mathematics. The Mathematics of Redistricting
CANCELED Fri, Mar. 13	Math Edu Rebecca Swanson (Colorado School of Mines) TBD
Mon, Mar. 23 7pm (Remote (Z…	Functional Analysis Alonso Delf�n (CU Boulder) View Online:97482826489 X Part I: Introduction, main definitions, and Banach-Lamperti's theorem. Zoom ID: 97482826489 Mini-course L^p-operator algebras: Part I
Tue, Mar. 24 2:30pm (MATH 3…	Lie Theory Juan Villareal X In this talk, I will present several scattering amplitude formulas arising in quantum field theory and explain how they give rise to new infinite-dimensional algebraic structures and associated symmetries. This work is based on ongoing collaboration with undergraduate students from the REU 2025. Lie algebras and celestial holography
Tue, Mar. 24 7pm (Remote (Z…	Functional Analysis Alonso Delf�n (CU Boulder) View Online:97482826489 X Part II: Group(oid) algebras, crossed-products, and rigidity. Zoom ID: 97482826489 Mini-course L^p-operator algebras: Part II
Wed, Mar. 25 2:10pm (MATH350)	Math Phys Evan Wickenden (CU Boulder Physics) Periodic Schr�dinger operators and Bloch theory I
Thu, Mar. 26 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X A common strategy for understanding the structure of a C-algebra is to decompose it into more manageable subcomponents�such as its lattice of ideals or subspaces arising from a grading�with the aim of reconstructing global information from local data and the way these pieces interact. Conversely, one can begin with structured pieces and ask how to assemble them into a C-algebra. A well-studied example of this approach is the theory of Fell bundles over discrete groups. In this talk, we present a generalization of Fell bundles from discrete groups to unital based rings, a broader algebraic framework that accommodates richer types of gradings. We describe how to construct a reduced C*-algebra of sections associated to such a bundle and discuss examples arising from group gradings and coactions of compact quantum groups. This is joint work in progress with Suvrajit Bhattacharjee, Bhishan Jacelon, and R�amonn � Buachalla. Fell bundles over unital based rings Sponsored by the National Science Foundation
Thu, Mar. 26 3:35pm (MATH 3…	Probability Andrew Campbell (ISTA) X A result dating back at least 40 years is that the roots of Hermite polynomials are asymptotically distributed according to the semicircle distribution, which is also serves the role of the normal distribution in�Voiculescu's�free probability theory. Hermite polynomials are also crucial to understanding the eigenvalues of the Gaussian Unitary Ensemble, a particularly important distribution of random matrices for which an infinite version is simple to define. We will discuss a class of polynomials which provide analogous approximations for other stable distributions in free probability and other infinite ensembles of random matrices. We will look at the asymptotic properties of the roots of these polynomials and how they arise naturally in the study of zeros of analytic functions.�As a special case we will look at the corresponding polynomial for the Riemann zeta function. This talk is based mostly on joint work with Jonas Jalowy. Polynomial approximations of free stable laws, infinite random matrices, and the Riemann zeta function.�
Fri, Mar. 27 12:20pm (Math …	Math Edu Nick Schneider (Astrophysical & Planetary Sciences, CU Boulder) X We report the findings of a study on career and advanced degrees outcomes for undergraduate majors in Astrophysical and Planetary Sciences. The APS major was created in 2021, with two primary intentions: (1) preparing students for graduate schools and careers in research, and (2) preparing students for careers in teaching, informal education, policy and journalism. Over 25 years of growth,� we have graduated nearly 900 students but have little information on their paths after graduation. Our 2-year study located ~75% of our graduates on LinkedIn, and tabulated their self-reported career and higher education information. While 10-15% of our students followed the research path, we find the vast majority entered the STEM workforce, with a significant fraction in aerospace and/or engineering. Few entered the teaching path, though statistics may be incomplete. These results are leading to significant changes in departmental mentoring, advising and professional development, to facilitate student awareness and preparation for the most commonly followed paths. We encourage other departments to undertake similar studies, and will describe�methodologies and insights to support these efforts. Career Outcomes for Majors in Astrophysical and Planetary Sciences
Mon, Mar. 30 3pm (Kitt Cent…	DeLong Guoliang Yu (Texas AM University) View Online:https://cuboulder.zoom.us/j/97834671785 X Mathematicians use groups to capture the idea of symmetry, and manifolds to describe the shapes of spaces�from the surface of the Earth to models of the universe. In this talk, I will show how drawing and visualizing groups can reveal surprising information about the shape of a space. Through pictures, examples, and geometric intuition, we will see how symmetry can constrain and sometimes completely determine the global structure of a manifold. The talk is designed to be accessible to students and non-experts. Geometry of groups and topological rigidity of manifolds Sponsored by the Meyer Fund
Mon, Mar. 30 7pm (Remote (Z…	Functional Analysis Alonso Delf�n (CU Boulder) View Online:97482826489 X Part III: Multiplier algebras Zoom ID: 97482826489 Mini-course L^p-operator algebras: Part III
Tue, Mar. 31 1:25pm (online)	Algebra/Logic Alex Nowak (Howard University) View Online:https://cuboulder.zoom.us/j/96896272260 X Drinfeld formulated the set-theoretic Yang Baxter equation (YBE) in an attempt to simplify the classification problem for solutions of the quantum YBE from physics. In the intervening 35 years, investigations of the set-theoretic YBE have called upon a wide array of algebraic structures: groups, quasigroups, racks, quandles, cycle sets, and (skew)-braces, just to name a few. In this talk, we will discuss how Bruck loops and Moufang loops are central to understanding a class of solutions that exhibit a ``dihedral" symmetry. This is joint work with Anna Zamojska-Dzienio. Dihedral solutions of the set theoretic Yang-Baxter equation
Tue, Mar. 31 7pm (MATH 350)	Functional Analysis Alonso Delf�n (CU Boulder) View Online:97482826489 X Part IV: Catch up and L^p-Spectral Triples. Zoom ID: 97482826489 Mini-course L^p-operator algebras: Part IV

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