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Events for the weeks of November 2nd – 14th

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Tue, Nov. 4 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
Tue, Nov. 4 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
Thu, Nov. 6 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
Thu, Nov. 6 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
Fri, Nov. 7 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
Tue, Nov. 11 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
Tue, Nov. 11 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
Tue, Nov. 11 1:30pm (MATH 3…	Topology Itamar Mor TBD
Tue, Nov. 11 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
Tue, Nov. 11 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
Wed, Nov. 12 4:30pm (TBD)	Algebraic Geometry Zhijia Zhang (NYU) X TBD TBD - Note the unusual time and date Sponsored by the Meyer Fund
Thu, Nov. 13 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?

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