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Events for the weeks of November 8th – 20th

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Tue, Nov. 10 10am (online)	Algebra/Logic Todor Tsankov (University of Lyon) View Online:https://cuboulder.zoom.us/j/96896272260 X Automorphism groups of structures in classical and continuous logic provide a rich source of examples of Polish groups and model-theoretic methods are central in their study. The setting in which there is a perfect correspondence (equivalence of categories) between model theory and groups is that of aleph_0-categorical structures and Roelcke precompact Polish groups. I will survey what is known about this and then discuss new work which extends the correspondence to a broader one between locally Roelcke precompact groups (studied by Rosendal) and locally aleph_0-categorical structures, which we define. This is joint work with Itai Ben Yaacov. Polish groups and model theory
Tue, Nov. 10 1:30pm (Math 3…	Homotopy Mike Hill (University of Minnesota) X In the last decade, we have seen tremendous progress in equivariant algebra, with significant classical algebraic geometry theorems being reproved in the equivariant context. One thing that makes the story trickier is that here we have lots of generalizations of an ordinary commutative ring: the incomplete Tambara functors. The additional data here makes the underlying algebra significantly harder to understand. In this talk, I will focus on a piece of that algebra: what do we mean by a module? There are several different answers to this question, and I will show how they fit together. Modules in equivariant algebra Sponsored by the Meyer Fund
Tue, Nov. 10 2:30pm (Math 3…	Lie Theory Tomoyuki Arakawa X We establish a Faithfulness Theorem for vertex algebra modules, showing that two complementary geometric localizations can jointly detect global algebraic structure. We apply this principle to vertex algebras obtained by BRST reduction from classical invariant theory and identify them, under natural geometric hypotheses, with global sections of sheaves of chiral differential operators. As consequences, we prove vanishing of BRST cohomology in nonzero degrees and simplicity, and show that every finitely strongly generated module is a finite direct sum of copies of the vacuum module. In particular, the corresponding module category is equivalent to the category of finite-dimensional vector spaces. For families associated with classical groups, we identify the associated varieties with Hamiltonian reductions, proving quasi-lisse-ness and the predicted identification with Higgs branches of the corresponding supersymmetric gauge theories. This provides geometric realizations of a broad class of vertex algebras arising from three- and four-dimensional quantum field theories. This is a joint work with Xuanzhong Dai and Bailin Song. Faithful Localization of Vertex Algebra Modules Sponsored by the Meyer Fund
Tue, Nov. 10 3:30pm (MATH 3…	Topology Howy Jordan X The classical smooth Morse theory provides a way to determine the homotopy and homology type of a smooth manifold by way of sublevelset filtrations of suitable smooth functions. The discrete case provides a comparable notion for simplicial complexes that is suitable for computations. In either case, we obtain a sublevelset persistent homology and a method for pairing bars in the barcode with critical points or simplices witnessing the birth and death of cycles. When a stratification is present, we can modify these theories to accommodate this extra data. In this talk we will introduce and relate these theories, providing examples of algorithms involved with applying these for topological data analysis. Morse Theory, Discrete and Stratified
Wed, Nov. 11 3:30pm (Math350)	Math Phys Tuscany McCann (CU Boulder) X In this talk, we will define and construct a classical field theory model suitable for the treatment of local symmetries (e.g. Yang–Mills theory) with an eye towards the deformation quantization of such a model, which will be the topic next week. In specific, we will regard observables as functionals on the configuration space of the theory, and employ the Batalin–Vilkovisky formalism in order to represent those functionals which are invariant under the symmetries of the theory as a cohomology group sourced from a bicomplex incorporating both functionals and symmetries. This follows the review given by Brunetti, Fredenhagen, and Rejzner in arXiv 2512.14227. Foundations of Classical Field Theory
Thu, Nov. 12 11:15pm (Math …	Noncomm Geometry Dmitry Kaledin (Steklov Math Institute/HSE) X In non-commutative algebraic geometry, an algebraic variety is replaced by a DG algebra A, and the role of de Rham cohomology is played by periodic cyclic homology HP(A). It is a standard expectation that all the additional motivic-type structure on de Rham cohomology should also exist in non-commutative generality. There has been a lot of progress on this in the p-adic situation, but the archimedian case is much more problematic. The missing ingredient is complex conjugation. While a Hodge filtration on periodic cyclic homology exists by definition, we also expect that HP(A) for a good A over C carries a functorial R-structure, and it is not clear at all where it might come from. I am going to present a proposal towards this based on L^2-completed version of HP. This is still work-in-progress, but the proposal looks viable, so hopefully, this won't be a complete waste of audience's time. This talk is joint with algebraic geometry seminar Towards non-commutative Hodge theory Sponsored by the Meyer Fund
Thu, Nov. 12 11:15pm (Math …	Algebraic Geometry Dmitry Kaledin ((Steklov Math Institute/HSE)) X In non-commutative algebraic geometry, an algebraic variety is replaced by a DG algebra A, and the role of de Rham cohomology is played by periodic cyclic homology HP(A). It is a standard expectation that all the additional motivic-type structure on de Rham cohomology should also exist in non-commutative generality. There has been a lot of progress on this in the p-adic situation, but the archimedian case is much more problematic. The missing ingredient is complex conjugation. While a Hodge filtration on periodic cyclic homology exists by definition, we also expect that HP(A) for a good A over C carries a functorial R-structure, and it is not clear at all where it might come from. I am going to present a proposal towards this based on L^2-completed version of HP. This is still work-in-progress, but the proposal looks viable, so hopefully, this won't be a complete waste of audience's time. Towards non-commutative Hodge theory Sponsored by the Meyer Fund
Fri, Nov. 13 10:10am (Math …	Math Edu Aidan Powers X Since Fall 2024 several Teaching Practice Groups (TPGs) have been meeting in our department to discuss graduate instructors' teaching-related concerns and ideas. The goal of this talk is to describe the history, design, and purpose of TPGs, and initiate discussion of their role in our department. We will overview participant experiences, challenges in implementation, and current and potential benefits of TPGs to our department. As the program is only just maturing, we especially welcome input about what potential TPGs may have. Grad students preparing to begin their teaching career, or in the early phases, are especially encouraged to join to learn about the program and contribute their perspective. Teaching Practice Groups to Support Graduate Instructors in Mathematics
Fri, Nov. 13 1:25pm (Math 3…	A. I. Lionel Levine (Cornell University) X Aligning AI with human values is a pressing unsolved problem. How can mathematicians contribute to solving it? I'll survey some research directions in the new field of math for AI safety. I'll also discuss pacing the frontier, and how humanity can coordinate to abstain from building superhuman AI. Math for AI Safety
Tue, Nov. 17 2:30pm (MATH 3…	Lie Theory Basia Klos (CU Boulder) X Suitable categories of vertex operator (super) algebra modules can be endowed with a braided tensor category structure. We'll start this talk by (hopefully gently) introducing VOSAs, their modules, and some examples. We will then describe progress on the vertex tensor category front for the super singlet VOAs, including the classification of irreducible modules and some fusion rules. Based on joint work in progress with T. Creutzig, F. Orosz Hunziker, Y. Wang and J. Yang. Representation Theory of the Super Singlet Vertex Operator Algebra
Tue, Nov. 17 3:30pm (MATH 3…	Topology Raphael Ponge (University of Wyoming) X We will explain how to construct explicit quasi-isomorphisms computing the cyclic and periodic cyclic homology of crossed-product algebras arising from group actions on manifolds. This simplifies and clarifies earlier results of Brylinski–Nistor and Crainic. We will also review the necessary background on cyclic and periodic cyclic homology and paracyclic spaces, and introduce para-S-modules, a new paracyclic version of the S-modules of Jones and Kassel. Cyclic homology and group actions on manifolds.
Wed, Nov. 18 3:30pm (Math350)	Math Phys Tuscany McCann (CU Boulder) Perturbative Algebraic Quantum Field Theory
Thu, Nov. 19 1pm (CSU)	Algebraic Geometry FRAG Day X Fall 2026 Front Range Algebraic Geometry Day at Colorado State University This day is in collaboration with the FRAGMENT seminar for algebraic geometers in the front range area to connect and discuss their research. In particular, we are committed to fostering connections among graduate students between CU and CSU For more information, please see our website: https://sites.google.com/colorado.edu/front-range-ag/home?authuser=0 FRAG Day
Thu, Nov. 19 2:30pm (MATH 3…	Functional Analysis Sarada Anoushka Nerella Kameswari Umamaheshwari (CU Boulder) X TBA TBA

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