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Events for the weeks of November 1st – 13th

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Tue, Nov. 3 1:25pm (MATH 2…	Algebra/Logic Florian Starke (TU Dresden) View Online:https://cuboulder.zoom.us/j/96896272260 X Datalog fragments have been used a lot to study constraint satisfaction problems (CSPs) that are solvable in polynomial time. Well known fragments are linear Datalog, symmetric linear Datalog, and arc monadic Datalog, better known as arc consistency. We introduce n-almost symmetric Datalog and study n-almost symmetric linear arc monadic Datalog. We characterize the finite relational structures whose CSP is solved by this Datalog fragment as those that can be primitive positively constructed from the transitive tournament on n + 2 vertices. We also give characterizations in terms of a certain homomorphism duality (which we call n-fixed unfolded caterpillar duality) and in universal-algebraic terms (the existence of k-absorptive operations and of operations forming an elevator chain of length n + 1). Almost symmetric linear arc monadic datalog and transitive tournaments
Tue, Nov. 3 2:30pm (MATH 3…	Lie Theory John McHugh (CU Denver) X One way to understand the modular (positive characteristic) representations of a finite group G is to consider the blocks of the group. The blocks have invariants associated to them which the entire group does not possess. For example, a block determines a fusion system --- a finite category with deep connections to the homotopy theory of the classifying space of G. Further, the fusion system has attached to it a family of second cohomology classes called the Kulshammer-Puig classes of the block. I will discuss the computation of these cohomology classes for unipotent blocks of finite groups of Lie type (in non-defining characteristic). It turns out that in this case all of the Kulshammer-Puig classes are trivial in a strong way. Joint with Mandi Schaeffer Fry of the University of Denver and Justin Lynd of the University of Louisiana at Lafayette. On the Kulshammer-Puig classes of unipotent blocks
Wed, Nov. 4 3:30pm (Math350)	Math Phys Adam Richardson (CU Boulder) Foundations of deformation quantization
Wed, Nov. 4 4:40pm (MATH 3…	Grad Student Seminar Omar Al - Khazali (CU Boulder) X In this talk, we introduce an algebra of graphs that was formalized and motivated due to its alternative algebraic solution to the Longest Path Problem (LPP) and k-path problem (kPP) on Tree-like classes of graphs. Furthermore, we will provide a simplified statement of the algebraic conditions that solve LPP and kPP, displaying an improved algorithm to compute the solution for a given Tree-like graph. Additionally, we exhibit a categorification of the algebraic structure, in which we define a graph-valued metric, named Hom-completion graphs, to compare homomorphisms of graphs. Finally, we show how setting some invariants on these Hom-completion graphs constructs formal metrics that allow for more refined comparison of these homomorphisms. A Categorification of An Algebra of Graphs
Thu, Nov. 5 2:30pm (MATH 3…	Functional Analysis Alonso Delfin (Swarthmore College) X Borrowing W. Paravicini’s linking Banach algebra framework, based on V. Lafforgue’s definition of Morita equivalence for Banach algebras, in this talk we present different ways of putting norms on the linking algebra associated to a Banach Morita equivalence. For equivalences arising from L^p-modules, we show that there is a canonical choice of norm that recovers the usual C*-algebraic setting when p=2. If time permits, I will discuss applications of this result to L^p-operator algebras associated with étale groupoids. This is based on joint work with Yeong Chyuan Chung (Jilin University) and Zhen Wang (HangZhou Normal University). Operator norms on linking Banach algebras Sponsored by the Simons Foundation
Fri, Nov. 6 1:25pm (Math 3…	A. I. Mohammed Abouzaid (Stanford) X In the past year AI systems have produced genuine research results in mathematics. What is much less clear is how to measure what these systems can actually do, and how to use them in one's own work. I will describe First Proof, which tests AI systems against unpublished mathematics, research mathematicians contribute problems with known but unpublished proofs, and the systems' solutions are refereed and graded, and report what successive batches of this have taught us. AI as a scientific instrument for mathematics
Tue, Nov. 10 1:30pm (Math 3…	Homotopy Mike Hill (University of Minnesota) TBD Sponsored by the Meyer Fund
Tue, Nov. 10 2:30pm (Math 3…	Lie Theory TBD TBD 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) 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. 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 1:25pm (Math 3…	A. I. Lionel Levine (Cornell University) TBA

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