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Events for the weeks of October 25th – November 6th

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Tue, Oct. 27 1:25pm (online)	Algebra/Logic Jakob Schreiber (TU Wien) View Online:https://cuboulder.zoom.us/j/96896272260 X Distalty is a model-theoretic tameness-notion, which generalizes o-minimality and strengthens NIP, containing important unstable theories such as DLO, real closed fields and Presburger arithmetic. Its consequences include the strong Erdős–Hajnal property. One interesting problem is that of preserving tameness when adding new predicates or functions. I will discuss some results around this problem from existing literature and some from my master’s thesis and from ongoing joint work with Alessio Mansutti and Michael Benedikt, all concerning distal expansions of Presburger arithmetic and RCF by functions and by additional relations on distinguished subsets. These include distality of Semenov arithmetic—the natural numbers with addition, order and the function n ↦→ 2n —and the corresponding expansions by the Fibonacci sequence, the Factorial function and other fast-growing functions. Distality and tame expansions
Tue, Oct. 27 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, Oct. 28 3:30pm (Math350)	Math Phys Austin Walsh (University of Colorado Boulder) C*-algebraic quantum mechanics
Wed, Oct. 28 4:40pm (MATH 3…	Grad Student Seminar Sylvia Maher (CU Boulder) X TBD A Brief Overview of the Weil Conjectures
Thu, Oct. 29 11:15am (MATH …	Algebraic Geometry Shend Zhjeqi (Michigan) X TBD TBD Sponsored by the Meyer Fund
Thu, Oct. 29 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) X We introduce a notion of a graph module which we will use as a unifying framework for the study of the graph algebras and graph groupoids. We will define graph modules and spell out some elementary properties. We will then explain how the Bowen Franks group and the dimension triple can be realized concretely by studying the category of modules over a graph. After this we will generalize this to bimodules and construct a bicategory of graphs and show how this is the category of flow equivalence of graphs. We will give examples and discuss their connection with wrong way maps between graph algebras. C*-algebras and finite graphs Part II
Fri, Oct. 30 10:10am (Math …	Math Edu Rebekah Jones X The first day of class is a unique opportunity to set your students' expectations for the course as well as to convey some important messages about your goals and values as an instructor. In this talk, we'll discuss some of the goals that you could accomplish on the first day (social goals, pedagogical goals, broad and content-specific goals) and give concrete examples from different courses. Setting the Tone on the First Day
Fri, Oct. 30 1:25pm (Math 3…	A. I. Matt Grimes (Amazon) X One of the oldest problems in software development is ensuring that your code does what you intended. In this talk, we will explore new formal reasoning-based techniques for ensuring code written in rust is provably correct. We will discuss the rust library verus, its integration with the Z3 theorem prover, and walk through several examples and applications. Finally, we’ll use our iron-clad software contracts to harness the full power of LLMs for rapidly-developed, performant software that does what we intend. No experience with rust or Z3 necessary. Verification of Code in Rust
Tue, Nov. 3 2:30pm (MATH 3…	Lie Theory John McHugh (CU Denver) TBD
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

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