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Events for the weeks of August 30th – September 11th

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Tue, Sep. 1 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X A poset congruence is the analogue for partially ordered sets of a lattice congruence. If a group G acts on the underlying set of a poset P, then we call a poset congruence "G-invariant" if the G-action respects the partition of P into congruence classes. This talk will discuss specific examples where G is a Weyl group of type A or D. This is partly based on joint work with Tianyuan Xu (University of Richmond). Invariant poset congruences
Wed, Sep. 2 4:40pm (MATH 3…	Grad Student Seminar Edouard Pierre Francois Heitzmann (CU Boulder) X As part of a recent research problem, I needed a cheap and sharp way to compute anytime-valid refineable lower bounds for directional derivatives of a high-dimensional function over a coordinate diamond. The Interval Branch and Bound (B&B) algorithm turned out to be a good fit for this task. In this talk I will tell you about the Mathematics involved in this algorithm – including the so-called “Fundamental Theorem of Interval Arithmetic” – as well as its history and the context I had to apply it in. A Conservative Optimization Algorithm Using the Fundamental Theorem of Interval Arithmetic
Fri, Sep. 4 1:25pm (Math 3…	A. I. Edgar Costa (MIT) X Large language models become more reliable when surrounded by well-designed instructions, reusable skills, persistent records, and independent checks. I will explain how to build and use these supporting structures for rigorous technical work. How to Tame Your LLM: Harnesses for Rigorous Work
Tue, Sep. 8 11am (MATH 350)	Number Theory Taku Ishii (Seikei University) X Explicit formulas for spherical Whittaker functions on GL(n,R) were obtained by Stade around 1990. As an application, Stade computed archimedean zeta integrals for automorphic L-functions on GL(n)×GL(n) and GL(n)×GL(n-1). In this talk, I will discuss joint work with Stade on extending these results to classical groups. Archimedean Whittaker functions and archimedean zeta integrals Sponsored by the Meyer Fund
Fri, Sep. 11 1:25pm (Math 3…	A. I. Ken Ono (Axiom Math) X Mathematics is entering a period of both promise and unease. AI systems now discover counterexamples and conjectures, produce research-level arguments, and generate formally verified proofs in systems like Lean. This talk offers a working map of the landscape, organized around three distinct modes: discovery, reasoning, and verification, and why confusing them is the fastest way to overclaim. After surveying recent landmarks, I will present case studies from my own work at Axiom Math. I will discuss what is real, what is hype, and how rigor survives. Mathematics in the Age of AI: Discovery, Verification, and the Future of Proof

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