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Events for July – November

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Tue, Aug. 4 2:30pm (Math 3…	Lie Theory Robert McRae (Tsinghua University) View Online:https://cuboulder.zoom.us/j/6741562716 X Let $𝔤$ be a finite-dimensional simple Lie algebra and let $Lk(g)$ be the simple affine vertex operator algebra associated to $𝔤$ at a level $k$ such that $k+hinQ>0$ , where $h^{\lor}$ is the dual Coxeter number of $𝔤$ . We explain how to use recent results on braided tensor categories to show that the category of $C1$ -cofinite $Lk(g)$ -modules is a semisimple rigid braided tensor category. For certain levels, $Lk(g)$ is known to be the same as the universal affine vertex operator algebra of $𝔤$ and level $k$ , so in these cases, it follows that all generalized Verma modules induced from finite-dimensional simple $𝔤$ -modules are simple, and the category of $C1$ -cofinite $Lk(g)$ is equivalent to a minor modification of the tensor category of finite-dimensional $𝔤$ -modules. This makes it possible to construct many new vertex operator algebras by extending tensor products of affine vertex operator algebras associated to $𝔤$ at different levels. Semisimplicity of ordinary modules for simple affine vertex operator algebras at positive rational shifted levels Sponsored by the Meyer Fund
Fri, Aug. 21 1:25pm (Math 3…	A. I. Agnès Beaudry, Katherine E. Stange, and Jonathan Wise X AI has arrived. We will survey the current landscape, give an overview of the upcoming course & seminar series, and invite everyone to share their experiences. The AI seminar is aimed at a general mathematical audience. AI and Math
Thu, Aug. 27 11:15pm (MATH …	Algebraic Geometry Sebastian Casalaina-Martin and Jonathan Wise X Our algebraic geometry research faculty, Sebastian (Yano) Casalaina-Martin and Jonathan Wise will each give a quick informal talk about their current research. This is a great opportunity for new graduate students who are interested in working in algebraic geometry! AG Open House
Fri, Aug. 28 1:25pm (Math 3…	A. I. Katherine Stange (CU Boulder) X An overview of the architecture of an LLM. The Math Behind LLMs
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
Fri, Sep. 4 1:25pm (Math 3…	A. I. Sachi Hashimoto (CU Boulder) AI-Assisted Coding for Mathematicians: How to Build Software Without Vibe Coding
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
Tue, Sep. 15 11pm (350)	Number Theory Jamie Juul (Colorado State University) TBA
Fri, Sep. 18 1:25pm (Math 3…	A. I. TBA TBA
Fri, Sep. 25 1:25pm (Math 3…	A. I. TBA TBA
Fri, Oct. 2 1:25pm (Math 3…	A. I. TBA TBA
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Tue, Oct. 13 11am (350)	Number Theory Faculty & Postdoc Number Theory Open House
Fri, Oct. 16 1:25pm (Math 3…	A. I. Zak Miller TBA
Fri, Oct. 23 1:25pm (Math 3…	A. I. TBA TBA
Fri, Oct. 30 1:25pm (Math 3…	A. I. TBA TBA
Thu, Nov. 5 2:30pm (MATH 3…	Functional Analysis Alonso Delfin TBA
Fri, Nov. 6 1:25pm (Math 3…	A. I. TBA TBA
Fri, Nov. 13 1:25pm (Math 3…	A. I. TBA TBA
Fri, Nov. 20 1:25pm (Math 3…	A. I. TBA TBA

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