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Events for the weeks of September 13th – 25th

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Tue, Sep. 15 1:25pm (MATH 2…	Algebra/Logic Keith Kearnes & Peter Mayr (CU) X The foundations group will talk about its research. Foundations Open House
Tue, Sep. 15 11pm (350)	Number Theory Jamie Juul (Colorado State University) X Iterating a polynomial or rational function produces a tree of preimages of a point, and the Galois group of the resulting tower of fields acts on this tree by symmetries — a dynamical analogue of the Galois representations attached to elliptic curves, and a natural place to ask how large this group of symmetries can be. I will describe a general criterion, based only on the combinatorics of a map's critical orbits, that determines whether this group is as large as possible, and if not, exactly how it falls short at every level. Along the way I'll work out an explicit family of examples where all the critical orbits eventually collide, and describe how recent work of König, Neftin, and Rosenberg makes the criterion apply automatically to a broad class of polynomials. Rational Functions with Large Iterated Monodromy Groups
Wed, Sep. 16 3:30pm (Math350)	Math Phys Markus J. Pflaum (CU Boulder) X This is an introductory talk to the semester topic of Mathematical Foundations of Quantum Theory. In the last 20 minutes potential topics for talks will be discussed and assigned. Students participation is strongly encouraged. State spaces in quantum mechanics Part 1 and seminar organization
Thu, Sep. 17 11:15pm (MATH …	Algebraic Geometry Jon Kim (University of Colorado Boulder) X The moduli space of cubic surfaces with a marked line lies naturally between the moduli space of fully marked and unmarked cubic surfaces and comes equipped with a W(D_5)-action corresponding to the stabilizer of the marked line. Hodge theoretic compactifications of these moduli spaces have been extensively studied by many, including Allcock—Carlson—Toledo, Dolgachev—van Geemen—Kondo, and Casalaina-Martin—Grushevsky—Hulek. In previous work, by using KSBA wall crossing, we described many different birational models of this moduli space via KSBA stable pairs. In this talk, we will discuss recent results regarding the W(D_5)-invariant birational geometry of these KSBA moduli spaces and ongoing work on the log minimal model program for these KSBA moduli spaces with respect to their log canonical divisor. The log MMP for the moduli space of cubic surfaces with a marked line
Fri, Sep. 18 1:25pm (Math 3…	A. I. Gregory Berkolaiko (Texas A&M) X Claude Code is a command-line AI assistant that reads and edits files directly in a project directory. This talk reports on using it for three tasks: (a) reading a paper in an unfamiliar area and writing a report on it, a task often faced by a student; (b) revising a paper draft; and (c) course preparation, specifically the design of student projects. For (a) we work through "Bakry-Émery curvature on graphs as an eigenvalue problem" by Cushing, Kamtue, Liu and Peyerimhoff (Calc. Var. PDE, 2022). The second half concerns guardrails: writing a rules file the assistant is expected to follow, keeping the human as the decision-maker on every edit, and tracking changes through git and Overleaf. We will see cases where the assistant caught errors a careful reader would miss, cases where it introduced errors of its own, and cases where it simply ignored an explicit instruction. The talk is an introduction, aimed at those who have not yet used Claude Code or a comparable tool (Cursor, Aider). Math editing with Claude Code: uses and guardrails
Tue, Sep. 22 1:25pm (MATH 2…	Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X I will discuss the classification of those finite algebras $A$ with the following property: there is no identity $s≈ t$ that is satisfied by $A$ with probability $p$ for any number $p$ satisfying 1/\|A\| < p < 1. Finite algebras whose equational probability spectrum contains a big gap
Wed, Sep. 23 4:40pm (MATH 3…	Grad Student Seminar Taylor Rogers (CU Boulder) X "Homotopy coherent algebra provides a family of fields interpolating between characteristic 0 and p for each prime p. Finite group representation theory extends to these higher categorical contexts, as do generalizations of finite groups called $π$ -finite spaces. In this talk we will translate representation theory to these homotopical contexts. Further, time permitting, we will see how some properties of representation theory change over these higher categorical fields and why one might care... and I may tell a joke or two. " Representation Theory of Finite Spaces
Fri, Sep. 25 10:10am (Math …	Math Edu Ally Graf X A flipped classroom is a method of instruction where the main ``lecture" occurs outside the classroom without the instructor, and time in class focuses on higher-order cognitive activities such as collaborative learning. In this presentation, I will use personal experience both as a student and facilitator in flipped classrooms to facilitate a discussion on current research and what should be considered when implementing this teaching method. A Reflection on Flipped Classrooms
Fri, Sep. 25 1:25pm (Math 3…	A. I. Sachi Hashimoto X New technologies often change our tools before they change the way we work. Large language models can now produce convincing mathematical code very rapidly through mathematical "vibe coding" (prompting AI and then accepting code if it seems to work). But when this code is intended for use in a publication or inclusion in a database, the stakes are higher: errors in the code become errors in the mathematical literature. Is the alternative to "vibe coding" reading the code line-by-line? I will talk about how we can build software development workflows for the AI age. Starting from the basics of version control and Git, and assuming no prior experience, I will discuss iterative AI-assisted development, subagents, code review, testing, and continuous integration. The talk will be aimed at mathematicians interested in developing large-scale mathematical software and databases without giving up oversight and trust. AI-Assisted Coding for Mathematicians: How to Build Software Without Vibe Coding

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