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Events for August – December

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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
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
Tue, Sep. 8 5pm (MATH 350)	Math Club Rebekah Jones X Come to our first meeting on Tuesday, Sept 8th, 5-6pm to learn about what we do at Math Club and what we have planned for the semester. We’ll also have some fun math games/activities and, as always, free pizza! If you RSVP at the link below, you can vote on your pizza preferences. RSVP link: https://forms.gle/HFgNJZg8RhNfVWJg6 Welcome Day
Wed, Sep. 9 3:30pm (Math350)	Math Phys Andrew Doumont (CU Boulder) X Many techniques for studying symplectic manifolds (e.g. Gromov-Witten invariants) rely on the ability to count certain pseudoholomorphic curves. In order to do this counting one must have some notion of fundamental class on the moduli space of pseudoholomorphic curves. However, such moduli spaces are generally very poorly behaved. In this talk, we will discuss Kuranishi spaces which are a geometric structure one can equip these moduli spaces with in order to define a virtual fundamental class. Kuranishi Space
Fri, Sep. 11 10:10am (Math …	Math Edu Rebekah Jones X Join us to discuss potential topics and speakers for the Seminar on Undergraduate Math Education (SUME) this semester. We encourage all those interested in attending SUME this semester to attend! SUME Open House
Fri, Sep. 11 1:25pm (Zoom (…	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. The speaker is on Zoom. We suggest you attend on zoom (better experience for the speaker). Math 350 will be available for those who wish to share in-person viewing. Mathematics in the Age of AI: Discovery, Verification, and the Future of Proof
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 3:30pm (Math350)	Math Phys Howy Jordan (CU Boulder) X This is a joint talk with the topology seminar. The space of mixed states of a quantum system can be decomposed by ranks. For purposes of differential topology and geometry, one wants subspaces in a decomposition to fit together in a natural way, in which case it is called a stratification and the pieces called strata. Moreover, in order to have a useful notion of stratified tangent bundle, certain regularity conditions such as Whitney (a)- and (b)-regularity are considered. In this talk, we discuss the necessary background in stratification theory and discuss the regularity conditions satisfied by the decomposition of mixed states by rank. State spaces in quantum mechanics Part 2: Stratifications
Wed, Sep. 23 3:30pm (MATH 3…	Topology Howy Jordan (CU Boulder) X This is a joint talk with the mathematical physics seminar. The space of mixed states of a quantum system can be decomposed by ranks. For purposes of differential topology and geometry, one wants subspaces in a decomposition to fit together in a natural way, in which case it is called a stratification and the pieces called strata. Moreover, in order to have a useful notion of stratified tangent bundle, certain regularity conditions such as Whitney (a)- and (b)-regularity are considered. In this talk, we discuss the necessary background in stratification theory and discuss the regularity conditions satisfied by the decomposition of mixed states by rank. State spaces of quantum systems Part 2: Stratifications
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
Tue, Sep. 29 2:30pm (MATH 3…	Lie Theory Katrina Barron (Notre Dame University) X We recall some aspects of the representation theory for Lie algebras and how some number theory makes an appearance through characters for modules. We motivate why this occurs by putting this in the setting of vertex operator algebras which are the algebras that naturally arise from the geometry of Conformal Field Theory (or string theory). We discuss how analytic properties can be proved in certain settings by the construction of a modular linear differential equation, including recently in a new setting through joint work with Florencia Orosz Hunziker and Gaywalee Yamskulna. Why should we expect number theoretic properties to arise in Lie theory and group theory? Sponsored by the Meyer Fund
Tue, Sep. 29 3:30pm (MATH 3…	Topology Emily Montelius (CU Boulder) Introduction to Topological Data Analysis and seminar organization
Wed, Sep. 30 2:30pm (Math350)	Math Phys Markus J. Pflaum (CU Boulder) State spaces in quantum mechanics Part 3: Invariant Theory
Wed, Sep. 30 4:30pm (Math 2…	Homotopy Jesse Keyes (University of Kentucky) X Using the Hill-Hopkins-Ravenel norm, one can produce a G-equivariant analog N_{C_2}^{G} MU_R of the Real bordism spectrum for any group G containing a cyclic group of order two. In the case that G is a cyclic 2-group, the slice spectral sequence associated to N_{C_2}^{C_{2^k}} MU_R was a critical component in the resolution of the Kervaire-invariant one problem by Hill-Hopkins-Ravenel. We focus on the case that G is the quaternion group Q_8 and give an identification of the zero slice of N_{C_2}^{Q_8} MU_R, highlighting a computational technique for determining objects like this. Further, we give a computation of a portion of the RO(Q_8)-graded homotopy of this zero slice. The Zero Slice of Quaternionic Real Bordism Sponsored by the Meyer Fund
Thu, Oct. 1 11:15pm (MATH …	Algebraic Geometry Sachi Hashimoto X Let X be a curve of genus at least 2. By Faltings’ theorem, we know that X has finitely many rational points, but how can we actually determine this set in practice? Around 40 years before Faltings’ proof, Chabauty proved this finiteness theorem for certain curves by studying the embedding of X inside an abelian variety, the Jacobian variety of X. In the first part of my talk, I will explain Chabauty’s original method and the modern day extension “Geometric linear Chabauty” that makes this effective. In the second part of my talk, I will describe recent progress to extend Chabauty’s method to a broader class of curves by studying line bundles over the Jacobian (arising from pullbacks of the Poincare bundle). The math in these talks arises out of work of Edixhoven and Lido, and also reflects joint work with Spelier, Lido, Lombardo, Mascot, and Parent. Geometric methods for determining rational points on curves I and II
Wed, Oct. 7 4:40pm (MATH 3…	Grad Student Seminar Colin Jackson (CU Boulder) X Some numbers are rational, a few more are algebraic, but most are transcendental. We will briefly cover some definitions, investigate some special cases of numbers, and finally look at some positive results in transcendental number theory. Rational, Algebraic, or Transcendental?
Thu, Oct. 8 11:15am (MATH …	Algebraic Geometry Sachi Hashimoto X Let X be a curve of genus at least 2. By Faltings’ theorem, we know that X has finitely many rational points, but how can we actually determine this set in practice? Around 40 years before Faltings’ proof, Chabauty proved this finiteness theorem for certain curves by studying the embedding of X inside an abelian variety, the Jacobian variety of X. In the first part of my talk, I will explain Chabauty’s original method and the modern day extension “Geometric linear Chabauty” that makes this effective. In the second part of my talk, I will describe recent progress to extend Chabauty’s method to a broader class of curves by studying line bundles over the Jacobian (arising from pullbacks of the Poincare bundle). The math in these talks arises out of work of Edixhoven and Lido, and also reflects joint work with Spelier, Lido, Lombardo, Mascot, and Parent. Geometric methods for determining rational points on curves I and II
Fri, Oct. 9 1:25pm (Math 3…	A. I. Zak Miller X Last year, based on several experiments, Jack Lindsey at Anthropic concluded that LLMs are (partially) introspectively aware of their internal states. If true, this would provide some evidence of LLM consciousness. We replicate the results concerning LLM detection of injected thoughts and test their robustness under different conditions. After running our own experiments, we now think that Lindsey’s detection results provide little evidence for LLM introspection. When it comes to detecting an injected thought, non-introspective forces predominate and explain the majority of how models respond. Even so, by extending Lindsey’s research, we can work toward a comprehensive introspection benchmark for future models. If I have time, I might also discuss some recently developed interpretability tools (such as natural language autoencoders, the J-lens, and the oracle lens) that let us "read the thoughts" of LLMs and look directly for evidence of introspection. Evidence that LLMs Aren't Aware of Their Thoughts
Tue, Oct. 13 11am (350)	Number Theory Faculty & Postdoc Number Theory Open House
Tue, Oct. 13 1:25pm (online)	Algebra/Logic Charlotte Aten View Online:https://cuboulder.zoom.us/j/96896272260 X In order to study a certain 3-dimensional analogue of the Mandelbrot set, I needed a notion of holomorphy for the corresponding 3-dimensional real algebra. While this motivation (to generalize the basic elements of complex dynamics) is analytic, the focus of this talk will be the connection between holomorphic functions over a real algebra and first-order properties of the algebra. It turns out that, under the assumption of a single (left or right) divisible element, the holomorphic functions over an arbitrary real algebra form a vector space. Properties such as the Product Rule and Chain Rule are equivalent to purely algebraic properties of the underlying real algebra. When our real algebra has a multiplicative identity element, the Product Rule is precisely equivalent to being both commutative and associative. I will present proofs of some of these statements, which are quite succinct once the proper groundwork has been done. Holomorphy over real algebras
Tue, Oct. 13 1:30pm (Math 3…	Homotopy Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University) X Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter. With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions Sponsored by the Meyer Fund
Tue, Oct. 13 1:30pm (Math350)	Math Phys Theo Johnson-Freyd (Perimeter Institute for Theoretical Physics and Dalhousie University) X Abstract: Kitaev has argued that the spaces of n-dimensional invertible phases of matter, as n varies, fit together into the structure of an Omega-spectrum. It follows that each n-dimensional phase determines a (possibly trivial) character on the nth stable homotopy group of spheres. I will present an enforced-gaplessness theorem (conditional on some reasonable semisimplicity assumptions about the category of topological phases of matter): if this character is nontrivial, and not one of the six nontrivial Kervaire invariants, then the invertible phase is a topological insulator: a material all of whose boundary conditions have gapless conducting modes. This is joint work in progress with David Reutter. With six exceptions, nontrivial characters of spheres do not admit gappable boundary conditions
Tue, Oct. 13 2:30pm (MATH 3…	Lie Theory Kelsey Brown (Colorado State University) TBD
Wed, Oct. 14 3:30pm (Math350)	Math Phys Markus Pflaum (University of Colorado Boulder) State spaces in quantum mechanics Part 4: Uhlmann connection
Wed, Oct. 14 4:40pm (MATH 3…	Grad Student Seminar Alex Lajeunesse (CU Boulder) X The rational numbers admit an infinite family of distinct absolute value functions, apart from the normal one. Completing with respect to these absolute values leads to the fields of p-adic numbers for primes p. This talk will introduce these fields, focusing on their nature as bridges between characteristic 0 and p. We will discuss how Galois theory can be transported along this bridge, culminating in the definition of perfectoid fields and the tilting correspondence of Fontaine-Wintenberger and Scholze. This is intended to be a warm-up for the DeLong lectures being given by Prof. Bhargav Bhatt the following week. The tilting correspondence in mixed characteristic
Thu, Oct. 15 11:15am (MATH …	Algebraic Geometry Jacob Cleveland (Colorado State University) X We show that birational toric Landau–Ginzburg models which are related by a crepant variation of GIT have isomorphic state spaces under mild assumptions, generalizing the state space LG/CY correspondence of Chiodo–Ruan. We prove that this isomorphism is canonical, and is induced by a Fourier–Mukai transform. In the special case that a toric LG model is a so-called geometric phase, we identify the LG state space with the cohomology of the associated hypersurface. The State Space Correspondence for Toric Landau-Ginzburg Models
Fri, Oct. 16 10:10am (Math …	Math Edu Emily Montelius X Undergraduate research can take on many forms. In this talk I will share my strategies for finding appropriate topics and problems, how I scaffold introductory material, and methods to get students asking and solving interesting questions. I will discuss options for intended research outcomes. I will also discuss how to create smaller math projects with undergraduates in mind. Strategies for Guiding Undergraduate Research
Tue, Oct. 20 2:30pm (MATH 3…	Lie Theory Spencer Daugherty (CU Boulder) TBD
Tue, Oct. 20 3:30pm (MATH 3…	Topology Coby Glass X Topological Data Analysis (TDA) is very promising in the field of cybersecurity anomaly detection, but is traditionally too computationally bottlenecked for use in real-time environments. This talk explores the pipeline from industrial application to hardware-accelerated mathematics, beginning with the challenges of embedding non-geometric cybersecurity data into valid metric spaces for Vietoris-Rips filtrations. After demonstrating a functional TDA-to-machine-learning pipeline, we will briefly examine the algebraic optimizations that make this possible on modern computing architectures. Finally, the presentation will discuss the potential for hardware-accelerated TDA, specifically designing systolic arrays to compute matrix rank over GF(2) via chunked Gaussian elimination. Topological Anomaly Detection on Real-Time Data
Wed, Oct. 21 3pm (KCEN MPR …	DeLong Bhargav Bhatt (Institute for Advanced Study & Princeton University) View Online:https://cuboulder.zoom.us/j/97834671785 X What if two numbers were considered close not when their difference is small, but when it is divisible by a large power of a fixed prime $p$ ? Following this seemingly strange idea leads to the $p$ -adic numbers, a concept introduced in the late nineteenth century that has transformed number theory and found applications throughout mathematics. This lecture will explain where the $p$ -adic numbers came from, how they differ from the familiar real numbers, and why they are useful. The p-adic world Sponsored by the Meyer Fund
Thu, Oct. 22 11am (KCEN MPR…	DeLong Bhargav Bhatt (Institute for Advanced Study & Princeton University) View Online:https://cuboulder.zoom.us/j/97834671785 X Over the past fifteen years, the discovery of perfectoid geometry and related ideas has provided new lenses through which to study $p$ -adic spaces at an extraordinarily fine scale. The resulting methods have resolved longstanding questions across algebraic geometry, number theory, homotopy theory, and beyond. In this lecture, I will recount some of this story, emphasizing the applications that motivated the conceptual developments. Recent developments in p-adic geometry Sponsored by the Meyer Fund
Fri, Oct. 23 1:25pm (Zoom)	A. I. Max Weinreich (CUNY) The Crisis of AI-Generated Mathematics
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
Fri, Oct. 30 1:25pm (Math 3…	A. I. Matt Grimes (Amazon) TBA
Tue, Nov. 3 2:30pm (MATH 3…	Lie Theory John McHugh (CU Denver) TBD
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
Fri, Nov. 13 1:25pm (Math 3…	A. I. Lionel Levine (Cornell University) TBA
Tue, Nov. 17 2:30pm (MATH 3…	Lie Theory Basia Klos (CU Boulder) TBA
Thu, Nov. 19 1pm (CSU)	Algebraic Geometry FRAG Day X Fall 2026 Front Range Algebraic Geometry Day at Colorado State University This day is in collaboration with the FRAGMENT seminar for algebraic geometers in the front range area to connect and discuss their research. In particular, we are committed to fostering connections among graduate students between CU and CSU For more information, please see our website: https://sites.google.com/colorado.edu/front-range-ag/home?authuser=0 FRAG Day
Fri, Nov. 20 1:25pm (Math 3…	A. I. TBA TBA
Tue, Dec. 1 3:30pm (Math350)	Math Phys Ezzra Getzler (Northwestern University) tba Sponsored by the Meyer Fund
Wed, Dec. 2 3:30pm (Math350)	Math Phys Ezzra Getzler (Northwestern University) tba Sponsored by the Meyer Fund
Thu, Dec. 3 11:15am (MATH …	Algebraic Geometry Ignacio Rojas (Colorado State University) X TBA TBA
Fri, Dec. 4 1:25pm (Math 3…	A. I. Emily Riehl (Johns Hopkins University) TBA

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