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Events for October 2026 – February 2027

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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) X In the 1990's, Proctor classified the d-complete posets, which correspond to λ-minuscule elements of Weyl groups of simply laced Kac-Moody algebras. These have the Jeu de Taquin property for the natural generalization of standard Young tableaux theory to posets. We define a notion of highest weight tableaux for several infinite families of d-complete posets. These constructions allow us to develop local algorithms for coswitching pairs of tableaux on these families, a coplactic version of tableau switching that, in the known setting of types A and B, connects naturally to Schubert calculus, crystals, and promotion and evacuation. Semistandard tableaux and (co)switching on d-complete posets
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
Fri, Oct. 16 1:25pm (Math 3…	A. I. Departmental Discussion X Recent events surrounding AI and mathematics have raised questions and uncertainties, and have set off a heated debate in our field. The goal of this discussion is to talk about what these changes mean for us as a department, and how we can stay cohesive as a community through this unsettling time. Some questions we will propose to guide the discussion are: 1. Current events are polarizing the mathematical community. Can we, as a department, stay cohesive through this? What can we do to make room for different points of view? 2. Who is losing out in this storm, and who is gaining? In what specific ways? How do we protect those at risk, and create opportunities, both for those who want to use AI and those who do not? 3. Optional (if not covered before): Students and advisors may see these changes differently. How can they navigate their differing views together? What do students want from their advisors for support and guidance? What do advisors want from their students? 4. Optional: What do we value as a community, for credit in the discipline (instead of first proof of a new fact), and in our peers? 5. Optional closing question: What are things we already do well as a community that we want to preserve, and how can we make sure to do so? Moderated by Nat Thiem AI and Our Community
Tue, Oct. 20 1:25pm (online)	Algebra/Logic Michael Kompatscher (Charles University Prague) View Online:https://cuboulder.zoom.us/j/96896272260 X An (abstract) minion M is a functor from the category of finite sets to the category of sets. So, for every finite set X, there is a set M(X) (the 'X-ary' part of M), and for every function f: X -> Y there is a function M(f) : M(X) -> M(Y) such that M preserves the identity and composition. Every variety V naturally gives rise to a minion F_V, where F_V(X) is the free algebra generated by X and F_V(f) : F_V(X) -> F_V(Y) is the unique homomorphism extending f: X -> Y. In this talk I would like to discuss a nice (multilinear) description of this minion for the variety of n-step nilpotent groups. This description is based on concepts from combinatorics on words (subword counting) and a result by Fox, Lyndon and Chen from 1958, and motivated by the study of uniform algorithms for constraint satisfaction problems (CSPs). The minion of free n-step nilpotent groups
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
Thu, Oct. 22 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) X A finite directed graph gives rise to several objects at once: dynamical systems, inverse semigroups, étale groupoids, and C-algebras. This talk is an introduction to these constructions and how they classify graphs. We will discuss classical invariants of graphs and how these are realized through topological invariants of groupoids and C-algebras. We will also discuss how these invariants and other objects classify graphs. No previous familiarity with symbolic dynamics is assumed. The talk also sets up the second part, where these equivalences are revisited from a combinatorial point of view. C*-algebras and finite graphs Part I
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
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 1:25pm (Math 3…	A. I. Matt Grimes (Amazon) TBA
Tue, Nov. 3 2:30pm (MATH 3…	Lie Theory John McHugh (CU Denver) TBD
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
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
Fri, Jan. 29 1:25pm (Zoom)	A. I. Sean Welleck (CMU) TBD
Fri, Feb. 26 1:25pm (Math 3…	A. I. Michael Mulligan (UC Riverside) TBA

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