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Events for September 2025 – January 2026

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Thu, Oct. 30 5pm (CSU)	Algebraic Geometry Multiple speakers X 3rd installment of Front Range Algebraic Geometry (FRAG) day happening at CSU in Weber 201 1:00-5:00 https://sites.google.com/colorado.edu/front-range-ag/home FRAG Day
Wed, Sep. 3 4:40pm (MATH 3…	Grad Student Seminar Omar Al - Khazali (CU Boulder) X The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a finite graph. In the general case, the problem is -hard. However, there is a subcollection of graph classes for which there exists an efficient solution. I will display my method which provides algorithms that are proven correct by their underlying algebraic operations unlike existing purely algorithmic solutions to this problem. We introduce a `booleanize' mapping on the adjacency matrix of a graph which we prove identifies the solution for Trees, Uniform Block Graphs, Block Graphs, and Directed Acyclic Graphs with exact conditions and associated polynomial-time algorithms. I will then show an algebraic construction with elements as graphs and two operations that have further underlying structure within them. Then, showcasing some results and theorems that exist behind the hidden structure of this algebraic construction. An Algebra of Graphs and the Longest Path Problem
Thu, Sep. 4 11:15am (MATH …	Algebraic Geometry Jon Kim X In this talk, I will introduce the moduli space of K3 surfaces. I will start with some preliminaries on K3 surfaces from Hodge theory and move onto their moduli. Specifically, the goal will be to introduce the Bailey-Borel compactification of a certain ball quotient and its relationship to the moduli space of K3 surfaces. If there is time, I will discuss degenerations, Kulikov models (type III), and recent work by Alexeev and Engel (2023) on the KSBA compactification of the moduli of K3 surfaces. Moduli of K3 Surfaces
Tue, Sep. 9 1:25pm (MATH 2…	Algebra/Logic Nik Ruskuc (St Andrews) X Let S be a semigroup, and suppose that the full relation SxS is finitely generated as a right congruence. When S is a group this happens if and only if S is finitely generated, but in general there are many more examples, of arbitrarily large cardinalities. Let X be a finite generating set for SxS. Then, for any two elements s,t in S, there is a finite chain of X-transformations connecting s and t. The longest such chain is the X-diameter of S, and the smallest X-diameter when X ranges over all finite generating sets is the (right congruence) diameter of S, denoted D(S). This parameter can be finite or infinite. It turns out that it is finite for many classical semigroups of transformations, linear transformations and partitions, and is then very small, i.e. . Usually some intriguing combinatorics is involved in these results, but the underlying reasons for this phenomenon remain mysterious. The new results presented in this talk are due to various subsets of J. East, V. Gould, C. Miller, T. Quinn-Gregson and myself. (Congruence) diameter of semigroups Sponsored by the Meyer Fund
Tue, Sep. 9 2:30pm (MATH 2…	Grad Algebra/Logic Aten, Kearnes, Mayr (CU) Organizational meeting
Thu, Sep. 11 11:15am (MATH …	Algebraic Geometry Jon Kim X We will continue our talk from last week starting with analytic moduli and discussing the moduli space of M-quasipolarized and M-polarized K3 surfaces. If time permits, we will discuss one-parameter degenerations. These talks follow Alexeev and Engel's "Compact moduli of K3 surfaces" paper in 2023. Moduli of K3 Surfaces II
Thu, Sep. 11 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X Given a compact metric space and self-homeomorphism, one can construct the associated crossed product C-algebra. There is a strong relationship between dynamical properties and C-algebraic properties. For example, the system is minimal if and only if the crossed product algebra is simple. I will discuss minimal crossed products, their K-theory, K-homology, and Poincare duality. The talk will be an introduction aimed at graduate students. Minimal crossed products and duality
Fri, Sep. 12 10:10am (Math …	Math Edu Peter Karanevich (CU Boulder School of Education) X In this hands-on workshop we will do a mathematics activity leveraging the 5 practices for orchestrating productive mathematical discussions to debrief it. We will then examine each practice and have time for reflection about how you can incorporate these ideas in your classroom. 5 practices of Orchestrating Productive Mathematics Discussions
Tue, Sep. 16 1:25pm (online)	Algebra/Logic Leandro Vendramin (Vrije Universiteit Brussel, Belgium) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk explores the interplay between set-theoretic solutions to the Yang-Baxter equation and structures arising in algebraic logic. Central to this connection is the recently introduced theory of L-algebras, which generalizes well-known logical systems such as Hilbert and Heyting algebras. The presentation assumes minimal background. We will discuss illustrative examples, highlight open problems, and share several conjectures. L-Algebras: A bridge between algebraic logic and the Yang-Baxter equation
Tue, Sep. 16 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten (CU Boulder) X We will begin covering background material pertaining to the recent paper "A categorical perspective on constraint satisfaction: The wonderland of adjunctions" by Hadek, Jakl, and Oprsal. Categorical methods for constraint satisfaction
Wed, Sep. 17 4:40pm (MATH 3…	Grad Student Seminar Matt Watson (CU Boulder) X Modular forms are functions on the upper half plane which satisfy certain transformation laws given by the action of certain arithmetic groups. Though often introduced as a complex analytic object, modular forms have a tendency to appear in seemingly unrelated areas of mathematics. How many ways can an integer be written as a sum of four squares? Modular forms can be used to solve this. What is the densest arrangement of non-overlapping spheres in ? Modular forms can be used to solve this. The coefficients of the Fourier expansion of some important modular function encode the dimensions of the irreducible representations of the monster group (moonshine!!!). In the context of geometry, modular forms give pluricanonical forms on some moduli space. The goal of this talk is to introduce modular forms, marvel at some of their interesting properties, and then explain why I care about modular forms as an algebraic geometer. Modular Forms and the Baily-Borel Theorem
Thu, Sep. 18 11:15am (MATH …	Algebraic Geometry Jon Kim X We continue the talk from last week, starting with quasipolarized and polarized K3 surfaces and their moduli spaces. Moduli of K3 Surfaces III
Fri, Sep. 19 10:10am (Math …	Math Edu Shelby Stanhope (US Air Force Academy) X Clear communication is an essential skill for success in mathematics, yet many undergraduates enter college-level courses without experience in writing solutions that are both clear and well-structured. This talk will explore strategies instructors can use to help learners begin developing effective communication practices as early as the calculus sequence, not just in proof-based courses. We will discuss the role of short phrases in guiding the reader, the importance of balancing notation with words, and techniques for establishing a logical flow that allows solutions to stand on their own. I will highlight a communication activity I have used in a multivariable calculus course that scaffolds the development of these skills, recognizing that such expectations may be new to many students. Developing Effective Communication Practices in Mathematics
Tue, Sep. 23 11am (MATH 350)	Number Theory Zheng Xiao (CU) X After Mordell’s conjecture for curves was proved by Faltings, attentions turn to the distribution of rational and integral points on higher dimensional varieties, which is encoded in the celebrated Vojta’s conjecture. Along this line we proved a subspace type inequality, improving the result of Ru-Vojta, on surfaces. Meanwhile, we obtain a sharp criterion of when some certain surfaces admit a non Zariski-dense set of integral points. Joint with Huang, Levin. Diophantine Approximation on Surfaces and Distribution of Integral Points
Tue, Sep. 23 1:25pm (MATH 2…	Algebra/Logic Peter Mayr (CU) X Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring), and let B be the countable atomless Boolean algebra. We show that the automorphism groups of filtered Boolean powers of A by B have ample generics, which gives a new proof of our previous results that these groups have the small index property, uncountable cofinality and the Bergman property. This is joint work with Nik Ruskuc. Generic automorphisms of Boolean powers
Tue, Sep. 23 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten (CU Boulder) X We will continue covering background material pertaining to the recent paper "A categorical perspective on constraint satisfaction: The wonderland of adjunctions" by Hadek, Jakl, and Oprsal. Topics will include the discrete Grothendieck construction, Kan extensions, and the nerve of a functor. Categorical methods for constraint satisfaction (Part 2)
Tue, Sep. 23 2:30pm (MATH 3…	Topology Howy Jordan X A topological space is stratified when it is equipped with a nice decomposition into nice subsets. In the classical case, the nice subsets are manifolds. When the decomposition is nice enough, one can equip the stratified space with a stratified tangent bundle. "Is there a category of stratified spaces whose fiber bundles include these stratified tangent bundles?" Motivated by this question, we will investigate categories of stratified spaces. In particular, we will consider cases where the underlying stratification can vary and cases where there is a fixed base stratification and find interesting topologies and group objects along the way. Categories of Stratified Spaces
Thu, Sep. 25 11:15am (MATH …	Algebraic Geometry Daniel Lyness X TBA TBA
Thu, Sep. 25 11:15am (MATH …	Algebraic Geometry Daniel Lyness X Geometric Invariant Theory is concerned with answering the following problem: Given a group G acting on a projective variety X, how can we construct a quotient of X by the group action, and give it the structure of an algebraic variety? We cannot simply take the orbit space, and hope that this will be a variety, so it is important to throw out some bad (unstable) orbits from X, and identify some ok (semistable) orbits together in the quotient. In this talk, I will show how to construct this quotient abstractly, and introduce the remarkable Hilbert-Mumford numerical criterion, which allows us to determine which orbits in X are stable, semistable and unstable, and therefore what our quotient looks like geometrically. In part 2 next week, I will show how I am applying GIT to my research. Introduction to Geometric Invariant Theory part 1
Thu, Sep. 25 2:30pm (MATH 3…	Functional Analysis Various X The members of the functional analysis group will give short talks introducing their research. Functional Analysis Open House
Tue, Sep. 30 1:25pm (online)	Algebra/Logic Anna Romanowska (Warsaw University of Technology) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we will use an algebraic approach to study convex subsets of affine spaces over the ring of dyadic rationals. Dyadic rationals are rationals whose denominator is a power of 2. A dyadic n-dimensional convex set is defined as the intersection with n-dimensional dyadic space of an n-dimensional real convex set. Such a dyadic convex set is said to be a dyadic n-dimensional polytope if the real convex set is a polytope whose vertices lie in dyadic space. Dyadic convex sets appear as subalgebras of reducts of faithful affine spaces over the ring of dyadic numbers, or equivalently as commutative, entropic and idempotent groupoids (binars or magmas) under the binary operation of arithmetic mean. We will examine algebraic concepts and properties of dyadic polytopes (especially polygons), and contrast their behavior with that of polytopes in real affine space. On the basis of older results about the generation and structure of dyadic polytopes, we will present recent results (obtained with A. Mucka) on the representation, characterization and classification of dyadic triangles. Algebraic properties of dyadic convex polytopes
Tue, Sep. 30 1:30pm (MATH 3…	Homotopy Jackson Morris (University of Washington) X The stable homotopy groups of spheres are an important and complicated invariant. However, there is a filtration which sorts the p-components of this group into vn-periodic layers, known as chromatic heights, which are themselves more computable. The height one piece is the only layer which we fully understand, and an invaluable tool to accessing v1-periodic stable homotopy is the BP<1>-based Adams spectral sequence. In this talk, I will discuss joint work with Petersen and Tatum which focuses on the analogue of this problem in motivic homotopy theory. The key idea is that there are similar periodic layers in the stable homotopy of the motivic sphere. We compute the E1-page of the analogous BPGL<1>-based motivic Adams spectral sequence at all primes p and over a myriad of base schemes. Time permitting, I will discuss future directions in chromatic motivic homotopy theory. Splittings of truncated motivic Brown-Peterson cooperations algebras
Tue, Sep. 30 2:30pm (MATH 3…	Topology Chindu Mohanakumar (CU Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology
Tue, Sep. 30 2:30pm (MATH 2…	Grad Algebra/Logic Orlando Reyes (CU) Categorical Perspective on Constraint Satisfaction (Part 3)
Tue, Sep. 30 2:30pm (MATH 3…	Lie Theory Chindu Mohanakumar (University of Colorado Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology
Thu, Oct. 2 11:15am (MATH …	Algebraic Geometry Daniel Lyness X In this talk we will be continuing where we left off last week, having just introduced the Hilbert-Mumford Numerical Criterion. Now we will see how to use this powerful computational tool to do GIT on the space of plane cubic curves. There will be lots of pictures! Then we’ll kick it up a notch to my research question: How to use GIT to find a moduli space for pairs (Q,C) of a conic and cubic plane curve, and how our moduli space will change depending on the ample line bundle used for our embedding in projective space. GIT on plane curves
Thu, Oct. 2 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X The main goal of this set of talks is to introduce twisted crossed products of Banach algebras by locally compact groups. Both talks will be accessible to anyone with basic Functional Analysis knowledge, but Part II will assume familiarity with Part I. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. Part I: We give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. Part II: We now focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. We present a generalization of the so called Packer–Raeburn trick to the L^p-setting, showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one. This is joint work with Carla Farsi and Judith Packer. Twisted Crossed Products of Banach Algebras (Part I)
Fri, Oct. 3 10:10am (Math …	Math Edu Joseph Timmer & Rebekah Jones X In this workshop, we'll analyze examples of teaching statements and discuss what makes a successful teaching statement. We'll also hear directly from faculty who've served on hiring committees about their evaluation process and priorities. Participants can bring their own teaching statements to receive more targeted guidance and feedback. Teaching Statement Workshop
Tue, Oct. 7 1:25pm (online)	Algebra/Logic Andrew Moorhead (TU Dresden, Germany) View Online:https://cuboulder.zoom.us/j/96896272260 X A strong Maltsev class of varieties is a class of varieties for which there exists a finitely presented variety (i.e. a variety in a finite signature satisfying finitely many identities) whose interpretability class is a lower bound to every variety in the interpretability order, while a Maltsev class of varieties is a class for which there exists a countably infinite descending chain of finitely presented varieties and each variety in the Maltsev class is bounded below by some of the chain. A Maltsev term is the original example of a strong Maltsev condition and the identities that define it define the class of congruence permutable varieties. On the other hand, the classes of congruence distributive and congruence modular varieties are not strong Maltsev classes, but rather Maltsev classes (the terms for distributivity were discovered by Jónsson and the terms for modularity were discovered by Day). There has been for some years a fertile area of research which connects Universal Algebra to the complexity theory of constraint satisfaction. While many of these results are largely important for complexity theory, some of them have been important for algebra. In particular, Siggers discovered that the class of locally finite Taylor varieties is captured by a finite package of identities. In 2015, Olsak made the surprising discovery that in fact the class of all Taylor algebras is strong Maltsev. A natural next question was: what about the class of congruence meet semidistributive varieties? This is an important class in fixed template finite domain CSP, since the class of locally finite congruence meet semidistributive varieties is exactly the class of varieties which correspond to CSP templates which can be solved with local consistency methods. Actually, Kozik, Krokhin, Valeriote, and Willard proved that locally finite congruence meet semidistributive varieties are characterized by a finite package of identities. We show that, unlike the class of Taylor varieties, this finiteness does not lift to the general case, that is, there does not exist a strong Maltsev condition that captures every congruence meet semidistirbutive variety. The class of congruence meet semidistributive varieties is not strong Maltsev
Tue, Oct. 7 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X Every permutation is associated to a classical combinatorial object called a Rothe diagram, where the number of points in the diagram is equal to the number of inversions in the permutation. In this talk, we generalize this notion by associating a Rothe diagram to a set of positive orthogonal roots for a finite simply-laced Weyl group. This construction turns out to have many applications to algebraic combinatorics and to the theory of invariant polynomials. This is based on joint work with Tianyuan Xu (University of Richmond). Orthogonal roots and generalized Rothe diagrams
Tue, Oct. 7 2:30pm (MATH 2…	Grad Algebra/Logic Omar Al - Khazali (CU Boulder) Graph algebras
Thu, Oct. 9 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Thu, Oct. 9 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X The main goal of this set of talks is to introduce twisted crossed products of Banach algebras by locally compact groups. Both talks will be accessible to anyone with basic Functional Analysis knowledge, but Part II will assume familiarity with Part I. Classical crossed products of Banach algebras have been extensively studied for different classes of representations, including contractive representations on L^p-spaces. Part I: We give a general formulation for Banach algebras associated with twisted dynamical systems. Recent developments in L^p-twisted crossed products have mostly focused on situations where either the algebra is the complex numbers or when the group is discrete (more generally for étale groupoids). We present a universal characterization of the twisted crossed product when the acting group is locally compact and the Banach algebra has a contractive approximate identity. Part II: We now focus on the case when the representations are contractive ones acting on L^p spaces. We briefly discuss a reduced version for L^p-operator algebras. We present a generalization of the so called Packer–Raeburn trick to the L^p-setting, showing that the universal L^p twisted crossed product is ``stably'' isometrically isomorphic to an untwisted one. This is joint work with Carla Farsi and Judith Packer. Twisted Crossed Products of Banach Algebras (Part II)
Thu, Oct. 9 3:30pm (Math 3…	Probability Ewan Davies (Colorado State University) X The hard-core model is a well-studied probability distribution in statistical physics and algorithms since it exhibits interesting behavior from probabilistic and algorithmic perspectives. We will survey the underlying mathematical phenomena that drive this interesting behavior and uncover some surprises. A first-order phase transition in the hard-core model
Fri, Oct. 10 10:10am (Math …	Math Edu Hilary Freeman (Colorado State University) X Math 160 Calculus I for Engineers at Colorado State University has been using a version of standards-based grading since Fall of 2020. In this talk I will discuss why I made the change to alternative grading and how I’ve been implementing this grading system and the changes we’ve gone through. I’ll address the particular challenges of coordinating multiple sections with a large total enrollment and what technology I’ve found helpful or not so helpful. Five Years of Standards-Based Grading in a First Semester Calculus Course
Tue, Oct. 14 12:10pm (MATH …	Kempner Constantin Dorin Dumitrascu (Adrian College) X We take a combinatorial approach to the classical problem of random walks in the d-dimensional Euclidean lattice Z^d, where the walker takes steps {-1, +1}^d, each with equal probability 1/(2d). We give precise asymptotics for the number of closed walks or excursions (the walks of a given length that return to the starting point). We also discuss the more complicated case of first-time returns. Recall that a sequence (f_n)_n is called P-recursive if it admits a recurrence relation with coefficients polynomials in n. This property is equivalent with holonomicity (or D-finiteness) of the generating function, meaning that the vector space of its formal derivatives is finite dimensional. We show that, in dimension greater or equal to 2, the sequence of excursions is P-recursive, while the sequence of first-time returns is not P-recursive. Techniques from the theory of Legendre polynomials, analytic combinatorics, holonomic functions, and Fuchsian ODEs are employed in the proofs. This presentation reports on joint work with Liviu Suciu. On the non-holonomic character of first time returns in the Euclidean lattice
Tue, Oct. 14 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU Boulder) Categorical Perspective on Constraint Satisfaction (Part 4)
Tue, Oct. 14 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X We explore further applications of the generalized Rothe diagrams associated to sets of orthogonal positive roots of simply laced root systems. We will discuss examples arising from labelled Fano planes and from the representation theory of simple Lie algebras. This talk is based on joint work with Tianyuan Xu (University of Richmond), and is a continuation of last week's talk. Orthogonal roots and generalized Rothe diagrams, part 2
Tue, Oct. 14 3:30pm (MATH 3…	Topology Taylor Rogers X Recently, higher categorical generalizations of semiadditivity have proven useful in stable homotopy theory; in particular, they demonstrate that certain localizations of the category of spectra are exceedingly well-behaved. Understanding higher semiadditivity has also produced an interesting theory of ambidextrous adjunctions, that may be useful in the study of other stable infinity categories. In this talk, we will introduce semiadditivity and ambidexterity in a general categorical setting. We will then specialize to the context of stable homotopy theory and discuss how the theory of higher semiaddtivity gives a proof of May's nilpotence conjecture. Ambidexterity and Nilpotence
Tue, Oct. 14 3:35pm (MATH 2…	PDE/Analysis Fernando Charro (Wayne State University) X In recent years there has been an increasing interest in whether a mean value property, known to characterize harmonic functions, can be extended in some weak form to solutions of nonlinear equations. This question has been partially motivated by the surprising connection between Random Tug-of-War games and the normalized p-Laplacian discovered some years ago by Peres et al., where a nonlinear asymptotic mean value property for solutions of a PDE is related to a dynamic programming principle for an appropriate game. In this talk, we discuss asymptotic mean value formulas for a class of nonlinear second-order equations that includes the classical Monge-Ampère and k-Hessian equations among other examples. Asymptotic Mean Value Formulas for Nonlinear Equations Sponsored by the Meyer Fund
Thu, Oct. 16 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Thu, Oct. 16 2:30pm (MATH 3…	Functional Analysis Gregory Berkolaiko (Texas A&M) X Duistermaat index is a symplectic invariant defined for triples of Lagrangian subspaces. We discuss its concise axiomatic definition, its relation to the Maslov index of paths of Lagrangian subspaces and its surprising application to eigenvalue interlacing for differential operators with different sets of boundary conditions. Based on joint work with Graham Cox, Yuri Latushkin and Selim Sukhtaiev. Duistermaat index and its application to eigenvalue interlacing
Tue, Oct. 21 2:30pm (MATH 3…	Lie Theory Andrew Reimer-Berg (Colorado State University) X We resolve a question of Gillespie, Griffin, and Levinson that asks for a combinatorial bijection between two classes of trivalent trees, tournament trees and slide trees, that both naturally arise in the intersection theory of the moduli space of stable genus zero curves with n marked points. In this talk, we give an explicit combinatorial bijection between these two sets of trees using an insertion algorithm, and also classify the words that appear on the slide trees of caterpillar shape via pattern avoidance conditions. Insertion algorithms and pattern avoidance on trees coming from the moduli space of curves Sponsored by the Meyer Fund
Tue, Oct. 21 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU) Categorical Perspective on Constraint Satisfaction (Part 5)
Wed, Oct. 22 4:40pm (MATH 3…	Grad Student Seminar Edouard Heitzmann (CU Boulder) X I will state Arrow's Impossibility Theorem, then give the definitions of some commonly used ranked-choice voting rules, and finally present some examples of common paradoxes that each of them suffer from. Some Common Voting Rule Paradoxes
Thu, Oct. 23 11:15am (MATH …	Algebraic Geometry Yota Maeda (TU Darmstadt) X See https://sites.google.com/view/fragmentseminar/ On the Kodaira dimension of even-dimensional ball quotients Sponsored by the Meyer Fund
Fri, Oct. 24 12:20pm (MATH …	Math Edu Constantin Dorin Dumitrascu (Adrian College) X What should preservice teachers learn in a college geometry course, and how should they learn it? To change the lack of national consensus on how to answer these two questions, an online community of faculty who teach or do research on college geometry courses taken by secondary teachers (GeT courses) was formed in the Summer of 2018, under the coordination of Pat Herbst and Amanda Brown from the University of Michigan GRIP lab (https://www.gripumich.org/). A group of GeT instructors worked for over two years toward the goal of identifying a list of essential student learning outcomes (SLOs) for inclusion in GeT courses – where essential means the identification of content knowledge that all prospective secondary geometry teachers should have the opportunity to learn. The public draft of the set of Student Learning Outcomes is available at https://getapencil.org/student-learning-objectives/. My presentation will discuss some of the SLOs, how I incorporated them in my own teaching of the GeT course at Adrian College, and how my participation in the GeT: A Pencil community influenced and enriched my teaching. A Student Learning Outcomes Perspective on the College Geometry Course for Secondary Teachers
Tue, Oct. 28 1:25pm (MATH 2…	Algebra/Logic Zak Mesyan (CU Colorado Springs) X Given a semigroup S and elements s,t in S, write s~t if s=pr and t=rp, for some p,r in S (with 1 adjoined). This relation, and its transitive closure, both known as "primary conjugacy", has been extensively used and studied in connection with many algebraic objects, including groups, rings, and C*-algebras. It is the standard tool for either measuring or forcing commutativity. We discuss a natural generalization, defined by s~t whenever s=p_{1}...p_{n} and t=p_{f(1)}...p_{f(n)}, for some p_{1},...,p_{n} in S (with 1 adjoined) and permutation f of {1,...,n}, together with its transitive closure, which we call the "permutation" relation. The permutation relation is actually the congruence generated by the primary conjugacy, and is the least commutative congruence on any semigroup. We explore general properties of the permutation relation, discuss it in the context of groups and rings, compare it to various known semigroup conjugacy relations, and describe its equivalence classes in different semigroups. Conjugacy and least commutative congruences in semigroups Sponsored by the Meyer Fund
Tue, Oct. 28 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten (CU Boulder) X I will state the fundamental theorem of the algebraic approach to promise constraint satisfaction and present a family of examples where we can explicitly see the connection between gadgets, nerves, and minion homomorphisms. Examples for the Fundamental Theorem of Algebraic PCSP
Tue, Oct. 28 3:30pm (MATH 3…	Topology Alex LaJeunesse X Machinery from homotopy theory allows us to define a Brauer space for any E_3-ring R whose homotopy groups carry important arithmetic information about R. If R is equivalent to a discrete commutative ring, for example, these homotopy groups agree with the classical (derived) unit, Picard, and Brauer groups. I will describe how one constructs this Brauer space and discuss the problem of "strictification" for Brauer classes. Unit, Picard, and Brauer Groups of Ring Spectra
Wed, Oct. 29 4:40pm (MATH 3…	Grad Student Seminar Colin Jackson (CU Boulder) X We discuss ideal class groups and how they tell us how numbers factor when we extend to rings larger than the integers. Factoring 101
Thu, Oct. 30 10am (Math 350)	Number Theory Wissam Ghantous (University of Central Florida) X The main hard problem underlying the field of isogeny-based cryptography is that of finding an isogeny between two given supersingular elliptic curves. An associated (and equivalent) problem is that of finding the endomorphism ring of a given elliptic curve. Indeed, endomorphisms of elliptic curves play a crucial role, and appear in many places in the literature: from the special soundness of the SIDH-based Identification Protocol, to the binding property of Sterner's isogeny graph commitment scheme, to that of finding collisions for the CGL hash function. From a graph theoretic point of view, these endomorphisms correspond to cycles in . We study these cycles in a very general way, and using two different methods: Brandt matrices and ideal counting. Indeed, this study is not limited to the usual isogeny graph. We instead consider the generalized supersingular -isogeny graph, where is a set of primes and isogenies are allowed to have degree in the set . Cycles in the generalized supersingular -isogeny graph
Thu, Oct. 30 11am (MATH 220)	Number Theory Gabrielle Scullard (University of Georgia) X The study of supersingular elliptic curves oriented by a quadratic imaginary order O, and the horizontal isogenies between them (induced by the action of an ideal in the class group), has become increasingly important in isogeny-based cryptography; these are the curves and isogenies which are fundamental to CSIDH and SCALLOP, for example. We relate N-isogenies between supersingular elliptic curves oriented by an order of discriminant D, to solutions of equations involving positive definite binary quadratic forms of discriminant D. In the case that -DN < 2p, we characterize when non-horizontal N-isogenies arise. As an application, when -D < 2p, we classify when an oriented supersingular elliptic curve has multiple orientations by the order O. Isogenies between oriented supersingular elliptic curves
Thu, Oct. 30 2:30pm (MATH 3…	Functional Analysis Maggie Reardon (CU Boulder) X Matui’s HK-conjecture proposes a connection between the homology of a nice enough étale groupoid and the -theory of the associated reduced -algebra. The HK-conjecture is not true in general and there are a number of counterexamples. The related AH-conjecture predicts an exact sequence involving the zeroth and first homology groups together with the abelianization of the topological full group. Unlike the HK-conjecture, no counterexamples are known for the AH-conjecture, though it remains unproven. Both conjectures are verified for a number of natural classes of groupoids, including AF groupoids. Putnam introduced a new class of groupoids in the paper titled “Some classifiable groupoid -algebras with prescribed -theory”. These new groupoids are related to AF groupoids and this prompts a natural question: does this new class of groupoids satisfy the HK- and AH-conjectures? The HK- and AH-conjectures for certain groupoids constructed by Putnam
Tue, Nov. 4 1:25pm (MATH 2…	Algebra/Logic Andrea Albano (Universita del Salento, Italy) X The Yang--Baxter equation (YBE) is a fundamental relation in mathematical physics that has its roots in the investigation of many-particle interactions in two-dimensional quantum dynamical systems, where it can be interpreted as governing integrability properties. When a system presents a boundary that interacts with the objects in motion, the Reflection Equation (RE) - as first studied by Cherednik and Sklyanin in 1984 and 1988, respectively - is a condition that ensures the persistence of integrability. To determine a uniform procedure that produces special solutions, in 1990 Drinfel'd suggested studying the set-theoretical YBE, thus paving the way for the introduction of new combinatorial tools in the subject. In recent years, Caudrelier and Zhang initiated the investigation of the set-theoretic formulation of the RE, taking inspiration from the study of soliton collisions on the half-line. The aim of this talk is to provide a self-contained overview of the set-theoretic YBE with a particular attention to the role played by self-distributive structures. Moreover, we study the interplay between bijective non-degenerate set-theoretic solutions of the YBE and their reflections, with a focus on solutions of derived type. Based on a joint work with M. Mazzotta and P. Stefanelli. Set-theoretic solutions of the Yang-Baxter equation and their reflections Sponsored by the Meyer Fund
Tue, Nov. 4 3:30pm (MATH 3…	Topology Ben Knudsen (Colorado State University) X The homology groups of the unordered configuration spaces of a graph form a finitely generated module over the polynomial ring generated by its edges; in particular, each Betti number is eventually equal to a polynomial in the number of particles, an analogue of classical homological stability. Wishing to lift this result to an analogue of representation stability, one encounters the unavoidable fact that the corresponding algebraic structure at the level of ordered configuration spaces is non-Noetherian. Thus, finite generation results are likely to be neither useful nor within easy reach. Drawing on ideas from twisted algebra and factorization homology, we circumvent this obstacle to give a complete asymptotic calculation of the Betti numbers of pure graph braid groups over any field and, in characteristic zero, of the multiplicities of many irreducible representations of the symmetric groups. This talk represents joint work with Hainaut and Wawrykow, building on joint work with An and Drummond-Cole. Representation asymptotics in the homology of pure graph braid groups
Thu, Nov. 6 11:15am (MATH …	Algebraic Geometry Lisa Marquand (NYU) X Abstract: Cubic fourfolds have been classically studied up to birational equivalence, with an eye towards rationality problems. We will discuss two other notions of equivalence: Fourier-Mukai equivalence, and `hyperkahler equivalence'. We'll discuss how these equivalences are conjecturely related. We will give new examples of pairs of cubic fourfolds satisfying all three equivalences. In particular, our examples will be pairs of birational cubic fourfolds, with birational Fano varieties of lines, a previously unknown phenomenon. This is joint work with Corey Brooke and Sarah Frei. Cubic fourfolds with birational Fano varieties of lines Sponsored by the Meyer Fund
Thu, Nov. 6 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) X Minimal homeomorphisms of topological spaces provide a source of simple C-algebras whose structure and K-theory can be understood through dynamical systems. I will present results on the existence of minimal homeomorphisms of flat manifolds with positive first Betti number. When the flat manifold has a spin^c structure we will show that the resulting cross product satisfies Poincare Duality for C-algebras. Finally, I will describe ongoing work toward constructing explicit KK-cycle representatives in the presence of minimal flows, in analogy with the classical case of irrational rotation algebras. Flat manifolds, C*-algebras, and duality
Fri, Nov. 7 10:10am (Math …	Math Edu Natalie Snow & JB Shilcutt (New Mexico State University & Utah Tech University) X This workshop will cover student-centered pedagogical practices that can be used in a higher education mathematics setting. We will talk about the pillars of the Activist Approach, discuss how we are employing these methods in both in-person and asynchronous courses at two universities, and share processes we use to build a foundation with our students in order to connect with their interests, motivations, and learning needs. At the end of the session, there will be time for participants to develop their own questions that they would like to ask their students to facilitate their learning. Redefining the Equation: Student-Centered Pedagogies in Mathematics
Tue, Nov. 11 12:10pm (MATH …	Kempner Gregory Berkolaiko (Texas A&M) X Quantum chaos is the study of signatures of chaotic dynamics at the quantum level. The objects of study include the energy (eigenvalue) or wavefunction (eigenfunction) statistics. Nodal fluctuations belong to the second class; they express deviations of the number of zeros (or nodal domains) of the eigenfunction from its expected value. We will discuss the nodal fluctuations in a particular model, discrete Schroedinger operators on graphs. The conjecture is that the nodal fluctuations are always Gaussian, in the appropriate limit and after appropriate normalization. While the conjecture has been established in some classes of graphs, it is mostly wide open. We will review recent progress in this area which combines many different approaches: Morse Theory, Random Matrices, Spectral Graph Theory and Algebraic Geometry. Universality of nodal fluctuations: from quantum chaos to algebraic geometry
Tue, Nov. 11 1:25pm (online)	Algebra/Logic George Metcalfe (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk will be about idempotent semifields, which, from a purely algebraic perspective are just lattice-ordered groups formulated in a restricted language with the group multiplication, neutral element, and lattice-join operation. We will see that although countably infinitely many equational theories of lattice-ordered groups have a finite equational basis, no non-trivial equational theory of idempotent semifields has this property. On the other hand, as in the case of lattice-ordered groups, there are continuum-many equational theories of classes of idempotent semifields. Finally, we will relate the problem of deciding equations in the class of idempotent semifields to the problem of deciding if there exists a right order on a free group satisfying a given finite set of inequalities, and show that these problems are, respectively, co-NP-complete and NP-complete. This is joint work with Simon Santschi. Equational Theories of Idempotent Semifields
Tue, Nov. 11 1:30pm (MATH 3…	Homotopy Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Tue, Nov. 11 1:30pm (MATH 3…	Topology Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Tue, Nov. 11 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X We will describe the bounded width portion of the CSP dichotomy theorem. In particular, we will explain what bounded width CSPs are, and present the proof by Barto and Kozik that CSPs whose polymorphism algebras have WNUs for all but finitely many arities, have bounded width. Bounded width CSPs
Tue, Nov. 11 2:30pm (MATH 3…	Lie Theory Peter Brooksbank (Bucknell University) X Tensors have roughly as many definitions and notations as there are fields that use them. Nevertheless there is some broad agreement on the sort of information one might wish to extract from a tensor given by an array of numbers. One common goal is to change the ambient reference frame in order to reveal some internal structure. For instance, one might wish to know if, by a suitable change of basis, the nonzero entries of the array can be made to cluster in some prescribed manner. In this talk I will discuss clustering techniques whose origins lie in computational algebra and show they can be adapted to tensors that occur in the real world. The algorithms that result from this algebraic perspective have certain advantages—such as provable efficiency and reproducibility—and they can detect cluster patterns that elude existing methods. This is a report on joint work with Martin Kassabov and James Wilson. Clustering algorithms for tensors: an algebraic approach Sponsored by the Meyer Fund
Wed, Nov. 12 4:30pm (MATH 3…	Algebraic Geometry Zhijia Zhang (NYU) X Abstract: The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces. Broadly speaking, a G-variety is a variety X carrying an action of a group G. The group can act via automorphisms of X or via Galois actions if the base field is non-closed. There are close connections, as well as drastic differences between these two types of actions from the perspective of birational geometry. In this talk, I will explore these similarities and differences with a focus on equivariant unirationality of (not only) Fano threefolds. This is joint work with Yuri Tschinkel and Ivan Cheltsov. Title: Equivariant unirationality of Fano threefolds - Note the unusual time and date Sponsored by the Meyer Fund
Thu, Nov. 13 3:35pm (MATH 3…	Grad Student Seminar Jon Kim (CU Boulder) X A moduli space is a parameter space where each point represents some mathematical object. For algebraic geometers, these objects are usually geometric, and moduli spaces help us see how these geometric objects deform and detect their "stability". In this GSS talk, I will give a short survey on the development of moduli spaces in algebraic geometry and provide examples on constructing these moduli spaces. The main result will be showcasing how the moduli space of acute triangles is closely related to the moduli space of elliptic curves. What even is a moduli space?
Tue, Nov. 18 1:25pm (MATH 2…	Algebra/Logic Simon Santschi (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X Lattice-ordered pregroups (l-pregroups) are exactly the involutive residuated lattices where addition and multiplication coincide. Among them, for every positive integer n, the n-periodic l-pregroup F_n(Z) of n-periodic order-preserving functions on the integers plays an important role in understanding distributive l-pregroups and also n-periodic ones. We give a finite axiomatization of the variety generated by F_n(Z). On the way we also obtain some more general results about periodic l-pregroups and we characterize the finitely subdirectly irreducibles of the variety generated by F_n(Z). Joint work with Nick Galatos. Axiomatizing small varieties of periodic l-pregroups
Tue, Nov. 18 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X Continuation of last week's talk. Bounded width CSPs, 2
Tue, Nov. 18 2:30pm (MATH 3…	Lie Theory Mandi Schaeffer-Fry (DU) X The McKay Conjecture (now a theorem due to Cabanes--Späth) says that there is a bijection between irreducible characters of a finite group G with degree not divisible by p and the corresponding set for the normalizer of a Sylow p-subgroup. Several Galois refinements of this Conjecture exist, positing that the bijection should be compatible with fields of values. I'll discuss joint work with Lucas Ruhstorfer, in which we complete the proof of the original of these Galois refinements, proposed by Isaacs--Navarro in 2002. I'll also discuss several consequences, giving additional local-global properties in the character theory of finite groups. The Isaacs--Navarro Galois Conjecture
Tue, Nov. 18 3:30pm (MATH 3…	Topology Rick TBD
Wed, Nov. 19 4:40pm (MATH 3…	Grad Student Seminar Basia Klos (CU Boulder) X Does that question keep you up at night? If yes, you're in luck - in this talk, we'll define these algebraic objects, which are ubiquitous in the representation theory of infinite-dimensional Lie algebras and also appear in number theory and physics. We'll give a friendly example of a VOA and might even mention why you should care. What even is a vertex operator algebra?
Thu, Nov. 20 11:15am (MATH …	Algebraic Geometry Jon Kim X In 2024, Schock constructed several KSBA compactifications of the moduli space of cubic surfaces. More precisely, he considered pairs consisting of a cubic surface and a boundary divisor given by the sum of the 27 lines, all with the same weight value in the interval (1/9, 1] and provided a finite wall-and-chamber decomposition and described the weighted stable pairs parameterized by the moduli spaces in each chamber. In this talk, I will describe recent work where I provide a similar finite wall-and-chamber decomposition for KSBA compactifications where we weight one “heavy” line with weight b, and the other 26 lines uniformly with weight c. Moduli of (b,c)-weighted stable marked cubic surfaces
Thu, Nov. 20 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X Orbit-breaking in topological dynamical systems was introduced by Ian Putnam in his study of the C-algebras associated to Cantor minimal systems. By breaking an orbit at a single point, Putnam was able to construct all simple unital AF algebras as subalgebras by way of a Cantor minimal system. Since then, orbit-breaking algebras have been used to construct dynamical models for many stably finite “classifiable” C-algebras, most notably the Jiang–Su algebra. In this talk I will highlight these results and also discuss recent work-in-progress with Robin Deeley and Ian Putnam, where we generalize orbit-breaking for a homeomorphism to the setting of a continuous, surjective, local homeomorphism, allowing for purely infinite constructions. Orbit breaking and C*-algebras Sponsored by the National Science Foundation
Wed, Dec. 3 4:40pm (MATH 3…	Grad Student Seminar Stephanie Oh (CU Boulder) X TBD What even is a spectral sequence?
Tue, Dec. 16 3:30pm (MATH 3…	Topology Bowen Yang (Harvard Center of Mathematical Sciences and Applications) TBD Sponsored by the Meyer Fund

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