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Events for October 2025 – February 2026

Return to this week

Oct. 30, 2025 1:36pm (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
Oct. 02, 2025 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
Oct. 02, 2025 2:30pm (MATH 3…	Functional Analysis Alonso Delf�n (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 �tale 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)
Oct. 03, 2025 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
Oct. 07, 2025 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 J�nsson 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
Oct. 07, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Omar Al - Khazali (CU Boulder) Graph algebras
Oct. 07, 2025 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
Oct. 09, 2025 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Oct. 09, 2025 2:30pm (MATH 3…	Functional Analysis Alonso Delf�n (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 �tale 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)
Oct. 09, 2025 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
Oct. 10, 2025 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
Oct. 14, 2025 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
Oct. 14, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU Boulder) Categorical Perspective on Constraint Satisfaction (Part 4)
Oct. 14, 2025 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
Oct. 14, 2025 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
Oct. 14, 2025 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-Amp�re and k-Hessian equations among other examples. Asymptotic Mean Value Formulas for Nonlinear Equations Sponsored by the Meyer Fund
Oct. 16, 2025 11:15am (MATH …	Algebraic Geometry Matt Watson X TBA TBA
Oct. 16, 2025 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
Oct. 21, 2025 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
Oct. 21, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson (CU) Categorical Perspective on Constraint Satisfaction (Part 5)
Oct. 22, 2025 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
Oct. 23, 2025 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
Oct. 24, 2025 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
Oct. 28, 2025 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
Oct. 28, 2025 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
Oct. 28, 2025 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
Oct. 29, 2025 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
Oct. 30, 2025 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
Oct. 30, 2025 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 �tale groupoid and the $K$ -theory of the associated reduced $C$ -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 $C$ -algebras with prescribed $K$ -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
Oct. 30, 2025 10pm (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 $Gp(ℓ)$ . 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 $L$ -isogeny graph, where $L$ is a set of primes $ℓ1, ℓ2, ... , ℓr$ and isogenies are allowed to have degree in the set $L$ . Cycles in the generalized supersingular $L$ -isogeny graph
Nov. 04, 2025 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
Nov. 04, 2025 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
Nov. 06, 2025 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
Nov. 06, 2025 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
Nov. 07, 2025 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
Nov. 11, 2025 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
Nov. 11, 2025 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
Nov. 11, 2025 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
Nov. 11, 2025 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
Nov. 11, 2025 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
Nov. 11, 2025 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
Nov. 12, 2025 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
Nov. 13, 2025 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?
Nov. 18, 2025 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
Nov. 18, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X Continuation of last week's talk. Bounded width CSPs, 2
Nov. 18, 2025 2:30pm (MATH 3…	Lie Theory Mandi Schaeffer-Fry (DU) X The McKay Conjecture (now a theorem due to Cabanes--Sp�th) 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
Nov. 18, 2025 3:30pm (MATH 3…	Topology Rick TBD
Nov. 19, 2025 4:40pm (MATH 3…	Grad Student Seminar Wei Wu Lu X I'd like to give an overview on some of the basics of automorphic forms, how they arise and avenues of open research regarding them. Automorphic Forms and Other Ellusive Functions
Nov. 20, 2025 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
Nov. 20, 2025 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
Dec. 02, 2025 1:25pm (online)	Algebra/Logic Andrea Montoli (Universita degli Studi di Milano) View Online:https://cuboulder.zoom.us/j/96896272260 X We will describe some categorical properties of preordered and right-preordered groups, giving an explicit description of limits and colimits in these categories, studying some exactness properties, and showing that both structures give rise to quasivarieties. We will show that, from an algebraic point of view, the categories of preordered groups and of right-preordered groups share several properties with the one of monoids. Joint work with Maria Manuel Clementino and Nelson Martins-Ferreira. (Right-)preordered groups from a categorical perspective
Dec. 03, 2025 4:40pm (MATH 3…	Grad Student Seminar Stephanie Oh (CU Boulder) X Spectral sequences are fundamental computational tools in algebraic topology/geometry and homotopy theory. In this talk, I will give an example-driven introduction to spectral sequences. Some familiarity with homological algebra and/or Top 2 will be helpful. What even is a spectral sequence?
Dec. 12, 2025 1:30pm (Math 2…	Noncomm Geometry Vladimir Baranovsky (University of California, Irvine) X Let (M, w) be a complex manifold with an holomorphic symplectic form, or an algebraic version of such a pair. Consider also a pair (X, E) consisting of a coisotropic submanifold X in M and a vector bundle E on X. Then (local) sections of E form a module over the ring O of (local) functions on M. Given a deformation quantization O_h of functions, one can ask whether E admits a similar deformation quantization E_h as a module over O_h. For Lagrangian X this is equivalent to existence of a projectively flat connection on E with specific properties. For general coisotropic X only necessary conditions on some characteristic classes are known. The plan is to present some results and conjectures related to the problem, based on recent work of Bogdanova-Vologodsky and a Harish-Chandra bundle approach to quantizations and their Deligne classes, introduced earlier by Bezrukavnikov-Kaledin. Quantization of symplectic manifolds and vector bundles on coisotropic submanifolds.
Dec. 16, 2025 3:30pm (MATH 3…	Topology Bowen Yang (Harvard Center of Mathematical Sciences and Applications) X I will outline a classification framework for quantum phases within the setting of stabilizer states and quantum cellular automata (QCA).� Both admit a precise algebraic formulation�stabilizer codes as modules over Laurent polynomial rings, and QCA as locality-preserving automorphisms of operator algebras�through which topological invariants such as Witt classes and boundary charge modules arise.� I will review my recent work classifying Clifford QCA and Pauli stabilizer codes, which fit naturally into the same mathematical framework. A Case Study in the Classification of Quantum Phase Sponsored by the Meyer Fund
Jan. 14, 2026 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?
Jan. 15, 2026 11:15am (MATH …	Algebraic Geometry AG Group Organizational meeting
Thu, Jan. 22 2:30pm (MATH 3…	Functional Analysis Dorin Dumitrascu (Adrian College) X I will discuss some aspects of the bivariant K-theory developed by Le Gall. (P. Y. LeGall, Th\'eorie de Kasparov \'equivariante et groupo\"{\i}des. I, K-Theory 16 (1999), 361--390.) Equivariant KK-theory for groupoids acting on C*-algebras (after Le Gall)
Tue, Jan. 27 1:25pm (online)	Algebra/Logic David Stanovsky (Charles University) View Online:https://cuboulder.zoom.us/j/96896272260 X How many groups of order n are there, up to isomorphism? And what about quasigroups, semigroups, and other types of algebraic structures? Why the combinatorial explosion for quasigroups and semigroups, and not for groups? Or, actually, what is the true asymptotic behavior behind enumeration of groups? I will show some number series. I will briefly discuss enumeration methods. I will start with a brief overview of classical results on groups. In the second half of the talk, I will turn to the class of quandles, which provides an exciting playground for various types of enumeration methods. Enumeration of groups and quandles
Tue, Jan. 27 5pm (Math 350)	Math Club Siddhant Agrawal X The Navier Stokes equation is a partial differential equation that describes the motion of viscous fluids. It arises naturally in engineering and other scientific fields. In this talk, we'll derive the Navier Stokes equation and discuss some of its basic properties. We'll also discuss the famous Millennium Prize Problem concerning the Navier Stokes equation. Note: The recommended prerequisite for this talk is Calculus 3, but all are welcome! What is the Navier Stokes Equation?
Thu, Jan. 29 2:30pm (MATH 3…	Functional Analysis Dorin Dumitrascu (Adrian College) X I will give the definition of Le Gall for the equivariant KK-theory under the action of a Hausdorff groupoid, propose a construction for locally compact locally Hausdorff groupoids, and work out an example coming from foliations. Equivariant KK-theory for groupoids acting on C*-algebras (part 2)
Thu, Jan. 29 11:15pm (MATH …	Algebraic Geometry Bob Kuo (University of Colorado Boulder) X Mustafin varieties are a particular class of degenerations of projective space. Projective space, and their subvarieties, have many nice properties. Thus, one might wonder what aspects of projective geometry transfers over to Mustafin varieties. In this talk, we will explore this question through the use of tropical geometry. In particular, we will discuss the Picard group of Mustafin varieties, then describe an analogue of Bezout's theorem for Mustafin varieties. A degenerate analogue of projective geometry
Fri, Jan. 30 12:20pm (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! We'll also spend some time exploring mathematical autobiography assignments�their purpose, how they can support certain instructional goals, and considerations for implementing these assignments in a math classroom. Following our discussion, participants will have the opportunity to write their own brief mathematical autobiographies and share reflections from the experience. Attendees are encouraged (but not required) to read the recent paper on this topic linked below. https://doi.org/10.1080/10511970.2025.2571610 SUME Open House / Discussion of mathematical autobiography assignments
Tue, Feb. 3 12:10pm (MATH …	Kempner David Renfrew (SUNY Binghamton) X We show for a large class of entire functions, f, that after proper rescaling, on compact sets, the derivatives of f converge to cosine, in particular their roots become evenly spaced. This proves a conjecture of Farmer and Rhoades [Trans. Amer. Math. Soc., 357(9):3789�3811, 2005] and Farmer [Adv. Math., 411:Paper No. 108781, 14, 2022] for our class of entire functions. A main ingredient of our proof is to show that high derivatives of high degree polynomials behave like Hermite polynomials, which we prove using the techniques from the newly developed field of finite free probability. This is joint work with Andrew Campbell and Sean O'Rourke. Universality for roots of derivatives of entire functions
Tue, Feb. 3 1:25pm (online)	Algebra/Logic Sara Ugolini (IIIA-CSIC Barcelona) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we begin by considering the semiring of the natural numbers with truncated difference, N = (N, +, *, -, 0, 1). Its equational theory is not recursively axiomatizable, due to the fact that one can essentially encode in it the undecidability of Hilbert�s tenth problem. Our aim is to study finitely axiomatizable varieties of semirings with difference which include the one generated by N, and are as close to it as possible. To this end, we introduce the variety of almost natural semirings with difference, AN. We show that the subdirectly irreducible algebras in this variety coincide with the models of PA, a weak form of Peano Arithmetic without induction that is an axiomatic extension of Robinson Arithmetic. Models of PA are known to satisfy all Sigma_1 sentences true in N. This variety can be axiomatized by a few simple equations and enjoys several appealing universal-algebraic properties: it is connected to lattice-ordered rings, it is a discriminator variety, ideal determined and 0-regular; thus it admits an associated 0-assertional logic. Nevertheless, we will see that its connection to arithmetic still yields an undecidable equational theory. This talk is based on ongoing joint work with Guillermo Badia, Xavier Caicedo, and Carles Noguera. Almost natural semirings with difference
Wed, Feb. 4 2:10pm (MATH350)	Math Phys Markus Pflaum (CU Boulder) X The semester theme will be the mathematics of Schr�dinger operators� and applications in quantum many-body theory and quantum chemistry. The meeting will be an introductory and organizational meeting. For more please see the seminar webpage under https://math.colorado.edu/mathphysics/ Intro to Schr�dinger operators and semester theme
Tue, Feb. 10 1:25pm (online)	Algebra/Logic Claudia Muresan (University of Bucharest) View Online:https://cuboulder.zoom.us/j/96896272260 Abstracting congruence extensions through complete join�semilattice morphisms between commutator lattices
Tue, Feb. 10 5pm (Math 350)	Math Club Nat Thiem X Come hear about the math department's summer REU program! REU stands for Research Experiences for Undergrads. Our summer REU program is an opportunity for you to gain experience and see what math research is like. Once available, descriptions of the different projects will be posted at www.colorado.edu/math/undergraduate-program/summer-research-undergraduate. Or come to the info session to hear about the projects and get your questions answered! Summer REU Info Session
Wed, Feb. 11 2:10pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M University) View Online:https://cuboulder.zoom.us/j/97049173677 X As a warm-up for the semester, we will explore the time evolution in a finite-dimensional (d=2 mostly) Schr�dinger equation, its relation to the quadratic form and their visualization on the Bloch sphere. If time permits, we will briefly discuss why a 2-dimensional picture is sometimes appropriate even when working with unbounded Schr�dinger operators. Warm-up: Visualizing Schr�dinger's equation in finite dimensions
Wed, Feb. 11 4:40pm (MATH 3…	Grad Student Seminar Colin Jackson X What makes a function earn the title of a zeta function? We will start by looking at the Riemann zeta function, and then generalizations of it and see that if it walks like a zeta function and quacks like a zeta function, then its a zeta function Zeta Function 101
Thu, Feb. 12 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce a class of dynamical systems called shifts of finite type. There are a number of C-algebras one can construct from a shift of finite type. I will discuss properties of these C-algebras such as rational Poincare duality and rational isomorphism. Rationalizing shifts of finite type - Part I
Thu, Feb. 12 11:15pm (MATH …	Algebraic Geometry Bob Kuo X In this talk, we'll discuss tropical and toric geometry, and a relationship between the two given by Mustafin varieties. A degenerate analogue to projective geometry part II
Fri, Feb. 13 12:20pm (MATH …	Math Edu Shelby Stanhope (US Air Force Academy) View Online:https://cuboulder.zoom.us/j/99367133807 X Students often find the transition from two-dimensional to three-dimensional thinking in multivariable calculus challenging. Computer visualization and tactile models can help bridge this gap and deepen students� spatial understanding of concepts. CalcPlot3D is a free, web-based applet for 3D graphing that is easy for students and instructors to use due to its code-free, menu-driven interface with fillable textboxes, dropdown lists, and checkboxes. In this presentation, I will show demonstrations that instructors can use to illuminate concepts and visualizations that students can easily create themselves. In addition, I will discuss several classroom activities that incorporate 3D-printed models, allowing students to physically explore concepts in small groups. Together, these tools provide engaging ways for instructors to support student learning and help cultivate stronger geometric intuition in multivariable calculus. Supporting conceptual understanding in multivariable calculus using computer visualization and classroom activities with 3D-printed models
Tue, Feb. 17 2:30pm (MATH 3…	Lie Theory Carlos Ortiz (Colorado State University) X A fundamental problem in topology is to determine when two spaces are distinct. For surfaces, classical invariants suffice, but for three-dimensional manifolds the question is considerably harder. The Witten-Reshetikhin-Turaev invariants, originating in quantum field theory, provide one family of tools. For torus bundles, i.e. 3-manifolds built by cutting a torus, applying a mapping class in SL(2,Z), and regluing, the skein algebra embeds into a non-commutative torus at roots of unity, yielding a finite-dimensional representation that makes these invariants concretely computable. Exploiting this structure, we develop a classical dynamic programming algorithm and a quantum algorithm that encodes the computation into logarithmically many qubits, achieving an exponential reduction in space. We further identify a natural coefficient-counting problem that is #P-complete yet admits efficient quantum approximation. The first half of the talk will be expository, requiring only linear algebra and modular arithmetic. The second half will outline the algorithmic results. How to tell shapes apart using quantum computers
Tue, Feb. 17 3:30pm (MATH 3…	Topology Gregory Berkolaiko (Texas A&M) X The Rayleigh-Ritz method approximates the eigenvalues of a large Hermitian matrix B with Ritz values, which are the eigenvalues of B's restriction() to a smaller trial subspace S. We can view the k-th Ritz value as a real-valued function ("Ritz energy landscape") on the manifold of all possible s-dimensional trial subspaces, the Grassmannian $Grs(Cn)$ (or $Grs(Rn)$ for the real symmetric case). Motivated by questions from quantum chemistry and spectral optimization, this talk explores the topology of the Ritz energy landscape. A Morse function is called "perfect" if it describes the topology of its domain in the most efficient way possible, meaning the number of its critical points of each type exactly matches the corresponding Betti number of the space. We demonstrate that for a matrix B with distinct eigenvalues, the Ritz landscape is indeed perfect. While the function itself is not everywhere smooth and its critical points are not isolated --- and not even Morse-Bott --- its critical structure is nevertheless well-defined and ultimately reflects the topology of the Grassmannian in a minimal, perfect way. To be more precise, we show that the filtration of the Grassmannian by the sublevel sets of the k-th Ritz value is homologically perfect. The proof proceeds by introducing a suitable perturbation which ensures that points of non-smoothness are not critical (by a theorem of Zelenko and the presenter) and that the remaining smooth critical points are isolated. Based on a joint work with Mark Goresky (IAS). Footnote (): the term "restriction" is appropriate in the equivalent formulation of eigenvalues of quadratic forms. For an operator B, we apply it to vectors in S and then project the result orthogonally back onto S; this is called a "compression" of B. Ritz energy landscape is perfect (almost) Morse
Tue, Feb. 17 5pm (Math 350)	Math Club Edouard Heitzmann X The legal standard set in Rucho v Common Cause puts the onus on the plaintiffs in a Voting Rights Act (VRA) case to demonstrate that a map is a racial rather than a partisan gerrymander in order for it to be struck down as unlawful. This means plaintiffs have to 'do the homework' of the defendants for them: they must produce a map that is at least as politically gerrymandered as the defendants drew, while achieving better racial representation outcomes. This standard was successfully met by a group of mathematicians in the El Paso redistricting case, winning in federal court before the Supreme Court shadow docket put a hold on the decision, allowing the racial gerrymander to go through. The mathematicians who accomplished this used Monte Carlo Markov Chain (MCMC) methods to draw a so-called 'ensemble' of millions of alternative congressional maps for Texas, and used statistical methods to show that the enacted map was an outlier for racial representation among the maps that had similar partisan outcomes. In this talk I will go over these mathematical details, as well as describe the computational tools currently used in this field. Note: If you have a working Jupyter Notebook installation, you are encouraged to bring it to the talk, as you will have the opportunity to follow along the computational demos included in the talk. The Mathematics of Redistricting�what they did in Texas
Wed, Feb. 18 2:10pm (Math350)	Math Phys Howy Jordan (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 The spectral theorem and projection valued measures I
Thu, Feb. 19 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce a class of dynamical systems called shifts of finite type. There are a number of C-algebras one can construct from a shift of finite type. I will discuss properties of these C-algebras such as rational Poincare duality and rational isomorphism. Rationalizing shifts of finite type - Part II
Fri, Feb. 20 12:20pm (Math …	Math Edu Peter Karanevich X This talk will introduce Lev Vygotsky's learning theory of the zone of proximal development. We will then transition to an application of the theory, the concept of productive struggle. Participants will define productive struggle and learn how to modify questions to encourage students to engage in productive struggle. Productive Struggle in the Zone of Proximal Development
Tue, Feb. 24 12:10pm (MATH …	Kempner Liviu Suciu (The Pennsylvania State University) X I plan to discuss several related arithmetic and analytic dualities governed by the M�bius function and the sawtooth function. While these dualities�whether pointwise (twisted or untwisted), or functional in the L^2 or continuous setting�are formally valid, identifying conditions under which they become genuine identities is a subtle and challenging problem. It draws on deep results in analytic number theory, including Vinogradov-type bounds for exponential sums over primes (Davenport; de la Bret�che�Tenenbaum), as well as Tauberian theory (Wintner; Ingham). Arithmetic and analytic dualities governed by the Mobius and sawtooth functions
Tue, Feb. 24 1:25pm (online)	Algebra/Logic Zoltan Vidnyanszky (ELTE Budapest) View Online:https://cuboulder.zoom.us/j/96896272260 X Descriptive combinatorics is a field concerned with graph theoretic problems on nice (definable) infinite graphs. In this first half of the talk, I will introduce the field of descriptive combinatorics and discuss some of the basic results of the area. Then, I will turn to the descriptive version of complexity problems, in particular, the CSP Dichotomy: it turns out that the finitary complexity landscape is only partially reflected in the descriptive context. CSPs in the descriptive context
Tue, Feb. 24 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X The E8 root system is a highly symmetric configuration of vectors, corresponding to the 240 spheres that touch a given one in the densest possible packing of spheres in 8-dimensional Euclidean space. Despite this eightness, some combinatorial features of the root system are much easier to understand in terms of 9-dimensional coordinates. We will use this point of view to gain insight into a certain tightly structured partially ordered set, by using the combinatorics of perfect matchings and Fano planes. This is based on work in progress with Tianyuan Xu (University of Richmond). The ninefold symmetry of the E8 root system
Wed, Feb. 25 2:10pm (Math350)	Math Phys Howy Jordan (CU Boulder) View Online:https://cuboulder.zoom.us/j/97049173677 X Zoom Password 080619 The spectral theorem and projection valued measures II
Wed, Feb. 25 4:40pm (MATH 3…	Grad Student Seminar Daniel Lyness (CU Boulder) X Tori are cool. Varieties are dope. Fans are� related somehow? Prepare to dive into the world of Toric Varieties, which are varieties with a torus embedded inside. We�ll see how lots of our favourite examples of varieties are actually toric varieties, and also how a Toric Variety can be defined from the combinatorial data of a fan (the type used in the 18th century on a hot day). I�ll define everything, but having taken AG1 or knowing what Spec(R) is for a ring R will be an advantage. What even is a Toric Variety?
Fri, Feb. 27 11:10am (MATH …	Algebraic Geometry Lior Alon (MIT) X Abstract: The Poisson summation formula tells us that a lattice and its dual lattice are related through Fourier transform: the Fourier transform of the counting measure of one is the counting measure of the other. The search for non-periodic analogues of Poisson summation�discrete sets whose Fourier transform is again a discrete measure�has appeared independently across number theory, harmonic analysis, and crystallography. In the physical setting, the Fourier transform of the counting measure of an atomic structure is exactly the diffraction pattern observed experimentally. The term quasicrystal refers to a non-periodic set whose diffraction is a pure point measure, and the discovery of such materials by Dan Shechtman in 1984 profoundly altered crystallography and led to a Nobel Prize. A major mystery that remained unresolved until very recently was whether one could find a quasicrystal whose Fourier transform is supported on a discrete (rather than merely countable) set. These objects are now called Fourier quasicrystals (FQs), and until 2020 only the trivial periodic examples were known. Kurasov and Sarnak constructed the first genuinely non-periodic one-dimensional FQ using Lee�Yang polynomials, multivariate polynomials whose zeroes avoid prescribed regions of the complex plane. In our recent work, we show that every one-dimensional Fourier quasicrystal arises from the Kurasov�Sarnak construction via Lee�Yang polynomials, yielding a complete classification in dimension one. We then extend this framework to all dimensions by introducing Lee�Yang varieties, high-codimension algebraic varieties whose geometric and analytic properties govern the Fourier structure of the associated quasicrystals. The talk will introduce Fourier quasicrystals, Lee�Yang polynomials, and Lee�Yang varieties, and explain the geometric mechanism of generating summation formulas from algebraic varieties and how it is related to real-rootedness of trigonometric equations. No prior background will be assumed. Joint work with Alex Cohen, Cynthia Vinzant, Mario Kummer, and Pavel Kurasov. Fourier Quasicrystals and Lee�Yang Varieties
Fri, Feb. 27 2:30pm (Math 3…	Probability Lior Alon (MIT) X Motivated by Berry�s random wave model for chaotic domains, high-energy eigenfunctions are expected, at the scale of the wavelength, to behave like random waves. Accordingly, the size of nodal sets is determined to first order by the Weyl law, while its second-order fluctuations are expected to be universal. In analogy with spectral statistics, we refer to these fluctuations of the nodal set size as nodal statistics. Beginning with work of Berry, and later of Blum�Gnutzmann�Smilansky and Bogomolny�Schmit, it was conjectured that in chaotic systems nodal statistics are asymptotically Gaussian. While striking mathematical results support this picture on the sphere (Nazarov�Sodin), arithmetic symmetries on the torus prevent chaoticity and lead to a breakdown of universality, as shown by Wigman and collaborators and by Marinucci, Rossi, and Peccati. In this talk I will follow Smilansky�s insight and focus on nodal statistics in graph-based models. For quantum graphs and discrete operators on graphs, Berkolaiko�s nodal magnetic theorem relates nodal statistics to the stability of eigenvalues under magnetic perturbations. This connection yields Gaussian limiting statistics for quantum graphs with disjoint cycles (Alon�Band�Berkolaiko), and, combined with Morse inequalities, extends to random discrete operators on finite graphs with disjoint cycles and to complete graphs with strong on-site disorder (Alon�Goresky). I will conclude with recent joint work on nodal statistics for random matrices (Alon�Mikulincer�Urschel), showing that nodal statistics for GOE matrices obey a semicircle law rather than the conjectured Gaussian behaviour. If time permits, I will briefly discuss ongoing work on the Rosenzweig�Porter model, where adding a random on-site potential to a GOE matrix leads to nodal statistics interpolating from semicircle behaviour at low disorder to Gaussian behaviour at strong disorder, suggesting a phase transition between universality classes and a connection to localization�delocalization phenomena. Nodal statistics from quantum graphs to random matrices: universality and phase transitions
Fri, Feb. 27 11:10pm (MATH …	Math Phys Lior Alon (MIT) X The Poisson summation formula tells us that a lattice and its dual lattice are related through Fourier transform: the Fourier transform of the counting measure of one is the counting measure of the other. The search for non-periodic analogues of Poisson summation � discrete sets whose Fourier transform is again a discrete measure � has appeared independently across number theory, harmonic analysis, and crystallography. In the physical setting, the Fourier transform of the counting measure of an atomic structure is exactly the diffraction pattern observed experimentally. The term quasicrystal refers to a non-periodic set whose diffraction is a pure point measure, and the discovery of such materials by Dan Shechtman in 1984 profoundly altered crystallography and led to a Nobel Prize. A major mystery that remained unresolved until very recently was whether one could find a quasicrystal whose Fourier transform is supported on a discrete (rather than merely countable) set. These objects are now called Fourier quasicrystals (FQs), and until 2020 only the trivial periodic examples were known. Kurasov and Sarnak constructed the first genuinely non-periodic one-dimensional FQ using Lee�Yang polynomials, multivariate polynomials whose zeroes avoid prescribed regions of the complex plane. In our recent work, we show that every one-dimensional Fourier quasicrystal arises from the Kurasov�Sarnak construction via Lee�Yang polynomials, yielding a complete classification in dimension one. We then extend this framework to all dimensions by introducing Lee�Yang varieties, high-codimension algebraic varieties whose geometric and analytic properties govern the Fourier structure of the associated quasicrystals. The talk will introduce Fourier quasicrystals, Lee�Yang polynomials, and Lee�Yang varieties, and explain the geometric mechanism of generating summation formulas from algebraic varieties and how it is related to real-rootedness of trigonometric equations. No prior background will be assumed. Joint work with Alex Cohen, Cynthia Vinzant, Mario Kummer, and Pavel Kurasov. Fourier Quasicrystals and Lee�Yang Varieties

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