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Events for December 2024 – April 2025

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Dec. 03, 2024 1:25pm (online)	Algebra/Logic Oyeyemi Oyebola (Brandon University, Canada) View Online:https://cuboulder.zoom.us/j/96896272260 X This work introduced and characterized a class of polyloops called Moufang Polyloop and is devoted to studying some algebraic properties of this special class of polyloops. The Moufang identities in classical loop theory were adopted to conceptualize the Moufang polyloop. Moufang polyloop identities were characterized into Moufang polyloop-1, 2, 3 and 4. The flexibility law and some algebraic properties satisfied by each of these identities were studied. Moufang Polyloop and its Algebraic Properties
Dec. 03, 2024 1:30pm (Math 3…	Functional Analysis Peter Haskell (Virginia Tech University) View Online:https://cuboulder.zoom.us/j/93768316922 X Jeff Fox and I met in 1983. We were intrigued by Kasparov's elegant and powerful bivariant K-theory, and we dared hope it would allow us to use Jeff's background in representation theory and mine in topology to prove cases of the Baum-Connes and Connes-Kasparov conjectures. The depth of the challenges posed by those conjectures was greater than we first imagined, but, largely due to Jeff's knowledge of representation theory, we did make a contribution to the area. We also proved some representation-multiplicity index theorems for transversally elliptic operators. These results illustrated K-theory's ability to extract representation-theoretic integer-valued invariants from group C*-algebras. Other work we did involved index theory for singular spaces, pushing inspiration from Riemann-Roch theorems in directions that involved enough analysis to suggest roles for spectral invariants. I learned much mathematics and much about how to do mathematics from Jeff. Working with him, I got to know one of the kindest, most generous people I have ever met. Note: Refreshments will be served 1:00 p.m. - 1:30 p.m. prior to the talk. My collaboration with Jeff Fox: Mathematical and personal connections formed as products of Kasparov's bivariant K-theory
Dec. 03, 2024 3:30pm (MATH 3…	Topology Alexander LaJeunesse X In this talk we will discuss the proof of the Land-Mathew-Meier-Tamme Purity Theorem in algebraic K-theory, and how the theorem implies half of the Chromatic Redshift conjecture. The Purity Theorem in Algebraic K-theory
Dec. 05, 2024 11:15am (MATH …	Algebraic Geometry Daniel Lyness X K3 surfaces are compact complex surfaces whose canonical bundle and first cohomology group are trivial. In this talk we will see how these properties allow for a much easier analysis than with more general complex surfaces, especially due to how they simplify Serre Duality and the Hirzebruch-Riemann-Roch theorem. These will allow us to completely describe the Hodge diamond, as well as giving some general facts about divisors on K3 surfaces. Introduction to K3 surfaces
Dec. 05, 2024 2pm (Zoom)	Algebraic Geometry Nicola Tarasca (Virginia Commonwealth University) View Online:https://cuboulder.zoom.us/j/97927772782 X Spaces of coinvariants have classically been constructed by assigning representations of affine Lie algebras, and more generally, vertex operator algebras, to pointed algebraic curves. Removing curves out of the picture, I will construct spaces of coinvariants at abelian varieties with respect to the action of an infinite-dimensional Lie algebra. I will show how these spaces globalize to twisted D-modules on moduli of abelian varieties, extending the classical picture from moduli of curves. This is based on the preprint arXiv:2301.13227. Coinvariants of metaplectic representations and abelian varieties.
Dec. 05, 2024 2pm (Online)	Rep Theory Nicola Tarasca (Virginia Commonwealth University) View Online:https://cuboulder.zoom.us/j/97927772782 X Spaces of coinvariants have classically been constructed by assigning representations of affine Lie algebras, and more generally, vertex operator algebras, to pointed algebraic curves. Removing curves out of the picture, I will construct spaces of coinvariants at abelian varieties with respect to the action of an infinite-dimensional Lie algebra. I will show how these spaces globalize to twisted D-modules on moduli of abelian varieties, extending the classical picture from moduli of curves. This is based on the preprint arXiv:2301.13227. Coinvariants of metaplectic representations and abelian varieties.
Dec. 05, 2024 2:30pm (MATH 3…	Functional Analysis Levi Lorenzo and Maggie Reardon (CU Boulder) X There will be two 25-minute talks. Abstract (Levi Lorenzo): K-theory is the generalized cohomology theory that has proven incredibly effective at classifying C- algebras. In this talk, we discuss its dual homology theory, K-homology. K-homology and K-theory admit a bilinear pairing to the integers, called the index pairing, which allows one to learn about K-theory using K-homology and vice versa. In general, this pairing is very difficult to compute; however, if a Calgebra admits a dense subalgebra on which its K-homology is finitely summable, Connes has equipped us with a more computable formula. Given a smooth manifold, M, of dimension n, the K-homology of is finitely summable on for In this way, the summability also sees the dimension of the manifold. It is natural to ask whether similar results hold in the noncommutative setting. Towards this end, Connes showed that the irrational rotation algebras have uniformly summable K-homology. The irrational rotation algebras are examples of crossed product algebras arising from minimal actions on a topological space. In my work, I study other noncommutative algebras and ask the same question. For example, we make the space a Cantor Set and examine the K-homology of crossed products arising from minimal actions on it. In this talk, we discuss progress in such directions. Abstract (Maggie Reardon): Matui’s HK-conjecture proposes a relationship between the homology groups of a nice enough groupoid and the -theory of the associated reduced -algebra. The conjecture is not true in general and there are a number of counterexamples. However, the conjecture holds for certain 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-conjecture? Finitely Summable K-homology and the HK-conjecture for certain groupoids constructed by Putnam
Dec. 06, 2024 10:10am (MATH …	Math Edu Rebecca Machen & Nancy Kress X Active learning classrooms are designed to encourage collaboration and engagement, but they can also be places where microaggressions occur and affect the sense of belonging for students and faculty. In this meeting, we’ll explore what microaggressions look like in math classrooms and how they impact the learning environment. I’ll share a simple theoretical framework to help us think about how we respond to these moments and invite everyone to reflect on their own experiences. Together, we’ll work toward strategies for fostering more inclusive and supportive spaces for everyone. This will be an open, welcoming conversation, and all are encouraged to join. We’ll also take some time to discuss getting started in math ed research, e.g. planning a study or finding and applying for grants. Fostering inclusion in active learning math classrooms
Dec. 12, 2024 11:15am (MATH …	Algebraic Geometry Daniel Lyness X This will be a continuation from last week. K3 Surfaces (cont.)
Dec. 12, 2024 2pm (Online)	Lie Theory Michael Lau (Université Laval) View Online:https://cuboulder.zoom.us/j/97927772782 X Affine Lie algebras are universal central extensions of algebras of matrices over Laurent polynomials. In the case of sl_2, the ring of Laurent polynomials can be replaced with any unital Jordan algebra. This gives a very large family of Lie algebras. Motivated by this connection between Lie and Jordan theory, we describe a category of Lie algebra weight modules, whose homological properties are related to the long-standing open problem of computing graded dimensions of free Jordan algebras. No prior knowledge of Jordan algebras will be assumed. This talk is based on joint work with Olivier Mathieu. Good filtrations, Lie algebras representations, and free Jordan algebras
Jan. 16, 2025 11:15am (MATH …	Algebraic Geometry Ruijie Yang (Kansas) Archimedean zeta function and Hodge theory Sponsored by the Meyer Fund
Jan. 16, 2025 3:35pm (MATH 3…	Probability Jonas Jalowy (University of Münster) X How do zeros of polynomials evolve under the action of differential operators? Consider a random polynomial with i.i.d. (rescaled) coefficients and look at the empirical distribution of their complex roots. We investigate the evolution of the roots when the polynomial undergoes the action of differential operators, such as the heat flow and repeated differentiation. In one prominent example of Weyl polynomials undergoing the heat flow, the limiting zero distribution evolves from the circular law into the elliptic law until it collapses to the Wigner semicircle law. In this talk, I present an overview over results of such type with a focus on complex zeros. We determine the general limiting zero distribution and describe the dynamics of the roots from various points of view such as (optimal) transport, differential equations and free probability. The connection to the latter is particularly fruitful for real rooted polynomials and will be the focus of a second part. This talk will include illustrative simulations leading to intriguing open questions. This is based on joint works with Brian Hall, Ching Wei Ho, Zakhar Kabluchko and Antonia Höfert. Evolution of complex zeros of random polynomials
Jan. 23, 2025 11:15am (MATH …	Algebraic Geometry AG Group Organizational Meeting
Jan. 23, 2025 3:35pm (MATH 3…	Probability Jonas Jalowy (University of Münster) X Following up on the evolution of complex roots of random polynomials and their advertised connection to free probability, this talk aims to give a full picture of this connection in the case of real rooted polynomials. First, I will present a general user-friendly approach for determining the limiting zero distribution as the degree tends to infinity in terms of the exponential profile of the coefficients. Then, we will explore a wide range of examples, covering many classical families of polynomials as well as certain operations on polynomials, such as Hadamard product, repeated differentiation, the heat flow and finite free convolutions. To this end, I will give a short crash-course on (finite) free probability theory. Finally, we close the circle by viewing the results of last week's talk from the perspective of free probability. Real rooted polynomials, exponential profiles and (finite) free probability
Jan. 28, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X We will conduct a learning seminar in Spring 2025 on the book, The Structure of Finite Algebras, by David Hobby and Ralph McKenzie. The structure of finite algebras, 1
Jan. 28, 2025 3:30pm (MATH 3…	Topology Howy Jordan (CU Boulder) X In this talk, we offer extensions and corrections to our previous work on Artin gluing of fiber bundles. In particular, we show that the notion of Artin gluing of sheaves can be applied to gluing arbitrary bundles provided with an evaluation map from an etale bundle associated to a sheaf. When specialized to fiber bundles, the gluing data allows for a generalized Whitney condition that, for instance, allows one to define a stratified tangent bundle for spaces decomposed into quite general infinite dimensional manifolds. Artin gluing of bundles
Jan. 29, 2025 3:30pm (MATH350)	Math Phys Andrew Doumont (CU Boulder) X We will discuss Gromov-Witten invariants with the aim of motivating the use of Kuranishi spaces to define virtual fundamental classes. Gromov-Witten Invariants
Jan. 29, 2025 5pm (Math 350)	Math Club Emily Montelius X Join us for an interactive talk exploring the wonderful world of tiling. Spend an hour exploring tessellations and playing with dominoes as we discover the fun properties they have. Together we will work to find and disprove the existence of different tilings on rectangles, cylinders, tori, and Möbius strips. Fault Free Tileability of Rectangles, Cylinders, Tori, and Möbius Strips with Dominoes
Jan. 30, 2025 11:15am (MATH …	Algebraic Geometry AG Group X AG graduate students will give a quick rundown of their thesis problems. This will also be a time for students to ask help from other graduate students and faculty. AG Support
Jan. 30, 2025 12:05pm (MATH …	Kempner Tadashi Tokieda (Dept of Physics, Stanford University) X Humans tend to be better at physics than at mathematics. When an apple falls from a tree, there are more people who can catch it — they sense physically how the apple moves — than people who can compute its trajectory from a differential equation. Applying physical ideas to discover and explain mathematical results is therefore natural, even if it has seldom been tried in the history of science. The exceptions include Archimedes, some old Russian sources, a recent book of Mark Levi’s, as well as my articles and lectures. A variety of elementary yet surprising examples will be presented. Pure mathematics as applied physics
Jan. 30, 2025 2:30pm (MATH 3…	Functional Analysis Darwin Tallana (CU Boulder) Proper actions and the Baum-Connes conjecture
Jan. 31, 2025 11:15am (Math …	Math Edu David Webb X In this interactive seminar, we will revisit core principles of active learning and explore how these are effectively enacted in undergraduate mathematics classrooms to enhance student engagement and success. Together, we will examine strategies that promote peer-to-peer interaction, foster deep mathematical reasoning, and advance equitable teaching practices, all grounded in the latest research on active learning and its impact on student outcomes. Additionally, we will discuss how to connect these curricular and instructional innovations to research and grant opportunities, offering practical insights into securing funding for transformative educational projects. Transforming Undergraduate Mathematics Education: From Active Learning Practices to Funded Research Projects
Feb. 04, 2025 1:25pm (MATH 2…	Algebra/Logic Peter Mayr (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X Commutators have been generalized from groups to arbitrary algebras in different ways. I will give an overview of the properties of the binary term condition commutator and higher commutators from universal algebra specialized to semigroups and the derived notions of nilpotence, supernilpotence, and solvability. Finite supernilpotent semigroups
Feb. 04, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 2
Feb. 04, 2025 2:30pm (MATH 3…	Lie Theory Nat Thiem (CU) X This talk is a largely expository how-to guide for building a representation theory that categorifies your favorite combinatorial Hopf algebra. The goal is to present a general framework that captures both the classical examples (symmetric group, general linear groups) and more modern examples (upper-triangular groups and tori) with an eye towards new families of examples. Turning the representation theory of matrix groups into combinatorial Hopf algebras
Feb. 04, 2025 3:30pm (MATH 3…	Topology Ezzeddine El Sai (CU Boulder) X It is very well known that homological algebra can be very ill behaved when enriched over topological spaces. This begs the question, how should one study geometry over topological fields? One radical idea by Clausen and Scholze is to do away with topology all together and start from scratch in what they call "Condensed Mathematics". In this talk we will discuss the merits of this approach and pose the question "what actually is a space?" Geometry without Topology
Feb. 05, 2025 3:30pm (MATH350)	Math Phys Gregory Berkolaiko (Texas A&M University) X Occurence of multiple eigenvalues in families of self-adjoint operators is a question with numerous applications in mathematical physics. In this expository talk we will review the "no accidental multiplicities in one parameter" result of Wigner and von Neumann, the "typical" conical shape of eigenvalue multiplicities in two parameters, and the use of geometric phase (often called the "Berry phase" but in this case used earlier by Herzberg and Longuet-Higgins) to understand why the conical intersections cannot be destroyed without leaving the class of real operators. Theory will be illustrated by numerical simulations and the content will be kept accessible to advanced undergraduate students. Geometric Phase and Stability of Conical Intersections
Feb. 06, 2025 11:15am (MATH …	Algebraic Geometry Matt Watson X D-Modules are algebraic objects which can be used in the study of linear PDEs on a complex algebraic variety. In this talk we will give a definition and see how D-modules correspond to flat connections. If time allows we may cover left and right D-modules, coherence, or good filtrations. Introduction to D-Modules
Feb. 06, 2025 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) The Baum-Connes assembly map
Feb. 10, 2025 3:35pm (MATH 3…	Grad Student Seminar Alex LaJeunesse (CU Boulder) X We'll discuss what it means to (repeatedly) categorify abelian groups and how this is related to higher notions of additivity in infinity-categories, as well as recent developments in chromatic homotopy theory. Delooping Primes
Feb. 11, 2025 1:25pm (MATH 2…	Algebra/Logic Mateo Muro (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X The Finite Basis Problem is a classical problem in universal algebra. In this talk, I will introduce the problem and necessary notions. Then I will present my recent contribution: an abelian Mal'cev variety is finitely based if and only if its ring of binary idempotent terms is finitely presented and its module of unary terms is finitely presented. A characterization of finitely based abelian Mal'cev varieties
Feb. 11, 2025 2:30pm (MATH 3…	Lie Theory Jinwei Yang (Shanghai Jiao Tong University) X In a series of celebrated work, D. Kazhdan and G. Lusztig constructed braided tensor category structure on the category of finite length modules for the affine Lie algebras when the level plus dual Coxeter number is not a positive rational number, and proved that the category is equivalent to the category of finite dimensional weight modules for the quantum groups. In this talk, we discuss our recent progress on tensor categories at positive rational levels using vertex operator algebra approach. Concretely, We construct braided tensor category structure on the category of ordinary modules for simple affine vertex operator algebras and prove rigidity in some cases. For affine sl_2 Lie algebra, we also study two bigger representation categories, one is the category of weight modules for the simple affine vertex operator algebra, which is neither finite or semisimple, we prove its rigidity, the other is the category of finite length modules for the universal affine vertex operator algebra, we show this category is derived equivalent to the category of the quantum groups. This talk is based on a series of joint work with T. Creutzig, Y.-Z. Huang and R. McRae. Representation and tensor category of affine sl_2 Lie algebra at positive rational level Sponsored by the Meyer Fund
Feb. 11, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 3
Feb. 11, 2025 3:30pm (MATH 3…	Topology James Woodcock TBD
Feb. 12, 2025 3:30pm (MATH350)	Math Phys Sheagan John (CU Boulder) X TBA Foundations of Measure Theory
Feb. 12, 2025 5pm (Math 350)	Math Club Nathaniel Thiem X Come hear about the math department's summer REU program. REU stands for Research Experiences for Undergrads and our summer REU program is an opportunity for you to get an idea of what math research is like. You can find info about the different projects here: https://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
Feb. 13, 2025 11:15am (MATH …	Algebraic Geometry Daniel Lyness X We will continue to introduce D-modules from last week's talk. Introduction to D-Modules (continued)
Feb. 14, 2025 11:15am (Math …	Math Edu Rebecca Machen X This workshop will introduce mathematics educators to the transformative potential of generative AI tools, such as ChatGPT, for fostering dynamic, student-centered learning experiences. We will focus on a customized GPT model designed for students to use this semester, which emphasizes problem-solving, self-reflection, and personalized feedback on mathematical concepts. By the end of the session, participants will gain practical strategies for leveraging generative AI to create engaging and supportive learning environments that encourage students to take active ownership of their education. No prior AI experience needed and plan to bring a laptop for use. Enhancing Mathematical Problem-Solving Skills and Academic Mindsets for Undergraduate Mathematics Students Through Interactions with Generative AI
Feb. 17, 2025 3:30pm (Kitt C…	DeLong Laura DeMarco (Harvard University) X The field of dynamical systems has a long and fascinating history: it originated with the study of planetary motion and has become a central part of mathematics today. In this talk, I will present some of its historical development, with emphasis on the subtle question of linearization and how that leads to deep and difficult problems that remain unsolved. From the solar system to the Mandelbrot set Sponsored by the Meyer Fund
Feb. 18, 2025 12pm (MATH 350)	Algebraic Geometry Mihnea Popa (Harvard) X The Hodge diamond of a smooth projective complex variety contains essential topological and analytic information, including fundamental symmetries provided by Poincaré and Serre duality. I will describe recent progress on understanding how much symmetry there is in the analogous Hodge-Du Bois diamond of a singular variety, and the concrete ways in which this symmetry reflects the singularity types. In the process, we will see how invariants from commutative algebra and birational geometry influence the topology of an algebraic variety, for instance by means of new weak Lefschetz theorems. Hodge symmetries of singular varieties Sponsored by the Meyer Fund
Feb. 18, 2025 1:25pm (online)	Algebra/Logic Johanna Brunar (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X Conservative graph-colouring problems, also known as list homomorphism problems, have been examined for various classes of finite digraphs. Each instance consists of a finite digraph along with a list of permitted values for each vertex. Lifting the scenario to infinite digraphs G, the 1-orbits of an oligomorphic subgroup of Aut(G) take the role of elements. A conservative template in this framework is enriched by a unary relation for all unions of 1-orbits of . Assuming only access to unions of pairs of 1-orbits, we obtain the first structural dichotomy for -categorical smooth digraphs of algebraic length 1, yielding a hardness criterion for the respective conservative graph-colouring problems. We thereby overcome previous obstacles to lifting structural results for digraphs in this context from finite to -categorical structures -- the strongest lifting results hitherto applying only to undirected graphs. This is joint work with Marcin Kozik, Tomas Nagy, and Michael Pinsker. The sorrows of a smooth digraph
Feb. 18, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 4
CANCELED Feb. 18, 2025	Topology Alex Lajeunesse TBD
Feb. 18, 2025 3:30pm (Kitt C…	DeLong Laura DeMarco (Harvard University) The geometry (and algebra) of the Mandelbrot set Sponsored by the Meyer Fund
Feb. 25, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 5
Feb. 25, 2025 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X Pfaffians, Hafnians, determinants, and permanents are invariants associated with square matrices of various kinds. We will show how to construct known q-analogues of these invariants using the combinatorics of root systems of types A and D. This is work in progress with Tianyuan Xu (University of Richmond). Quantum Pfaffians and quantum Hafnians
Feb. 25, 2025 3:30pm (MATH 3…	Topology Taylor Rogers X Stable infinity categories are the infinity categorical analogue of abelian categories and axiomatize features of stable homotopy theory. In this talk we will introduce basic stable infinity category theory which will be useful for describing connections between stable homotopy theory and KK theory in the following weeks. Introduction to Stable ()-Categories
Feb. 26, 2025 3:30pm (MATH350)	Math Phys Howy Jordan (CU Boulder) X Hilbert spaces (that is, complete inner product spaces) are fundamental to the mathematical description of quantum mechanics, in particular providing a formalization of the notion of physical state in this context. We will cover their definition and basic examples. We will consider important related concepts such as classes of operators which formalize observables, the notion of measurement, and the spectral theorem and discuss how they are used in understanding the physics of quantum phenomena. Foundations of Quantum Mechanics
Feb. 27, 2025 11:15am (MATH …	Algebraic Geometry Jon Kim X In 2024, Shock 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 weighted by the same number in the interval (1/9,1]. For weights close to 1/9, one obtains the Naruki compactification, resulting from Gallardo—Kerr—Schaffler. For weights close to 1, the compactification was done by Hacking—Keel—Tevelv. For weights in-between, Schock provided a finite wall-and-chamber decomposition of the weight domain (1/9, 1], and described the weighted stable pairs parameterized by the moduli spaces in each chamber. In this preparatory talk, I will introduce the preliminary material regarding KSBA compactifications and this work done by Schock. Moduli of Weighted Stable Marked Cubic Surfaces
Feb. 27, 2025 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) The Dirac-dual Dirac method
Feb. 27, 2025 3:35pm (MATH 3…	Probability Mike Cranston (UCI) X The Riemann zeta function evaluated at a parameter s>1 induces a nice probability distribution on the positive integers. Sampling positive integers using this distribution has many nice properties and leads to the same results as sampling using the uniform distribution on 1,2,...,N and letting N tend to infinity. There are many zeta functions in other contexts such as the Dedekind zeta function and sampling ideals using this zeta function exhibits similar nice properties. In this talk we will discuss joint work on this subject with Peltzer, Mountford and Hsu. Sampling numbers and algebraic objects using zeta functions
Mar. 04, 2025 1:25pm (online)	Algebra/Logic Moritz Schöbi (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X The Bodirsky-Pinsker conjecture is an infinite counterpart to the Feder-Vardi dichotomy conjecture for Constraint Satisfaction Problems (CSPs) with finite templates. While the latter has been confirmed independently by Bulatov and Zhuk, the former remains wide open. In this talk, we shed light on three meta-problems regarding the scope of this conjecture. Our first result provides a significant structural simplification of this scope: we prove that the conjecture is equivalent to its restriction to templates without algebraicity, a crucial assumption in many powerful classification methods. The second result provides a simplification of algebraic nature: any algebraic condition characterizing any complexity class within the conjecture must be satisfiable by injections. In particular, this offers insight into which universal-algebraic conditions for the complexity of finite-template CSPs may be successfully lifted to the infinite case. The third result we are going to explore links the conjecture to so-called Promise Constraint Satisfaction Problems (PCSPs): using the construction from the first result, virtually every structure from the scope of the conjecture allows us to construct a sandwich structure for a non-finitely tractable finite-domain PCSP. This is joint work with Michael Pinsker, Jakub Rydval and Christoph Spiess. Eliminating algebraicity and enforcing injectivity in infinite-domain constraint satisfaction
Mar. 04, 2025 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X We will show how to use root systems of types E6, E7, and E8 to construct generalizations of quantum Pfaffians and quantum Hafnians. These constructions are closely related to the combinatorics of del Pezzo surfaces, and they give rise to new q-analogues of an invariant cubic polynomial in type E6,and a quartic polynomial in type E7. This is work in progress with Tianyuan Xu (University of Richmond). Generalized quantum Pfaffians and quantum Hafnians
Mar. 04, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 6
Mar. 04, 2025 3:30pm (MATH 3…	Topology James Woodcock TBD
Mar. 05, 2025 5pm (Math 350)	Math Club Clyde Kertzer X Circle packing is the study of arranging circles on a surface so that no overlap occurs and no circle can be enlarged without creating overlap. This interactive talk was developed by the speaker as part of an Experimental Math Lab and the content of the talk is based on work he did with Dr. Kate Stange for his honor's thesis. Circle Packing
Mar. 06, 2025 11:15am (MATH …	Algebraic Geometry Nolan Schock (UIC) X The moduli space of marked cubic surfaces is one of the most classical moduli spaces in algebraic geometry, dating back to the nineteenth century work of Cayley and Salmon. I will discuss a number of results describing geometrically meaningful and interesting compactifications of the moduli space of marked cubic surfaces from the perspectives of modern moduli theory, birational geometry, tropical geometry, classical algebraic geometry, and Hodge theory. These results include explicit descriptions of the combinatorics, intersection theory, and birational geometry of these compactifications, as well as a complete, detailed description of the surfaces they parameterize. Geometry of moduli of marked cubic surfaces Sponsored by the Meyer Fund
Mar. 07, 2025 11:15am (Math …	Math Edu Lee Roberson X As teachers, we use the power of questions to assess and build our students’ mathematical understanding. The questions we ask can determine how our students think about concepts, respond to inquiry, collaborate with others, connect ideas, and ask their own questions. Because of this, we will take time to pause and reflect on the questions we ask in our classes. We will question the purpose of our questions, the types of questions we ask, and the questioning strategies we use to better understand our own pedagogical practices so that we can improve our students’ mathematical understanding. Questioning Our Questions
Mar. 11, 2025 11am (MATH 350)	Number Theory Sarah Arpin X The isogeny-based cryptographic protocol CSIDH is based on the group action of the class group of a particular imaginary quadratic order on certain elliptic curves. The efficiency and security of CSIDH has inspired variant protocols, such as SCALLOP and OSIDH. Such protocols are based on the vectorization problem: Given elliptic curves E, E', find the ideal class whose action on E yields E'. In this work, we provide a general understanding of this question in the context of orientations and level structure on elliptic curves. In particular, we study a large family of generalized class groups of imaginary quadratic orders O and prove that they act freely and (essentially) transitively on the set of primitively O-oriented elliptic curves over a field k (assuming this set is non-empty) equipped with appropriate level structure. This is joint work with Wouter Castryck, Jonathan Komada Eriksen, Gioella Lorenzon, and Frederik Vercauteren. Generalized class group actions on oriented elliptic curves with level structure
Mar. 11, 2025 12:10pm (MATH …	Kempner Edmund Harriss (University of Arkansas) X Euclid's elements is regarded as an early example of proof and axiomatic methods but it also has a tradition within carpentry and construction. The straight line and circle can just as easily be regarded as abstract representations of the action of straight edge and compass just as easily as the other way round. Today we have many machines that can play the same role creating a bridge between the abstract and the physical. What potentials do they provide for realising mathematical concepts in physical space and creating manufacturing techniques? In this talk I will look at several examples of machines with mathematical models, including affine spaces, ruled and developable surfaces and the gradient present in the grain of wood. Mathematical Manufacturing since Euclid
Mar. 11, 2025 1:15pm (MATH 3…	PDE/Analysis Tristan Léger (Yale University) X In this talk I will discuss recent and upcoming results on the boundedness of spectral projectors. The seminal work of C. Sogge gives the optimal result on any Riemannian manifold with bounded geometry for spectral windows of size 1. However when the width is smaller, the spectral projector bounds become sensitive to the global geometry of the underlying manifold. I will focus on the case of hyperbolic surfaces of infinite area, and present new estimates that hold universally in that setting. This is joint work with Jean-Philippe Anker and Pierre Germain. Spectral projector bounds on hyperbolic surfaces of infinite area Sponsored by the Meyer Fund
Mar. 12, 2025 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X In this talk, we will introduce the basic tools and terminology for future talks on Machine Learning and Statistical Applications. Fitting with the theme of this seminar, we will also touch on concepts regarding the physical meaning of "information" and its connections with Statistics. Statistics and Mathematical Physics
Mar. 12, 2025 3:30pm (MATH 2…	Algebra/Logic Joel David Hamkins (Notre Dame University) X I shall introduce and describe the subject of modal model theory, in which one studies a mathematical structure within a class of similar structures under an extension concept, giving rise to mathematically natural notions of possibility and necessity, a form of mathematical potentialism. We study the class of all graphs, or all groups, all fields, all orders, or what have you; a natural case is the class of all models of a fixed first-order theory. In this talk, I shall describe some of the resulting elementary theory, particularly the remarkable expressive power of modal graph theory. This is joint work with my Oxford student Wojciech Woloszyn. Introduction to modal model theory
Mar. 13, 2025 11:15am (MATH …	Algebraic Geometry Leo Herr (Virginia Tech) X Joint work with Sara Mehidi, Marta Pieropan, Thibault Poiret Let X --> Y be a morphism of varieties and k a field. Consider the set X(k) of k-points, or solutions to the equations defining X with coordinates in k. If X = V(x^2 + y^2 - 1) for example, then the set of Q-points consists of primitive Pythagorean triples and the geometry of X shows there are infinitely many solutions. According to Hindry-Silverman, "Geometry determines Arithmetic." We want to determine the image of the map on k-points X(k) --> Y(k). Suppose X --> Y arises as the fiber over 0 of a family of varieties X' --> Y'. The geometry of the family X' --> Y' can also constrain the type of k-points that land in the image of X(k) --> Y(k), as Campana observed. Abramovich generalized this notion in a beautiful, incomplete manuscript called "birational geometry for number theorists" and gave us permission to realize this vision using log geometry. Log structures on X, Y remember enough about the families X', Y' to constrain the rational points. "Birational geometry for number theorists" for log geometers
Mar. 13, 2025 1:30pm (MATH 2…	Grad Student Seminar Édouard Heitzmann X A districting of a graph G is a partition of G into simply connected subgraphs P_i. MCMC methods are frequently used to sample the space of districtings, with Recombination Steps being a computationally inexpensive and rapidly mixing transition rule to run such a chain. This talk will define Recombination Steps, survey the literature surrounding them, and outline the proof of an irreducibility result for this proposal when G is a triangular subset of the triangular lattice. An irreducibility result for districtings of triangular subsets of the triangular lattice
Mar. 13, 2025 2:30pm (MATH 3…	Functional Analysis Jordan Watts (University of Central Michigan) X Moving from finite-dimensional calculus to an infinite-dimensional setting immediately forces one to contend with a lot of point-set topology and analysis that was less of a concern before. In this talk, we examine a classical way of taking derivates of a function between locally convex spaces from a diffeological and Sikorski perspective. We apply our results by studying several infinite-dimensional groups of relevance to symplectic topologists. Joint work with Yael Karshon. Infinite-Dimensional Calculus and Symplectic Topology
Mar. 14, 2025 11:15am (Math …	Math Edu Rebekah Jones & Courtney Hauf X In this interactive seminar, we will be discussing excerpts from Building Thinking Classrooms by Peter Liljedahl. This book focuses on research-backed strategies to foster engagement and critical thinking in the mathematics classroom. Participants will reflect on their own experiences and discuss practical ways to implement the strategies discussed in excerpts, so please look at the reading ahead of time (link to reading). Building Thinking Classrooms Discussion
Mar. 18, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 7
Mar. 18, 2025 3:30pm (MATH 3…	Topology Alex LaJeunesse (CU Boulder) X Topological K-theory was the first seriously studied example of a generalized cohomology theory, leading to the incredibly rich world of spectra and stable homotopy theory that we see today. In this talk we will give a remarkable description of the spectrum KU representing this theory, due to Snaith. We will also look at a generalization of this construction to chromatic homotopy theory due to Westerland, and sketch how it relates to the failure of Ravenel’s Telescope Conjecture. Snaith's Theorem
Mar. 19, 2025 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X TBA Statistical Learning
Mar. 20, 2025 11:15am (MATH …	Algebraic Geometry Ruijie Yang (Kansas) X We will discuss some number theoretic motivation for studying minimal exponent of a hypersurface, which is the nonarchimedean counterpart of the Archimedean zeta function. Then I will explain a toy model, i.e. Milnor fiber of an isolated singularity, for the proof of the main theorem. We will see why Hodge theory naturally enters into the picture. Minimal exponent of hypersurfaces, p-adic integration and Milnor fibers Sponsored by the Meyer Fund
Mar. 20, 2025 2:30pm (MATH 3…	Functional Analysis Laura Scull (Fort Lewis College) X One common way of representing spaces with singularities is via topological groupoids. However, such a representation is not unique, and a space may be represented by many different groupoids, leading to the idea of Morita equivalence of groupoids. To work with these spaces, we define a localised bicategory of groupoids in which Morita equivalences become isomorphisms. This localisation can be done in several equivalent ways, as developed by Pronk and Roberts. Our interest lies in a particularly nice and ubiquitous class of examples, the action groupoids which represent the quotient of a space by an action of a group. Such groupoids come with their own notion of morphisms given by equivariant functors. Our aim is to connect these two viewpoints. We create a localised bicategory built on equivariant functors of groupoids, and show that for action groupoids, this is equivalent to the bicategories of Pronk and Roberts. Using this viewpoint, Morita equivalences may be defined using a certain class of equivariant projection functors, and many common conditions on the singularities can be integrated into this construction. This also gives us a way of examining invariants from equivariant homotopy to see if they can be made Morita invariant and extended to our setting. This talk is based on joint work with J. Watts and C. Farsi. The talk will include many pictures and examples illustrating the underlying geometric intuition behind the abstraction of the bicategories. Localising Action Groupoids
Mar. 20, 2025 3:35pm (MATH 3…	Probability Giorgio Cipolloni (University of Arizona) X We study the Brownian evolution of large non-Hermitian matrices and show that their log-determinant converges to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class, i.e. logarithmically correlated for the parabolic distance. This gives a dynamical extension of the celebrated result by Rider and Virag (2006) proving that the fluctuations of the eigenvalues of Gaussian non-Hermitian matrices converge to a 2 dimensional log-correlated field. Our result, previously not known even in the Gaussian case, holds out of equilibrium for general matrices with i.i.d. entries. We also study the extremal values of these fields and demonstrate their logarithmic dependence on the matrix dimension. Logarithmically correlated fields from non-Hermitian random matrices
Mar. 27, 2025 12:30pm (Online)	Rep Theory Thomas Creutzig (FAU Erlangen-Nürnberg) X A while ago and with David Ridout a Verlinde formula for the affine VOAs of sl(2) at admissible level was conjectured. This is a VOA whose representation category is neither finite nor semisimple. Our idea was to replace the Verlinde S-matrix by an S-kernel and atypical modules by their resolutions of typical modules to get a natural Verlinde formula conjecture. I will explain why this formalism is true. Verlinde's formula in logarithmic CFT
Apr. 01, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 8
Apr. 01, 2025 3:30pm (MATH 3…	Topology XiaoLin Danny Shi (University of Washington) X I will talk about equivariant homotopy theory and its role in the proof of the Segal conjecture and the Kervaire invariant one problem. Then, I will talk about chromatic homotopy theory and its role in studying the stable homotopy groups of spheres. These newly established techniques allow one to use equivariant machinery to attack chromatic computations that were long considered unapproachable. Equivariant methods in chromatic homotopy theory
Apr. 02, 2025 3:30pm (MATH350)	Math Phys Markus Pflaum (CU Boulder) X TBA Born-Oppenheimer Approximation
Apr. 03, 2025 12:30pm (Online)	Rep Theory Arim Song (University of Denver) View Online:https://cuboulder.zoom.us/j/97927772782 X Supersymmetric(SUSY) W-algebras are vertex algebras constructed through SUSY Hamiltonian reduction based on Lie superalgebras with osp(1\|2) embeddings. By construction, they have a supersymmetric structure that naturally couples the generators of the algebras. Madsen and Ragoucy conjectured that SUSY W-algebras are isomorphic to W-algebras up to a tensor product with free field algebras. In recent joint work with Genra and Suh, we proved this conjecture for principal SUSY W-algebras. In this talk, I will introduce SUSY W-algebras and the concept of SUSY vertex algebras, which provides a mathematical framework for the study. Then, I will discuss key properties of SUSY W-algebras in comparison to W-algebras, a part of which contributes to the proof of the conjecture. This talk is based on my recent paper and the one with Genra and Suh. Supersymmetric W-algebras vs. W-algebras
Apr. 03, 2025 1:30pm (MATH 3…	Algebraic Geometry Patricio Gallardo (UC Riverside) X I will discuss my ongoing work with J. Mukherjee on the classification and moduli of varieties of general type constructed via abelian covers. In particular, I will describe the behavior of their numerical invariants, the ratio of their Chern numbers, and conditions under which abelian covers can be used to construct an open subset within a component of the corresponding moduli space. This is part of AG day: https://sites.google.com/colorado.edu/front-range-ag/ Invariants and moduli spaces of abelian covers Sponsored by the Meyer Fund
Apr. 04, 2025 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X The talk will be about a generalization of Hölder duality to algebra-valued pairings. Roughly, Hölder duality states that if and satisfy . In finite dimension, this is easy to see as both and are algebraically isomorphic to and it’s just a matter of checking that the pairing does indeed define a linear functional that recovers the p’-norm of . In this talk we now take to be the -column direct sum of a fixed algebra and to be the -row direct sum of . We now naturally get an -valued dual pairing, so it makes sense to ask whether a version of Hölder duality still holds. I will present examples of A for which a Hölder-like duality still holds, but also discuss other examples for which it doesn’t. The talk is based on an REU project that ran in CU-Boulder during Summer 2024. C*-like modules and matrix p-operator norms
Apr. 04, 2025 3:35pm (MATH 2…	PDE/Analysis Juhi Jang (University of Southern California) X We will discuss recent progress on the vacuum free boundary problems arising in the dynamics of isolated gases with or without gravity. We give an overview of the well-posedness and stability theory, and present some new results on waiting time solutions. Vacuum Free Boundary Problems in Gas Dynamics Sponsored by the Meyer Fund
Apr. 08, 2025 1:25pm (online)	Algebra/Logic Bertalan Bodor (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X The Constraint Satisfaction Problem (CSP) over a structure with a finite relational signature is the problem of deciding whether a given finite input structure with the same signature as has a homomorphism to . According to the famous result of Bulatov and Zhuk we know that CSPs over finite template structures exhibit a complexity dichotomy: they are all in or -complete. Generalizing this theorem to infinite structures has been a topic of active research in the past few decades. A currently standing conjecture in this direction is by Bodirsky and Pinsker which states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. In my talk I am exploring some ideas on how this conjecture could be attacked under some strong model theoretical assumptions such as -stability or first-order interpretability in the pure set. This approach often requires a detailed understanding of structures arising in this context which also leads to some questions in model theory that could be of independent interest. This is joint work with Manuel Bodirsky and Paolo Marimon. Model theoretical tameness and CSPs
Apr. 08, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 9
Apr. 08, 2025 2:30pm (MATH 3…	Lie Theory Shigenori Nakatsuka (FAU Erlangen-Nurnberg) X W-superalgebras are a large class of vertex algebras obtained from affine Lie algebras. Due to their duality, hook-type W-superalgebras have captured a lot of attention in the last decade. I will explain the duality in their representation theory and the phenomenon appearing at the level of characters. Duality of hook-type W-superalgebras and characters Sponsored by the Meyer Fund
Apr. 09, 2025 3:30pm (MATH350)	Math Phys Wilson Wu (CU Boulder) X TBA Neural Networks
Apr. 10, 2025 2:30pm (MATH 3…	Functional Analysis Angel Roman (University of Washington St Louis) X A double groupoid is a type of higher groupoid structure in which there are two distinct groupoid products on the same set of arrows and must satisfy a certain compatibility law. A particular example we will focus on is that of an irrational torus, and more generally, strict 2-groups. Since groupoid structures give rise to convolution algebras, a double groupoid gives rise to two convolution products. We ask, in what sense are the two convolution products compatible? This is based on joint work with Joel Villatoro. Convolution Algebras of Double Groupoids and Strict 2-Groups
Apr. 11, 2025 3:35pm (MATH 2…	PDE/Analysis Willie Wong (Michigan State University) X Our understanding of cosmological processes, like many other predictions of physical theories, are based on studying regimes where the equations of motion reduce to a finite dimensional dynamical system. An example of a conclusion derived from such reductions is the idea of a big bang cosmology in general relativity. Such reductions are physically justified by the working assumption that when viewed from the largest scales, the inhomogeneities average out and the matter content can be approximated by a homogeneous compressible fluid. Jointly with Shih-Fang Yeh, we probe whether this working assumption is justified mathematically. Our results show that on the cosmological timescale, some big bang solutions are susceptible to instabilities generated through nonlinear self-interactions of the constituent matter when inhomogeneities are present. The goal of this talk is to present the mathematical context of this result and briefly describe the mechanism driving the instability, focusing on the relevance of the conformal (or causal) geometry of the big bang solutions. (No prior familiarity with mathematical relativity is assumed.) Some Big Bangs are Unstable Sponsored by the Meyer Fund
Apr. 14, 2025 3:35pm (MATH 3…	Grad Student Seminar Chris Eblen (CU Boulder) X Schur--Weyl duality is a fundamental paradigm in representation theory relating representations of the general linear group to those of the symmetric group. We will discuss the classical case of Schur--Weyl duality and an analog for the unipotent upper triangular matrix group over a finite field. Then we will define supercharacter theory and how a particular supercharacter theory for the unipotent upper triangulars, within the context of this Schur--Weyl duality analog, lead to a class of modules called beach modules and a collection of projection-like maps in the centralizer algebra. A Day at the Beach
Apr. 15, 2025 1:25pm (MATH 2…	Algebra/Logic Temitope Gbolahan Jaiyeola (Obafemi Awolowo University, Nigeria) View Online:https://cuboulder.zoom.us/j/96896272260 X This study is based on ‘algebraic-analytic’ approach to some non-associative hyper-structures with application to physical systems. This was with a view of understanding the non-associatve algebraic behaviour of: (i) the elementary particle physics (lepton group) which forms an Hv-group (Nezhad et al. 2012), the elementary particles (including the Higgs Boson) originally studied by (Davvaz et al. 2020) and (ii) some dismutation reactions in chemical systems (Davvaz et al. 2012). Non-commutative groupoid (quasigroup and loop) was used to construct polygroupoid (polyquasigroup, polyloop) and examples given. The Kuratowski closure axioms was used for an appropriate closure operator that is nuclear in nature (relative to polygroupoid) to produce a Kuratowski induced topological space and consequently a polygroupoid-topological space. This study introduced and investigated the properties of left (right) nuclei Kuratowski closure operator induced topological space on polygroupoid (polyquasigroup, polyloop). This was used to analyse (with the aid of probability) the nuclear and alternative properties of the lepton group. The analysis of algebraic properties (with the aid of probability of elements) in dismutation reaction of some chemical systems of Tin (Sn), Indium (In) and Vanadium (V) which are represented by hyper-algebraic structures were carried out. A study of non-associative hyper-structures and algebraic analysis of selected physical systems
Apr. 15, 2025 2:30pm (MATH 3…	Lie Theory Gurbir Dhillon (UCLA) X The representation theory of affine Lie algebras in characteristic zero has been well studied for over fifty years, and has rich connections with algebraic geometry, mathematical physics, and number theory. By contrast, in positive characteristic, much less is known. In the talk, I will review some earlier results in this area, and state some new ones, namely the determination of the Harish--Chandra center and the linkage principle for highest weight representations at all levels. Time permitting, we will discuss some further conjectures. This is based on joint work in progress with Ivan Loseu. Representations of affine Lie algebras in positive characteristic
Apr. 15, 2025 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 10
Apr. 15, 2025 3:30pm (MATH 3…	Topology Stephanie Oh (CU Boulder) X The (classical) Adams spectral sequence was one of the first major computational tools developed in stable homotopy theory. In this talk we will give an overview of the construction of the spectral sequence and, time permitting, perform some low-dimensional computations. The Adams Spectral Sequence
Apr. 16, 2025 3:30pm (MATH350)	Math Phys Noah Song (CU Boulder) X TBA Hartree-Fock Method
Apr. 16, 2025 5pm (Math 350)	Math Club Emily Montelius X Sona are geometric sand drawings that are used in conjunction with traditional storytelling by the Chokwe people of Angola Africa. In the tradition, a storyteller smooths and pokes a grid of dots into the sand. As they tell their story, they draw lines weaving between the dots, following certain rules and matching the rhythm of their story. Whenever a line hits a boundary, it reflects back into the grid, and by the end of the story, every dot is surrounded and all of the lines have reconnected to themselves creating loops (see the linked poster for an example). Join us for an interactive activity exploring fascinating the mathematics behind these drawings! There will be free pizza as always, but we just ask that you RSVP at the link so that we can plan to order an appropriate amount. Link to RSVP: https://tinyurl.com/5dy7tnep Sona Interactive Activity
Apr. 17, 2025 12:30pm (Online)	Rep Theory Antoine Caradot (Jean Monnet University) View Online:https://cuboulder.zoom.us/j/97927772782 X In order to investigate the representation theory of a vertex algebra , a fruitful strategy is to look at the properties of its -algebra . This Poisson algebra reflects interesting properties of the vertex algebra and is often easier to handle than the vertex algebra itself. In this talk, we are interested in studying vertex algebras in a closed monoidal category, and in providing a description of the dual versions of and when those exist. We introduce vertex algebras graded by an abelian group and explain how to "dualize" the definition to obtain a graded vertex coalgebra. This leads to the notion of the -coalgebra of a vertex coalgebra. We will describe its properties and show that the duality vertex algebra / vertex coalgebra passes down to a duality -algebra / -coalgebra. We will also explain how this dualities carry on to the respective modules / comodules. C_2-(co)algebras and vertex (co)algebra duality
Apr. 17, 2025 2:30pm (MATH 3…	Functional Analysis Samantha Brooker (Virginia Tech) X The Effros-Shen algebra corresponding to an irrational number is classically described by an inductive sequence of direct sums of matrix algebras determined by the continued fraction expansion of . In recent work, Mitscher and Spielberg present an Effros-Shen algebra as the -algebra of a category of paths -- a generalization of a directed graph — also corresponding to the continued fraction expansion of . With this approach, the algebra is realized as the inductive limit of a sequence of infinite-dimensional (rather than finite-dimensional) subalgebras. In this talk, we will see approaches to constructing spectral triples on an Effros-Shen algebra, both in the classical picture (based on work of Adams, Aguilar, Ayala, Knight, and Marple), and in terms of the category of paths presentation, in both cases drawing on a construction of Christensen and Ivan. This is joint work with Konrad Aguilar and Jack Spielberg. Spectral triples on Effros-Shen algebras
Apr. 18, 2025 11:15am (Math …	Math Edu Padi Fuster Aguilera X In this talk I will present two of my passion projects around the topic of belonging in mathematics: the Math For All conference and the Meet a Mathematician interview collection. Math For All is a conference with the goal of creating a welcoming environment to enjoy and discuss mathematics. Meet a Mathematician is a collection of video interviews to mathematicians mostly from historically excluded groups in mathematics. Both projects aim to spotlight role models for students from underrepresented groups in mathematics at the same time as highlighting their other identities and career life. Belonging in Mathematics
Apr. 21, 2025 3:35pm (MATH 3…	Grad Student Seminar Nicholas Christoffersen X In this talk we use a toy problem to describe the probabilistic method. The toy problem is a non-adaptive group testing problem, which has well-developed theory. We will assume no knowledge of probability. Drinking Problems: A fun application of the probabilistic method
Apr. 22, 2025 1:10pm (MATH 3…	Kempner Robert S. Maier (Univ of Arizona and CU) X The single-oscillator Heisenberg algebra arises in quantum mechanics, and is seemingly less sophisticated than the algebras (infinite-oscillator, Virasoro) arising in quantum field theory. It is isomorphic to the algebra generated over C by non-commuting operators x and D (the derivative with respect to x), acting on any suitable space of functions. `Ordering identities' in this algebra include the rewriting of a word (a specified product of x's and D's) as a combination of normally ordered words: ones in which D's appear to the right of x's. In the relatively easy `derivation' case, when each word is based on (a power of) a word containing only a single D, the coefficients turn out to be Stirling numbers, which have a combinatorial interpretation. Ordering identities can be much more complicated, though any such identity can be viewed as an element of a two-sided ideal in the free associative algebra generated by x and D. Exploring the space of ordering identities, we introduce triangles of recursively defined generalized Stirling and Eulerian numbers, and identities in which these numbers appear as coefficients. Many of these triangles have no easy combinatorial interpretation, but satisfy triangular recurrences from which generating functions can be computed by the method of characteristics. Combinatorics in the single-oscillator Heisenberg algebra
Apr. 22, 2025 2:30pm (MATH 3…	Lie Theory Juan Villarreal (University of Colorado Boulder) X In this talk, we will show how to associate certain varieties to algebras and modules, called associated varieties. Then, we will explain how some geometric properties of these varieties have deep implications in representation theory. Finally, we will explain how some of these relations also holds in infinite dimensions. Filtrations and associated varieties.
Apr. 22, 2025 3:30pm (MATH 3…	Topology Alexander Waugh (University of Washington) X In this talk, I willI introduce a general framework for how we can understand properties of power operations via "Eulerian sequences". I will also discuss how various properties of these operations are encoded by these sequences (e.g. geometric fixed points, Cartan formula, etc...). When the group of equivariance is trivial or has order two, all known Steenrod and Dyer-Lashof operations are recovered in this framework. As a final application, I will show how to construct new nonzero mod p Steenrod and Dyer-Lashof operations for every finite group. This is based on joint work with Prasit Bhattacharya and Foling Zou. Power Operations via Eulerian Sequences
Apr. 23, 2025 3:30pm (MATH350)	Math Phys Wilson Wu (CU Boulder) X TBA Mathematical Foundations of Deep Learning
CANCELED Thu, Apr. 24	Rep Theory Hao Zhang (Tsinghua University) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) -cofinite VOA . This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707, 2503.23995) joint with Bin Gui. The sewing-factorization theorem for C_2-cofinite VOAs
CANCELED Fri, Apr. 25	Math Edu Peter Karanevich 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
Fri, Apr. 25 3:35pm (MATH 2…	PDE/Analysis Maja Taskovic (Emory University) X The wave kinetic equation is one of the fundamental models in the theory of wave turbulence, and provides a statistical description of weakly nonlinear interacting waves. This talk will address the global in time well-posedness of the spatially inhomogeneous wave kinetic equation by applying techniques inspired by the analysis of the Boltzmann equation – another model of statistical mechanics that describes evolution of rarefied gases in which particles undergo predominantly binary interactions. We will also discuss the well-posedness of the wave kinetic hierarchy – an infinite system of coupled equations closely related to the wave kinetic equation. Two essential tools for obtaining these results are the Hewitt-Savage theorem, which allows us to lift the existence result for the equation to the hierarchy, and the Klainerman-Machedon board game argument, which allows us to control the factorial growth of the Dyson series and consequently prove uniqueness of solutions. This is a joint work with Ioakeim Ampatzoglou, Joseph K. Miller and Natasa Pavlovic. On the inhomogeneous wave kinetic equation and its associated hierarchy Sponsored by the Meyer Fund
Mon, Apr. 28 3:35pm (MATH 3…	Grad Student Seminar Colin Jackson, Sky Jackson (CU Boulder) X In this talk, we will recall some things about Galois groups and look at the "Inverse Galois Problem", which asks which groups appear as Galois groups of polynomials over the rational numbers. The Inverse Galois Problem
Tue, Apr. 29 1:25pm (online)	Algebra/Logic Nebojsa Mudrinski (Novi Sad, Serbia) View Online:https://cuboulder.zoom.us/j/96896272260 X We prove that supernilpotent and nilpotent semirings with absorbing zero are the same and provide a necessary and sufficient condition for supernilpotency (nilpotency). Supernilpotent semirings
Tue, Apr. 29 3:30pm (MATH 3…	Topology Emily Montelius (CU Boulder) X We will cover a brief overview of how to view tiling spaces topologically and then overview different directions that mathematicians expand on this approach. The talk covers chapter 1 of "Topology of Tiling Spaces" by Lorenzo Sadun. It is meant to be a friendly exposition to increase our knowledge of other work in topology, similar to last year's talk "How is knot theory related to topology?". How is tiling related to topology?
Wed, Apr. 30 3:30pm (Math350)	Math Phys Tim Schumacher X The balls-and-bins problem is a fundamental problem in probability theory, analyzing the distribution of m balls randomly placed into n bins. It examines the likelihood of finding a certain number of balls in any given bin. This problem has many practical applications in computer science, such as load balancing in distributed systems. Weighted rendezvous hashing is one approach where bins have different weights (capacities), and the goal is to assign balls to bins such that no bin is unbalanced and, at the same time, all bins are approximately equally utilized. Weighted rendezvous hashing uses a deterministic algorithm to achieve this balance, though the foundations of the algorithm come from probability theory. We will discuss some of the applications and the theory behind these algorithms. Balls in bins

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