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Events for November 2024 – March 2025

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Fri, Nov. 1 10:10am (Math …	Math Edu Justin Barhite X We will explore two alternatives to traditional percentage-based grading schemes: standards-based grading and specifications-based grading. Both aim to provide clear measures of student progress that are more directly tied to learning objectives, and to give students ample opportunity to revise work in response to feedback. We will discuss the benefits and trade-offs of each approach, as well as some practical tips based on the experiences of several instructors implementing these methods in a wide variety of courses at the University of Kentucky. Alternative Grading
Fri, Nov. 1 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson X We discuss properties of commutators for algebras in congruence modular varieties. The commutator in congruence modular varieties
Tue, Nov. 5 1:25pm (online)	Algebra/Logic Gergo Gyenizse (University of Szeged, Hungary) View Online:https://cuboulder.zoom.us/j/96896272260 X A variety is Hobby-McKenzie if it satisfies an idempotent Mal’tsev condition that fails in semilattices. Such varieties form a Mal’tsev class which resembles that of Taylor varieties: the idempotent condition can be chosen to be a set of linear identities in two variables. For locally finite varieties, this class contains precisely the varieties omitting TCT types 1 and 5. In this talk, we provide a characterization of general (not necessarily locally finite or idempotent) Hobby-McKenzie varieties based on their compatible 3-ary relations. As a consequence, we prove that these varieties form a prime filter in the interpretability lattice of varieties. We also propose a nice characterization that depends instead on the compatible digraphs of the variety, but which is only proven to be correct in the locally finite case. Joint work with B. Bodor, M. Maróti and L. Zádori On general Hobby-McKenzie varieties
Tue, Nov. 5 3:30pm (MATH 3…	Topology Taylor Rogers X This semester we have introduced chromatic homotopy theory and the modern formulation of algebraic K-theory. In this talk, we will discuss chromatic redshift, a recently proven result that describes a way in which chromatic homotopy theory and algebraic K-theory interact. This interaction is an important ingredient in the recent disproof of the longstanding telescope conjecture. Chromatic Redshift
Thu, Nov. 7 3:35pm (MATH 3…	Probability Curtis Grant (Northwestern) X Metastability is a phenomenon widely believed to hold for Markov chains associated with spin glass models. Roughly, for a complex energy landscape, one should have a decomposition into wells, and the corresponding dynamics tracking which well the original Markov chain is in should be asymptotically Markovian. We will provide an overview of known results for spin glass dynamics, and then explain recent results with Reza Gheissari on metastability for heavy-tailed spin glasses. Metastability in Heavy Tailed Spin Glass Dynamics
Fri, Nov. 8 2:30pm (MATH 2…	Grad Algebra/Logic Peter Mayr X We discuss properties of commutators in congruence modular varieties. Basic properties of commutators
Tue, Nov. 12 11am (MATH 350)	Number Theory Number Theorists (CU) X The faculty from the number theory group will each give a brief overview of what we do for research. Open House
Tue, Nov. 12 1:25pm (Math 3…	Geometry/Analysis Gregory Berkolaiko (Texas A&M) X In this overview talk we will explore a variational approach to the problem of Spectral Minimal Partitions (SMPs). The problem is to partition a domain or a manifold into k subdomains so that the first Dirichlet eigenvalue on each subdomain is as small as possible. We expand the problem to consider Spectral Critical Partitions (partitions where the max of the Dirichlet eigenvalues is experiencing a critical point) and show that a locally minimal bipartite partition is automatically globally minimal. Extensions of this result to non-bipartite partitions, as well as its connections to counting nodal domains of the eigenfunctions and to a two-sided Dirichlet-to-Neumann map defined on the partition boundaries, will also be discussed. The talk is based on joint papers with Yaiza Canzani, Graham Cox, Bernard Helffer, Peter Kuchment, Jeremy Marzuola, Uzy Smilansky and Mikael Sundqvist. Spectral minimal partitions: local vs global minimality
Tue, Nov. 12 1:25pm (online)	Algebra/Logic Paolo Marimon (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a theorem of Rosenberg says that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen. Building on these results, we answer some questions of Bodirsky related to infinite-domain constraint satisfaction problems (CSPs). This is joint work with Michael Pinsker. Minimal operations over permutation groups
Tue, Nov. 12 3:30pm (Online)	Topology Thomas Brazelton (Harvard University) View Online:https://cuboulder.zoom.us/j/93758128989 X Moved to online https://cuboulder.zoom.us/j/93758128989 In this talk we'll touch on how an Euler class valued in equivariant homotopical bordism can reveal conserved symmetries in the solutions to equivariant enumerative problems. We apply this idea in joint work with C. Bethea to compute bitangents to symmetric plane quartics where we will see that homotopical techniques directly reveal patterns which are not obvious from a classical moduli perspective. We will also discuss ongoing work with S. Raman, in which we initiate a study of Galois groups of symmetric enumerative problems, leveraging tools from Hodge theory and computational numerical analysis. Equivariant enumerative geometry
Thu, Nov. 14 11:15am (MATH …	Algebraic Geometry Jonathan Wise TBA
Thu, Nov. 14 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X One of the most dramatic recent advances in operator algebras is the classification of separable, unital, simple, nuclear C-algebras which are Jiang–Su stable and satisfy the UCT. With this abstract classification theorem in hand, we are left with questions about which ”naturally occurring” C-algebras are covered by the theorem. By “naturally occurring” I mean operator algebraic models of various mathematical structures. These have long played an important role, as they allow one to use a well-stocked toolkit consisting of both algebraic and analytic equipment to study such various mathematical objects. An example of this is the relationship between topological dynamical systems and C-algebras. In this talk I will discuss examples of classifiable C-algebras given by various constructions arising from topological dynamical systems. Classifiable C*-algebras from topological dynamics Sponsored by the Simons Foundation
Fri, Nov. 15 10:10am (Math …	Math Edu Maggie Reardon and Emily Montelius X Student skills are a vital component of teaching first-year courses. Focusing on developing skills which make it easier to succeed in the university setting will benefit students in your classroom and beyond. In this talk we will present easy to implement methods to help students learn skills for preparing for class, engaging during class, reviewing recent material, and synthesizing semester long concepts. Additionally, we will discuss how to identify students struggling in these areas and how to implement interventions. Incorporating student skills in your classroom
Fri, Nov. 15 2:30pm (MATH 2…	Grad Algebra/Logic Peter Mayr X We characterize abelian algebras in congruence modular varieties. Abelian algebras
Tue, Nov. 19 1:25pm (online)	Algebra/Logic Max Hadek (Charles University Prague) View Online:https://cuboulder.zoom.us/j/96896272260 X An algebra is called minimal Taylor if its clone satisfies a non-trivial minor condition, but no proper subclone does so. Recently, Barto, Brady, Bulatov, Kozik and Zhuk initiated the systematic study of minimal Taylor algebras, intending to build a unified theory to understand the complexity of constraint satisfaction problems. They conjecture that every minimal Taylor algebra is finitely related, which we disprove by giving a counterexample. This result can be interpreted as follows: there is an infinite sequence of tractable finite domain CSPs, such that every CSP harder than all problems in the sequence, is already NP-complete. A non-finitely related minimal Taylor algebra
Tue, Nov. 19 2:30pm (Math 3…	Lie Theory Spencer Daugherty (CU Boulder) X The q,t-Catalan numbers can be described elegantly in terms of pairs of statistics on Dyck paths: area and bounce, or area and dinv. Mahonian permutation statistics, such as coinversion, disorder, and the sorting index, are some of the most thoroughly studied statistics on permutations. Using bijective methods, we prove new expressions of the q,t-Catalan numbers over subsets of permutations in terms of at least one Mahonian statistic. In the process, we develop new Catalan subsets of permutations, new bijections from Dyck paths to these subsets, and new permutation statistics. Mahonian Statistics and the q,t-Catalan Numbers
Tue, Nov. 19 3:30pm (MATH 3…	Topology Andrew Doumont X We will construct Lagrangian Floer homology. Time permitting, we will also discuss Fukaya categories and the homological mirror symmetry conjecture. Lagrangian Floer Homology
Wed, Nov. 20 1:30pm (MATH 3…	Kempner Rodrigo Ribeiro (Denver University) X Networks are everywhere, from social media platforms to intricate systems in nature. But how do we study and understand them? Different fields like computer science, math, and statistics offer their own tools and views. In this talk, we'll explore how these areas approach network analysis and how mathematicians formalize intuition and results from other areas. The talk will cover joint works with Rémy Sanchis (UFMG), Roberto I. Oliveira (IMPA) and Caio Alves (Oak Ridge National Lab). Interdisciplinary Perspectives on Network Analysis: A Confluence of Computer Science, Mathematics, and Statistics
Thu, Nov. 21 2pm (CSU)	Algebraic Geometry Carl Lian (Tufts Univerisity) X Let Gr(k,n) be the Grassmannian of k-planes in C^n. The standard torus action on C^n induces a torus action on Gr(k,n), whose orbits encode interesting combinatorial and geometric invariants. I will describe an explicit degeneration of the “generic” torus orbit closure into a union of Richardson varieties (intersections of two Schubert varieties). This gives a new proof of a formula of Berget-Fink for the Chow class of this subvariety of X, and the technique has further (but not yet fully realized) applications in enumerative geometry. The method also works for the variety of full flags in C^n, giving a new proof of an earlier result of Anderson-Tymoczko. Via the toric moment map, the combinatorial shadow of this degeneration is a polyhedral decomposition of the permutohedron due to Harada-Horiguchi-Masuda-Park. Time-permitting, I will mention some ongoing work with Grace Chen extending this story to type B. Degenerations of torus orbits
Tue, Dec. 3 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
Tue, Dec. 3 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
Tue, Dec. 3 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
Thu, Dec. 5 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
Thu, Dec. 5 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.
Thu, Dec. 5 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.
Thu, Dec. 5 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
Fri, Dec. 6 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
Thu, Dec. 12 11:15am (MATH …	Algebraic Geometry Daniel Lyness X This will be a continuation from last week. K3 Surfaces (cont.)
Thu, Dec. 12 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
Thu, Jan. 16 11:15am (MATH …	Algebraic Geometry Ruijie Yang (Kansas) Archimedean zeta function and Hodge theory Sponsored by the Meyer Fund
Thu, Jan. 16 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
Thu, Jan. 23 11:15am (MATH …	Algebraic Geometry AG Group Organizational Meeting
Thu, Jan. 23 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
Tue, Jan. 28 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
Tue, Jan. 28 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
Wed, Jan. 29 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
Wed, Jan. 29 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
Thu, Jan. 30 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
Thu, Jan. 30 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
Thu, Jan. 30 2:30pm (MATH 3…	Functional Analysis Darwin Tallana (CU Boulder) Proper actions and the Baum-Connes conjecture
Fri, Jan. 31 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
Tue, Feb. 4 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
Tue, Feb. 4 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 2
Tue, Feb. 4 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
Tue, Feb. 4 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
Wed, Feb. 5 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
Thu, Feb. 6 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
Thu, Feb. 6 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) The Baum-Connes assembly map
Mon, Feb. 10 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
Tue, Feb. 11 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
Tue, Feb. 11 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
Tue, Feb. 11 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 3
Tue, Feb. 11 3:30pm (MATH 3…	Topology James Woodcock TBD
Wed, Feb. 12 3:30pm (MATH350)	Math Phys Sheagan John (CU Boulder) X TBA Foundations of Measure Theory
Wed, Feb. 12 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
Thu, Feb. 13 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)
Fri, Feb. 14 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
Mon, Feb. 17 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
Tue, Feb. 18 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
Tue, Feb. 18 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
Tue, Feb. 18 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 4
Tue, Feb. 18 3:30pm (Kitt C…	DeLong Laura DeMarco (Harvard University) The geometry (and algebra) of the Mandelbrot set Sponsored by the Meyer Fund
CANCELED Tue, Feb. 18	Topology Alex Lajeunesse TBD
Tue, Feb. 25 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 5
Tue, Feb. 25 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
Tue, Feb. 25 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
Wed, Feb. 26 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
Thu, Feb. 27 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
Thu, Feb. 27 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) The Dirac-dual Dirac method
Thu, Feb. 27 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
Tue, Mar. 4 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
Tue, Mar. 4 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
Tue, Mar. 4 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 6
Tue, Mar. 4 3:30pm (MATH 3…	Topology James Woodcock TBD
Wed, Mar. 5 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
Thu, Mar. 6 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
Fri, Mar. 7 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
Tue, Mar. 11 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
Tue, Mar. 11 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
Tue, Mar. 11 1:15pm (MATH 3…	Geometry/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
Wed, Mar. 12 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
Wed, Mar. 12 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
Thu, Mar. 13 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
Thu, Mar. 13 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
Thu, Mar. 13 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
Fri, Mar. 14 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
Tue, Mar. 18 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 7
Tue, Mar. 18 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
Wed, Mar. 19 3:30pm (MATH350)	Math Phys Ezzeddine El Sai (CU Boulder) X TBA Statistical Learning
Thu, Mar. 20 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
Thu, Mar. 20 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
Thu, Mar. 20 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
Thu, Mar. 27 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

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