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Events for May – September

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Thu, May. 1 12:30pm (Online)	Rep Theory Juan Villarreal (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk we introduce a canonical decreasing filtration on intertwiners of a vertex algebra. We study the associated graded spaces. Then, we define Poisson vertex intertwiners and Poisson intertwiners. We obtain relations between the associated varieties of modules of a vertex algebra. Intertwiners and filtrations
Thu, May. 1 2:30pm (MATH 3…	Functional Analysis David Blecher (University of Houston) X Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in modern analysis and also in modern quantum physics (such as quantum information theory). They have an extensive theory, and have very important applications in all of these subjects. We present recent work (2025) on the real case of the theory of (complex) operator systems, and also the real case of their remarkable tensor product theory, due in the complex case to Paulsen and his coauthors and students, building on pioneering earlier work of Kirchberg and others. We uncover several notable differences between the real and complex theory, including the absence of minimal and maximal functors in the category of real operator systems. We show how this is related to entanglement. We also develop very many foundational structural results for real operator systems, and elucidate how the complexification interacts with the basic constructions in the subject. We give the real analogues of the Kirchberg conjectures (and of several important related problems that have attracted much interest recently such as the Tsirelson problem on quantum correlations), and the deep relationships between them. Joint work with Travis Russell. Real operator systems
Wed, May. 7 3:30pm (Math350)	Math Phys Andrew Hamilton (CU Boulder Astrophysics) X String theory offers a viable theory of quantum gravity, with spin 2 gravitons encoded in closed strings. But the failure to find evidence for supersymmetry at the LHC has left string theory in disarray. A solution to the problem is in plain sight: revert to old-fashioned, 1970s-style, nonsupersymmetric, bosonic string theory, reenvisaged as a theory of all the forces, not just the strong force. The old theory correctly reproduces the Brauer-Weyl (1935) algebraic relation between fermions and bosons seen in the standard model, whereas supersymmetry does not. Sages of string theory commonly reject bosonic string theory on the grounds that (1) it does not admit fermions, and (2) its ground state is tachyonic. But rejection (1) assumes that fermions are strings, wheres the fermions of bosonic string theory are the endpoints of strings, and are not themselves strings; in modern parlance, the fermions are excitations of the D-brane boundary of strings. As to rejection (2), the properties of the tachyon are precisely those of a Higgs field: it is a multiplet of the unbroken symmetry; the "vacuum" state where the Higgs field vanishes identically is tachyonically unstable; and it has spin zero. I propose Clifford(11,1) string theory, a 26-dimensional, tachyonic, bosonic, open string theory, whose bosons occupy all 26 dimensions while their fermionic endpoints are confined to an 11+1 dimensional D-brane. The 26 dimensions compactify to 12 on the 14-dimensional self-dual torus of the rank 14 SU(8)xSU(8) subgroup of the group G^2(10)=U(16) generated by Clifford(11,1) multivectors of grade 2 (mod 4). Clifford(11,1) string theory
Wed, May. 14 3:30pm (MATH 2…	Math Phys Noah Song (CU Boulder) X TBA Coupled Cluster Theory
Thu, May. 22 9am (Online)	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
Thu, Jun. 5 3:30pm (MATH 3…	Functional Analysis PIOTR M. HAJAC (IMPAN, Warsaw, Poland) X Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphims. As both functors are often used at the same time, one needs a new category of graphs that allows a “common denominator” functor unifying the covariant and contravariant constructions. In this talk, I will show how to solve this problem by first introducing the relation category of graphs RG, and then determining the concept of admissible graph relations that yields a subcategory of RG admitting a contravariant functor to k-Alg simultaneously generalizing the aforementioned covariant and contravariant functors. I will illustrate relation morphisms of graphs by many naturally occurring examples, including Cuntz algebras, quantum spheres and quantum balls. Although I will focus on Leavitt path algebras and graph C-algebras, time permitting, I will unravel functors given by path algebras, Cohn path algebras and Toeplitz graph C-algebras from suitable subcategories of RG to k-Alg. Based on joint work with Gilles G. de Castro and Francesco D'Andrea. RELATION MORPHISMS OF DIRECTED GRAPHS
Fri, Jun. 6 2:30pm (Math 2…	Noncomm Geometry Paul Bressler (Universidad de los Andes) X I will describe a construction of a complex associated to a Lie algebroid originally due to V. Schechtman and use it to obtain interesting representatives of a characteristic classes of manifolds. Characteristic classes of natural bundles Sponsored by the Meyer Fund
Thu, Jul. 17 2:30pm (MATH 3…	Lie Theory Robert McRae (Tsinghua University) View Online:https://cuboulder.zoom.us/j/97927772782 X This will be an overview talk on braided tensor categories obtained from representation categories of vertex operator algebras. I will describe how the tensor category structure is defined and also discuss what is currently known about examples and further properties (especially rigidity/existence of duals) of this tensor category structure. Tensor categories from vertex operator algebras Sponsored by the Meyer Fund
Tue, Jul. 29 2:30pm (MATH 2…	Lie Theory David Ridout (University of Melbourne) View Online:https://cuboulder.zoom.us/j/97927772782 X In this informal chat with Dr. Ridout we will learn why modularity plays a fundamental role in 2 dimensional conformal field theory. Please join us if you are around! Why is modularity expected in a physical conformal field theory?
Tue, Aug. 26 2:30pm (MATH 3…	Lie Theory Katrina Barron (Notre Dame University) X Through the framework of Conformal Field Theory (i.e. string theory), linear algebra and Lie theory meet up with number theory in fundamental ways. In particular, the graded traces and pseudo-traces of families of linear operators corresponding to the fields (vertex operators) of interacting particles exhibit certain invariance properties with respect to action of the modular group SL(2,Z). We discuss aspects of modular symmetries that appear in graded trace and pseudo-trace functions for various classes of algebras of fields (vertex algebras) and their modules, including for the new notion of strongly interlocked module introduced by Barron, Batistelli, Orosz Hunziker, and Yamskulna. Several examples will be discussed. Graded (pseudo-)traces and number theory in Lie theory and physics. Sponsored by the Meyer Fund
Tue, Aug. 26 3:30pm (MATH 3…	Topology Mayuko Yamashita (Perimeter Institute for Theoretical Physics) X In this talk, I will explain the recent development in the Segal-Stolz-Teichner (SST) paradigm. The SST paradigm is a set of ideas connecting stable homotopy theory, especially the theory of elliptic cohomology theory, with supersymmetric quantum field theories in physics. Thanks to the recent mathematical development of equivariant elliptic cohomology thoery, we are currently experiencing a great enrichment the SST paradigm. In the talk, I will illustrate this by explaining my work with Y.Lin on Topological Elliptic Genera. Equivariant elliptic cohomology and supersymmetric quantum field theories Sponsored by the Meyer Fund
Tue, Aug. 26 3:30pm (Math350)	Math Phys Mayuko Yamashita (Perimeter Institute for Theoretical Physics) X In this talk, I will explain the recent development in the Segal-Stolz-Teichner (SST) paradigm. The SST paradigm is a set of ideas connecting stable homotopy theory, especially the theory of elliptic cohomology theory, with supersymmetric quantum field theories in physics. Thanks to the recent mathematical development of equivariant elliptic cohomology thoery, we are currently experiencing a great enrichment the SST paradigm. In the talk, I will illustrate this by explaining my work with Y.Lin on Topological Elliptic Genera. Equivariant elliptic cohomology and supersymmetric quantum field theories Sponsored by the Meyer Fund
Wed, Aug. 27 4:30pm (MATH 2…	PDE/Analysis Neel Patel (University of Maine) X The Muskat problem describes the dynamics of an interface between two fluids in porous media driven by gravity. For a graphical interface with a denser fluid below a lighter fluid, the interface is in a stable regime. On the other hand, a closed curve interface, or bubble, is always in the unstable regime. This instability can be seen in the linearized equation. In this talk, we will discuss how to formulate the bubble problem to deal with this instability. Stability of Bubbles in Porous Media Sponsored by the Meyer Fund
Fri, Aug. 29 10:10am (MATH …	Math Edu Rebekah Jones X We will discuss potential topics and speakers for the Seminar on Undergraduate Math Education (SUME) this semester. All those interested in attending SUME are welcome. SUME Open House
Wed, Sep. 3 4:40pm (MATH 3…	Grad Student Seminar Omar Al - Khazali (CU Boulder) X The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a finite graph. In the general case, the problem is -hard. However, there is a subcollection of graph classes for which there exists an efficient solution. I will display my method which provides algorithms that are proven correct by their underlying algebraic operations unlike existing purely algorithmic solutions to this problem. We introduce a `booleanize' mapping on the adjacency matrix of a graph which we prove identifies the solution for Trees, Uniform Block Graphs, Block Graphs, and Directed Acyclic Graphs with exact conditions and associated polynomial-time algorithms. I will then show an algebraic construction with elements as graphs and two operations that have further underlying structure within them. Then, showcasing some results and theorems that exist behind the hidden structure of this algebraic construction. An Algebra of Graphs and the Longest Path Problem
Thu, Sep. 4 11:15am (MATH …	Algebraic Geometry Jon Kim X In this talk, I will introduce the moduli space of K3 surfaces. I will start with some preliminaries on K3 surfaces from Hodge theory and move onto their moduli. Specifically, the goal will be to introduce the Bailey-Borel compactification of a certain ball quotient and its relationship to the moduli space of K3 surfaces. If there is time, I will discuss degenerations, Kulikov models (type III), and recent work by Alexeev and Engel (2023) on the KSBA compactification of the moduli of K3 surfaces. Moduli of K3 Surfaces
Tue, Sep. 9 1:25pm (MATH 2…	Algebra/Logic Nik Ruskuc (St Andrews) X Let S be a semigroup, and suppose that the full relation SxS is finitely generated as a right congruence. When S is a group this happens if and only if S is finitely generated, but in general there are many more examples, of arbitrarily large cardinalities. Let X be a finite generating set for SxS. Then, for any two elements s,t in S, there is a finite chain of X-transformations connecting s and t. The longest such chain is the X-diameter of S, and the smallest X-diameter when X ranges over all finite generating sets is the (right congruence) diameter of S, denoted D(S). This parameter can be finite or infinite. It turns out that it is finite for many classical semigroups of transformations, linear transformations and partitions, and is then very small, i.e. . Usually some intriguing combinatorics is involved in these results, but the underlying reasons for this phenomenon remain mysterious. The new results presented in this talk are due to various subsets of J. East, V. Gould, C. Miller, T. Quinn-Gregson and myself. (Congruence) diameter of semigroups Sponsored by the Meyer Fund
Tue, Sep. 9 2:30pm (MATH 2…	Grad Algebra/Logic Aten, Kearnes, Mayr (CU) Organizational meeting
Thu, Sep. 11 11:15am (MATH …	Algebraic Geometry Jon Kim X We will continue our talk from last week starting with analytic moduli and discussing the moduli space of M-quasipolarized and M-polarized K3 surfaces. If time permits, we will discuss one-parameter degenerations. These talks follow Alexeev and Engel's "Compact moduli of K3 surfaces" paper in 2023. Moduli of K3 Surfaces II
Thu, Sep. 11 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X Given a compact metric space and self-homeomorphism, one can construct the associated crossed product C-algebra. There is a strong relationship between dynamical properties and C-algebraic properties. For example, the system is minimal if and only if the crossed product algebra is simple. I will discuss minimal crossed products, their K-theory, K-homology, and Poincare duality. The talk will be an introduction aimed at graduate students. Minimal crossed products and duality
Fri, Sep. 12 10:10am (Math …	Math Edu Peter Karanevich (CU Boulder School of Education) X In this hands-on workshop we will do a mathematics activity leveraging the 5 practices for orchestrating productive mathematical discussions to debrief it. We will then examine each practice and have time for reflection about how you can incorporate these ideas in your classroom. 5 practices of Orchestrating Productive Mathematics Discussions
Tue, Sep. 16 1:25pm (online)	Algebra/Logic Leandro Vendramin (Vrije Universiteit Brussel, Belgium) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk explores the interplay between set-theoretic solutions to the Yang-Baxter equation and structures arising in algebraic logic. Central to this connection is the recently introduced theory of L-algebras, which generalizes well-known logical systems such as Hilbert and Heyting algebras. The presentation assumes minimal background. We will discuss illustrative examples, highlight open problems, and share several conjectures. L-Algebras: A bridge between algebraic logic and the Yang-Baxter equation
Tue, Sep. 16 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten (CU Boulder) X We will begin covering background material pertaining to the recent paper "A categorical perspective on constraint satisfaction: The wonderland of adjunctions" by Hadek, Jakl, and Oprsal. Categorical methods for constraint satisfaction
Wed, Sep. 17 4:40pm (MATH 3…	Grad Student Seminar Matt Watson (CU Boulder) X Modular forms are functions on the upper half plane which satisfy certain transformation laws given by the action of certain arithmetic groups. Though often introduced as a complex analytic object, modular forms have a tendency to appear in seemingly unrelated areas of mathematics. How many ways can an integer be written as a sum of four squares? Modular forms can be used to solve this. What is the densest arrangement of non-overlapping spheres in ? Modular forms can be used to solve this. The coefficients of the Fourier expansion of some important modular function encode the dimensions of the irreducible representations of the monster group (moonshine!!!). In the context of geometry, modular forms give pluricanonical forms on some moduli space. The goal of this talk is to introduce modular forms, marvel at some of their interesting properties, and then explain why I care about modular forms as an algebraic geometer. Modular Forms and the Baily-Borel Theorem
Thu, Sep. 18 11:15am (MATH …	Algebraic Geometry Jon Kim X We continue the talk from last week, starting with quasipolarized and polarized K3 surfaces and their moduli spaces. Moduli of K3 Surfaces III
Fri, Sep. 19 10:10am (Math …	Math Edu Shelby Stanhope (US Air Force Academy) X Clear communication is an essential skill for success in mathematics, yet many undergraduates enter college-level courses without experience in writing solutions that are both clear and well-structured. This talk will explore strategies instructors can use to help learners begin developing effective communication practices as early as the calculus sequence, not just in proof-based courses. We will discuss the role of short phrases in guiding the reader, the importance of balancing notation with words, and techniques for establishing a logical flow that allows solutions to stand on their own. I will highlight a communication activity I have used in a multivariable calculus course that scaffolds the development of these skills, recognizing that such expectations may be new to many students. Developing Effective Communication Practices in Mathematics
Tue, Sep. 23 11am (MATH 350)	Number Theory Zheng Xiao (CU) X After Mordell’s conjecture for curves was proved by Faltings, attentions turn to the distribution of rational and integral points on higher dimensional varieties, which is encoded in the celebrated Vojta’s conjecture. Along this line we proved a subspace type inequality, improving the result of Ru-Vojta, on surfaces. Meanwhile, we obtain a sharp criterion of when some certain surfaces admit a non Zariski-dense set of integral points. Joint with Huang, Levin. Diophantine Approximation on Surfaces and Distribution of Integral Points
Tue, Sep. 23 1:25pm (MATH 2…	Algebra/Logic Peter Mayr (CU) X Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring), and let B be the countable atomless Boolean algebra. We show that the automorphism groups of filtered Boolean powers of A by B have ample generics, which gives a new proof of our previous results that these groups have the small index property, uncountable cofinality and the Bergman property. This is joint work with Nik Ruskuc. Generic automorphisms of Boolean powers
Tue, Sep. 23 2:30pm (MATH 3…	Topology Howy Jordan X A topological space is stratified when it is equipped with a nice decomposition into nice subsets. In the classical case, the nice subsets are manifolds. When the decomposition is nice enough, one can equip the stratified space with a stratified tangent bundle. "Is there a category of stratified spaces whose fiber bundles include these stratified tangent bundles?" Motivated by this question, we will investigate categories of stratified spaces. In particular, we will consider cases where the underlying stratification can vary and cases where there is a fixed base stratification and find interesting topologies and group objects along the way. Categories of Stratified Spaces
Tue, Sep. 23 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten (CU Boulder) X We will continue covering background material pertaining to the recent paper "A categorical perspective on constraint satisfaction: The wonderland of adjunctions" by Hadek, Jakl, and Oprsal. Topics will include the discrete Grothendieck construction, Kan extensions, and the nerve of a functor. Categorical methods for constraint satisfaction (Part 2)
Thu, Sep. 25 11:15am (MATH …	Algebraic Geometry Daniel Lyness X TBA TBA
Thu, Sep. 25 11:15am (MATH …	Algebraic Geometry Daniel Lyness X Geometric Invariant Theory is concerned with answering the following problem: Given a group G acting on a projective variety X, how can we construct a quotient of X by the group action, and give it the structure of an algebraic variety? We cannot simply take the orbit space, and hope that this will be a variety, so it is important to throw out some bad (unstable) orbits from X, and identify some ok (semistable) orbits together in the quotient. In this talk, I will show how to construct this quotient abstractly, and introduce the remarkable Hilbert-Mumford numerical criterion, which allows us to determine which orbits in X are stable, semistable and unstable, and therefore what our quotient looks like geometrically. In part 2 next week, I will show how I am applying GIT to my research. Introduction to Geometric Invariant Theory part 1
Thu, Sep. 25 2:30pm (MATH 3…	Functional Analysis Various X The members of the functional analysis group will give short talks introducing their research. Functional Analysis Open House
Tue, Sep. 30 1:25pm (online)	Algebra/Logic Anna Romanowska (Warsaw University of Technology) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we will use an algebraic approach to study convex subsets of affine spaces over the ring of dyadic rationals. Dyadic rationals are rationals whose denominator is a power of 2. A dyadic n-dimensional convex set is defined as the intersection with n-dimensional dyadic space of an n-dimensional real convex set. Such a dyadic convex set is said to be a dyadic n-dimensional polytope if the real convex set is a polytope whose vertices lie in dyadic space. Dyadic convex sets appear as subalgebras of reducts of faithful affine spaces over the ring of dyadic numbers, or equivalently as commutative, entropic and idempotent groupoids (binars or magmas) under the binary operation of arithmetic mean. We will examine algebraic concepts and properties of dyadic polytopes (especially polygons), and contrast their behavior with that of polytopes in real affine space. On the basis of older results about the generation and structure of dyadic polytopes, we will present recent results (obtained with A. Mucka) on the representation, characterization and classification of dyadic triangles. Algebraic properties of dyadic convex polytopes
Tue, Sep. 30 1:30pm (MATH 3…	Topology Jackson Morris (University of Washington) X The stable homotopy groups of spheres are an important and complicated invariant. However, there is a filtration which sorts the p-components of this group into vn-periodic layers, known as chromatic heights, which are themselves more computable. The height one piece is the only layer which we fully understand, and an invaluable tool to accessing v1-periodic stable homotopy is the BP<1>-based Adams spectral sequence. In this talk, I will discuss joint work with Petersen and Tatum which focuses on the analogue of this problem in motivic homotopy theory. The key idea is that there are similar periodic layers in the stable homotopy of the motivic sphere. We compute the E1-page of the analogous BPGL<1>-based motivic Adams spectral sequence at all primes p and over a myriad of base schemes. Time permitting, I will discuss future directions in chromatic motivic homotopy theory. Splittings of truncated motivic Brown-Peterson cooperations algebras
Tue, Sep. 30 2:30pm (MATH 3…	Lie Theory Chindu Mohanakumar (University of Colorado Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology
Tue, Sep. 30 2:30pm (MATH 3…	Topology Chindu Mohanakumar (CU Boulder) X The goal of this talk is to give an intuitive idea of coherent orientations and why they provide a useful invariant for symplectic manifolds. I will start from the definition of a symplectic manifold, and motivate the study of J-holomorphic curves in Symplectic Geometry. From there, I will give a loose idea of Floer theory and how it relates to Morse theory, and use this relation to motivate coherent orientations. Coherent orientations of J-holomorphic curves in Symplectic Topology

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