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Events for April – August

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Tue, Apr. 1 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 8
Tue, Apr. 1 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
Wed, Apr. 2 3:30pm (MATH350)	Math Phys Markus Pflaum (CU Boulder) X TBA Born-Oppenheimer Approximation
Thu, Apr. 3 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
Thu, Apr. 3 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
Fri, Apr. 4 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
Fri, Apr. 4 3:35pm (MATH 2…	Geometry/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
Tue, Apr. 8 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
Tue, Apr. 8 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 9
Tue, Apr. 8 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
Wed, Apr. 9 3:30pm (MATH350)	Math Phys Wilson Wu (CU Boulder) X TBA Neural Networks
Thu, Apr. 10 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
Fri, Apr. 11 3:35pm (MATH 2…	Geometry/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
Mon, Apr. 14 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
Tue, Apr. 15 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
Tue, Apr. 15 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
Tue, Apr. 15 2:30pm (MATH 2…	Grad Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 The structure of finite algebras, 10
Tue, Apr. 15 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
Wed, Apr. 16 3:30pm (MATH350)	Math Phys Noah Song (CU Boulder) X TBA Hartree-Fock Method
Wed, Apr. 16 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
Thu, Apr. 17 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
Thu, Apr. 17 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
Fri, Apr. 18 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
Mon, Apr. 21 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
Tue, Apr. 22 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
Tue, Apr. 22 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.
Tue, Apr. 22 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
Wed, Apr. 23 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…	Geometry/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
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

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