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Events for the weeks of April 20th – May 2nd

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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) TBD
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

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