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Events for the weeks of March 30th – April 11th

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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 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

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