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Events for the weeks of April 13th – 25th

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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 2:30pm (MATH 3…	Lie Theory Juan Villarreal (University of Colorado Boulder) TBA
Tue, Apr. 22 3:30pm (MATH 3…	Topology Alexander Waugh (University of Washington) TBD
Wed, Apr. 23 3:30pm (MATH350)	Math Phys Wilson Wu (CU Boulder) X TBA Mathematical Foundations of Deep Learning
Thu, Apr. 24 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
Fri, Apr. 25 11:15am (Math …	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) TBA Sponsored by the Meyer Fund

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