Algebraic Geometry Algebra/Logic DeLong Diversity Functional Analysis Geometry/Analysis Init Conditions Kempner Lie Theory MathClub Math Phys Noncomm Geometry Number Theory Probability Rep Theory Grad Student Seminar Thesis Defenses Topology Ulam Math Edu

Events for November 2023 – March 2024

Return to this week

Tue, Mar. 5 5pm (MATH 350)	Probability Kyle Luh & Sean O'Rourke (CU Boulder) X This will be an introductory talk on the theory of random polynomials and random matrices for the visiting graduate students. We will give a broad overview of the fields as well as some of the research directions being pursued in this department. Overview of Random Polynomials and Random Matrices
Nov. 01, 2023 4:40pm (MATH 3…	Grad Student Seminar Edouard Heitzmann (University of Colorado) X Hawking and Penrose’s Singularity Theorems are advanced results in General Relativity which describe Big Bang and Black Hole singularities given minimal topological information about the manifold they live in, using the language of Semi-Riemannian Geometry. This talk presents two proofs of the former Theorem: one stronger version which gives a picture of the Big Bang similar to the Robertson-Walker model, and the other which assumes less and proves less. Along the way, we will develop the theory of Focal Points and Index Forms, which play a pivotal role in these proofs, and provide some Physical intuition to justify the Timelike Convergence Condition assumed in Hawking’s Theorem. Hawking's Singularity Theorem
Nov. 02, 2023 11:15am (MATH …	Algebraic Geometry Sebastian Casalaina-Martin (University of Colorado Boulder) TBA
Nov. 02, 2023 2pm (Online)	Rep Theory Sergei Gukov (California Institute of Technology) View Online:https://cuboulder.zoom.us/j/97927772782 X At its core, this talk will be about a relation between characters of modules of logarithmic vertex algebras in the positive and negative Kazhdan-Lusztig (KL) zones. The main concrete result will be an easy-to-use step-by-step computational algorithm that produces a character of a log-VOA, say, in the positive KL zone from the expression in the negative KL zone, and vice versa. An equally (if not more!) valuable conceptual message of this talk will be an explanation that the same bijective relation plays an important role in very different areas of mathematics (and even physics) under other guises. Going to the other side
Nov. 06, 2023 3:30pm (Math350)	Math Phys Mert Okyay (CU Boulder) View Online:https://cuboulder.zoom.us/j/94002553301 X For online participation: Zoom Meeting ID: 940 0255 3301 Passcode: 790356 The geometric phase phase à la M. Berry
Nov. 07, 2023 1:25pm (MATH 2…	Algebra/Logic Nik Ruskuc (University of St Andrews, UK) View Online:https://cuboulder.zoom.us/j/96896272260 X Let S be a semigroup. A (right) S-act X is a representation of S by transformations on X. S-acts can be regarded as (unary) algebras in their own right. Thus we can talk about subacts, homomorphisms, quotients, generating sets and defining relations for S-acts. This in turn opens up a possibility of attempting to study/understand/classify semigroups according to properties of their S-acts. In this talk I will report on some recent work on some such properties: - Noetherian: S is Noetherian if every finitely generated S-act is finitely presented; - Coherent: S is coherent if every finitely generated subact of a finitely presented S-act is finitely presented; - The trivial S-act is finitely presented; - Pseudofiniteness: the trivial S-act is finitely presented and there is a uniform bound on the length of derivation sequences. I will also indicate some intriguing open problems that have arisen in each area. This work is currently being pursued under an EPSRC-funded project held jointly with Victoria Gould from York, and involves several collaborators, including Matthew Brookes, Craig Miller, James East and Thomas Quinn-Gregson. Semigroup actions and finiteness conditions Sponsored by the Meyer Fund
Nov. 07, 2023 2:30pm (MATH 3…	Lie Theory Chris Eblen (CU) X The classical case of Schur--Weyl duality links the representation theory of the general linear group to that of the symmetric group, enabling the study of both simultaneously. Generalizations of this kind of duality have yielded pathways to study the representation theory of some common groups in interesting ways. Such pathways are especially valuable when the group in question has an intractable representation theory, as in the case of the group of unipotent upper triangular matrices with entries in a finite field, $U_{n}$ . We discuss an analogue of Schur--Weyl duality for $U_{n}$ and a class of $U_{n}$ -modules called beach modules arising from the study of this duality within the framework of a particular supercharacter theory for $U_{n}$ . Unipotent Beach Modules and Schur--Weyl Duality
Nov. 07, 2023 3:30pm (MATH 3…	Topology Rachel Chaiser X I will give an introduction to the K-theory of Banach algebras, with a C-algebraic lean. I will define Banach algebras and C-algebras, so prior knowledge of these is helpful but not required. I will also discuss the relationship between K-theory for C*-algebras and K-theory for topological spaces. K-Theory for Banach Algebras
Nov. 08, 2023 3:30pm (Math350)	Math Phys Ezzedine El Sai (CU Boulder) X For online participation: Zoom Meeting ID: 940 0255 3301 Passcode: 790356 The Bures metric and Uhlman's connection
Nov. 09, 2023 11:15am (MATH …	Algebraic Geometry Bob Kuo (University of Colorado Boulder) X Smooth cubic surfaces (over the complex numbers) contain exactly 27 lines. Degenerating them, and following where the lines go, leads to a rich theory of combinatorics. Beniamino Segre, in his book "The non-singular cubic surfaces" (1942), uses the symmetries inherent in this combinatorial framework to classify the symmetries of cubic surfaces. In this talk, we'll do some early 20th-century math and follow how Segre classifies cubic surfaces defined over the real numbers. Classifying real cubic surfaces
Nov. 14, 2023 1:25pm (online)	Algebra/Logic Nóra Szakács (University of Manchester, UK) View Online:https://cuboulder.zoom.us/j/96896272260 X Inverse monoids are an important generalization of groups, and they form a variety of algebras. We focus on the class of inverse monoids called F-inverse: this is not closed under taking inverse subsemigroups or homomorphic images, but does form a variety in the signature enriched with an extra unary operation. Recently, Auinger, Kudryavtseva and M. Szendrei gave an elegant model for free F-inverse monoids in this extended signature. More generally, they describe the initial object in the category of X-generated F-inverse monoids with greatest group image G. We show that this category is equivalent to the category of finitary (i.e. algebraic) G-invariant closure operators on subgraphs of the Cayley graph of G, and adapt Stephen's approach to study the word problem in presentations of inverse monoids for F-inverse monoids in the enriched signature. Closure operators on group Cayley graphs, and presentations of F-inverse monoids
Nov. 14, 2023 2:30pm (MATH 3…	Lie Theory Karola Meszaros (Cornell) X The central question of knot theory is that of distinguishing links up to isotopy. The first polynomial invariant of links devised to help answer this question was the Alexander polynomial (1928). Almost a century after its introduction, it still presents us with tantalizing questions, such as Fox’s conjecture (1962) that the absolute values of the coefficients of the Alexander polynomial $ΔL(t)$ of an alternating link $L$ are unimodal. Fox’s conjecture remains open in general with special cases settled by Hartley (1979) for two-bridged knots, by Murasugi (1985) for a family of alternating algebraic links, and by Ozsv\’ath and Szab\’o (2003) for the case of genus 2 alternating knots, among others. We settle Fox’s conjecture for special alternating links. We do so by proving that a certain multivariate generalization of the Alexander polynomial of special alternating links is Lorentzian. As a consequence, we obtain that the absolute values of the coefficients of $ΔL(t)$ , where $L$ is a special alternating link, form a log-concave sequence with no internal zeros. In particular, they are unimodal. This talk is based on joint work with Elena Hafner and Alexander Vidinas. Log-concavity of the Alexander polynomial Sponsored by the Meyer Fund
Nov. 14, 2023 2:30pm (MATH 2…	Math Edu Rebecca Machen (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/my/rebeccamachen X In this training, participants will examine how their own mathematical backgrounds can impact their teaching choices in the classroom. The session will go beyond individual perspectives to promote a community mindset that fosters inclusivity and student belonging. Participants will explore the relationship between deficit language and its effects on students, learn about the pedagogical concepts of "warm demander and the hidden curriculum", and acquire practical strategies to transform the student experience in mathematics classrooms. This session welcomes anyone interested in learning more about how to promote student belonging in mathematical spaces. Promoting Student Belonging in Mathematics Classrooms through Equity-Driven Pedagogies
Nov. 14, 2023 3:30pm (MATH 3…	Topology Celia Hacker (Max-Planck-Institute Leipzig) View Online:https://cuboulder.zoom.us/j/94002553301 X At the intersection of Topological Data Analysis and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each signal on the cells of a complex is processed using the combinatorial Laplacian and the resulting Hodge decomposition. Meanwhile, discrete Morse theory has been widely used to speed up computations by reducing the size of complexes while preserving their global topological properties. In this talk, we introduce an approach to signal compression and reconstruction on complexes that leverages the tools of discrete Morse theory. The main goal is to reduce and reconstruct a cell complex together with a set of signals on its cells while preserving their global topological structure as much as possible. This is joint work with Stefania Ebli and Kelly Maggs. Signal processing on cell complexes using discrete Morse theory
Nov. 15, 2023 3:30pm (Math350)	Math Phys Shreya Arya (Duke University) X Brownian motion is the most basic diffusion process on Euclidean space. The goal of this talk is to understand diffusion on spaces beyond Euclidean space. While Brownian motion on manifolds has been extensively studied, expanding this construction to stratified spaces proves challenging. Sturm introduced an approach for constructing diffusion processes on metric measure spaces, relying on the theory of Dirichlet forms and their well-established connection to Markov processes. These forms generate diffusion only if the space satisfies a geometric condition known as the "measure contraction property," which can be viewed as a regularity condition for measures. We explore the geometric condition in the context of Whitney stratified spaces, equipped with the Riemannian distance and a volume measure. I will talk about the relationships between diffusion and Dirichlet forms and their generalization to stratified spaces. No prior knowledge of Dirichlet forms and Markov processes is assumed. This is ongoing work with Celia Hacker, Markus Pflaum and Sayan Mukherjee. Brownian Motion on Singular Spaces Sponsored by the Meyer Fund
Nov. 15, 2023 4:40pm (MATH 3…	Grad Student Seminar Jon Kim (University of Colorado) X When working with curves and surfaces, it's much nicer to work with them when they are smooth. Alas, we can't always have these nice assumptions, so we gotta ask when smoothness fails and whether if we can resolve it. Well, we know how to identify singularities, but if we can resolve them, we then gotta figure out how to do it in a manner where we can preserve information away from it. Thankfully, it turns out that we do have such a method called blowing-up. This talk will be an introduction to blow-ups in an illustrated manner to via worked examples with and (cartoon)-pictures. An Illustrated Introduction to Blow-ups
Nov. 16, 2023 11:15am (MATH …	Algebraic Geometry Adrian Neff (University of Colorado Boulder) X Stable maps spaces arise naturally when trying to answer questions in enumerative geometry, e.g., in the proof of Konstevich's formula for the number of rational plane curves passing through a fixed number of points. However, once the genus of the curve is greater than 0, the stable maps spaces become highly singular, having multiple irreducible components of varying dimensions. In order to have more refined enumerative counts, one tries to find desingularizations of these spaces. In this talk, I'll discuss the history of this desingularization problem for genus 1 stable maps to projective space, and conclude with a discussion of a new approach with the potential to work for higher genera (work in progress). Stable maps from genus 1 curves to projective space
Nov. 16, 2023 2pm (Online)	Rep Theory Agustina Czenky (University of Oregon) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk, we look at the classification problem for symmetric fusion categories in positive characteristic. We recall the second Adams operation on the Grothendieck ring and use its properties to obtain some classification results. In particular, we show that the Adams operation is not the identity for any non-trivial symmetric fusion category. We also give lower bounds for the rank of a (non-super-Tannakian) symmetric fusion category in terms of the characteristic of the field. As an application of these results, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self-dual simple objects. Low rank symmetric fusion categories in positive characteristic.
Nov. 28, 2023 12:10pm (MATH …	Kempner Uri Shapira (Technion Israel, Israel) X The aim of this talk is to introduce the area of homogeneous dynamics to a general audience and to survey some key instances in which number theory interacts with it. I hope to touch upon the following: (1) Margulis' resolution of Oppenheim's conjecture regarding values of indefinite irrational quadratic forms at integral points. (2) Einsiedler-Lindenstrauss-Katok work towards Littlewood's conjecture in Diophantine approximation. (3) Linnik/Duke theorem that says (loosely) that integral points on large spheres are spread randomly on these spheres. (4) I will also try to mention a few results that I have been involved in proving. Homogeneous dynamics and number theory
Nov. 28, 2023 1:25pm (online)	Algebra/Logic Clemens Schindler (Technical University Vienna, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X The set of all increasing functions on the rational numbers carries an algebraic structure (the standard composition operation of functions, yielding a semigroup) and a topological structure (the topology of pointwise convergence in which a sequence of functions converges if and only if it is eventually constant at every argument). These structures are compatible in the sense that the operation is continuous with respect to the topology. Whenever one considers such a combined algebraic-topological structure, one can ask the following general question: Is the topology predetermined by the compatibility with the operations, i.e., does the algebra have a unique (Polish?) topology? In other words: Can the (Polish) topology be "reconstructed" from the algebra? I will present several examples of Polish groups and semigroups that do (not) have this property and introduce the known proof techniques. Afterwards, I will discuss why these successful techniques fail for the space of all increasing functions on the rational numbers and outline how this shortcoming can be mitigated to show that, indeed, the increasing functions on the rational numbers carry a unique Polish topology. This is joint work with Michael Pinsker. Unique Polish semigroup topology: novel techniques to crack the semigroup of increasing functions on the rational numbers
Nov. 28, 2023 3:30pm (MATH 3…	Topology Howy Jordan X Given a space, consider a decomposition into a pair of complementary open and closed subspaces. Artin gluing tells us which open sets of the subspaces can glue to an open set of the whole space and what data is needed to glue sheaves on the subspaces to obtain a sheaf on the whole space. This can be readily generalized to decompositions into locally closed subspaces. Artin gluing describes how to glue sheaves, hence etale bundles. In this talk we will consider how to also apply Artin gluing to fiber bundles. If the fibers are isomorphic we can obtain another fiber bundle, but in general we obtain stratified fiber bundles. In the case of tangent bundles, properties of the Artin gluing data are related to the Whitney regularity conditions. Artin Gluing of Fiber Bundles and the Whitney Conditions
Nov. 29, 2023 4:40pm (MATH 2…	Grad Student Seminar Daniel Lyness (University of Colorado) X Given a map between compact Riemann surfaces, the Riemann-Hurwitz formula relates the Euler characteristics of the surfaces and the degree of the map. In this talk we will discuss the various components of this formula towards giving a sketch of the proof, and seeing some simple consequences in Topology and Algebraic Curves. We will define CW complexes in order to compute the Euler characteristic of surfaces, and then analyse the rigid structure of maps between Riemann surfaces to define the degrees of such maps, before seeing how to relate these numbers. I intend this to be a very accessible talk which will introduce some interesting ideas from Topology and Algebraic Curves. There will be lots of pictures! The Riemann-Hurwitz formula
Nov. 30, 2023 11:15am (MATH …	Algebraic Geometry Jon Kim (University of Colorado Boulder) TBA
Nov. 30, 2023 2pm (Online)	Rep Theory Vladimir Kovalchuk (University of Denver) View Online:https://cuboulder.zoom.us/j/97927772782 X W-(super)algebras have generated great interest in recent years due to their numerous applications in mathematics and physics. The process of Hamiltonian reduction in stages suggests that W-(super)algebras often arise as extensions of tensor products basic building blocks. In type A, we expect that the building blocks are the Gaiotto-Rapcak Y-algebras which arise as 1-parameter quotients of the universal 2-parameter VOA of type W(2,3,…). For types B, C, and D, the quotients of the universal 2-parameter VOA of type W(2,4,…) provide some, but not all, of the necessary building blocks. In this talk we discuss a new universal 2-parameter VOA of type W(1^3,2,3^3,4,…), whose 1-parameter quotients are expected to account for the missing building blocks for W-(super)algebras of types B, C, and D. There are 8 infinite families of such quotients, which are analogues of the Gaiotto-Rapcak Y-algebras. We will explain the process behind the construction of this universal two-parameter VOA and discuss several applications. This is a join work with Thomas Creutzig and Andrew Linshaw. On the universal 2-parameter VOA of typeW(1^3,2,3^3,4,...).
CANCELED Nov. 30, 2023	Functional Analysis Andrew Toms (Purdue University) View Online:TBA Toward the rank problem for simple nuclear C*-algebra
Dec. 05, 2023 2:30pm (Zoom)	Math Edu Austin Mohr (Nebraska Wesleyan University) View Online:https://cuboulder.zoom.us/j/95717237725 X Mastery-based testing is an assessment style that challenges students to provide complete solutions to problems derived from clear course concepts. Students are allowed multiple attempts to demonstrate mastery with no penalty for failed attempts. I argue that mastery-based exams encourage sustained progress toward thorough understanding as compared with traditional points-based exams. Moreover, I believe they offer increased equity with respect to student experience in previous mathematics courses. We will conclude with brief guidelines on how you can easily implement mastery-based exams in your existing courses. Assessment That Promotes Persistence and Equity
Dec. 06, 2023 3:30pm (MATH 3…	Topology Bob Kuo (CU Boulder) X One can view closed symmetric monoidal categories as a linearization of category theory. It is a framework that allows one to talk about linear algebraic notions in categories without an obvious linear structure. Some examples include compactly generated pointed topological spaces, chain complexes, and spectra. In this talk, I'll introduce the definition of closed symmetric monoidal categories, and then discuss how the notions of duals and traces generalized to these examples. Traces and duality in closed symmetric monoidal categories
Dec. 06, 2023 4:40pm (MATH 2…	Grad Student Seminar Sylvia Maher (University of Colorado) X In this talk I will discuss derived functors, which are universal homotopy-theoretic approximations to functors between categories equipped with a notion of homotopy theory. I will show how they generalize derived functors from homological algebra, and then talk about homotopy (co)limits, an important class of derived functors. Model Categories (part 3): Derived Functors
Dec. 12, 2023 12:10pm (MATH …	Kempner Jun Ho Lee (Mokpo Nat'l Univ, Korea) X Arithmetic of the units of number fields gives a lot of information about number fields. According to Dirichlet's unit theorem, the structure of units of the orders in number fields. In this talk, we are interested in exact expression of the units. Moreover, we will share the conjectures for units. We will talk about our results in this direction if time permits. Note on the units of algebraic number fields
Dec. 12, 2023 1:25pm (online)	Algebra/Logic H. Peter Gumm (Philipps University Marburg, Germany) View Online:https://cuboulder.zoom.us/j/96896272260 X Universal Coalgebra is a general theory of state based systems, encompassing all sorts of automata, transition systems, Kripke structures, etc., be they deterministic, non-deterministic, probabilistic, second order, or else. This diversity of examples is covered by choosing as signature F of the mentioned coalgebras an appropriate Set-Functor, rather than just a sequence of arities, like in Universal Algebra. Preservation properties of that signature functor F determine much of the structure of the corresponding classes of coalgebras. Of particular interest, it turns out, is the question, whether F preserves preimages or (weak) pullbacks. This provides only the backdrop and the motivation for us to study a class of functors arising from classical Universal Algebra as "free-algebra-functors" where FV(X) is taken as the base set of the free algebra over X in a variety V. We show amongst other things, that FV(-) preserves preimages if and only if V can be defined by essentially balanced (also called regular) equations. Regarding preservation of kernel pairs, the picture is still fragmented. For instance, if V is a Malcev variety then FV weakly preserves kernel pairs, and if V is n-permutable and FV weakly preserves kernel pairs, then V is Malcev. In joint work with R. Freese we study the case when V is a variety L of lattices, with further order preserving operations permitted. It turns out that FL(-) always weakly preserves kernel pairs. In purely lattice theoretical terms, this shows that in any lattice variety L any balanced equation p(u1,...,um) = q(v1,...,vn), where {u1,...,um} = {v1,...,vn} must have an obvious reason, namely that both p and q are substitution instances of a common "ancestor"-term s, from which the said equation arises by further identification of variables, resulting in syntactically identical terms. For arbitrary nontrivial idempotent varieties V of algebras we additionally show, using Olshak's theorem, that (strong) preservation of pullbacks is impossible. Free algebra functors are special instances of copower functors which we can define in any concrete and cocomplete category. For instance, if M is a (commutative) monoid, the functor M[X] arising as X-fold sum of M, preserves preimages iff M is positive, and weakly preserves pullbacks iff M is (refinable) equidivisible. Lucid reasons behind balanced identities
Dec. 12, 2023 3:30pm (MATH 3…	Topology Justin Barhite X Traces arise in many different places in math: traces of matrices, characters of group representations, and even the Euler characteristic of a CW complex! There are very general notions of trace, expressed in the language of category theory, that capture these examples of traces and whose properties imply familiar results like the Lefschetz fixed point theorem and the induction formula for characters. The formalism of traces doesn't tell the whole story though; there are some constructions that feel trace-like in certain ways but also have a distinct flavor, and what's really needed to explain them from this category-theoretic perspective is a dual notion of "cotrace." I will talk about some of these things that I have been working to understand by developing a theory of bicategorical cotraces. Traces and Cotraces in Bicategories
Tue, Jan. 23 3:30pm (MATH 3…	Topology Ben Spitz (UCLA) X “Classically”, Mackey and Tambara functors are equivariant generalizations of abelian groups and commutative rings, respectively. What this means is that, in equivariant homotopy theory, Mackey functors appear wherever one would expect to find abelian groups, and Tambara functors appear wherever one would expect to find commutative rings. More recently, work by Bachmann and Hoyois has garnered interest in related structures which appear in motivic homotopy theory – these motivic Mackey functors and motivic Tambara functors do not have anything to do with group-equivariance, but somehow share the same axiomatics. In this talk, I’ll introduce a general context for interpreting the notions of Mackey and Tambara Functors, which subsumes both the equivariant and motivic notions. The aim of this approach is to translate theorems between contexts, enriching the theory and providing cleaner proofs of essential facts. To this end, I’ll discuss recent progress in boosting a foundational result about norms from equivariant algebra to this more general context. Mackey and Tambara Functors Beyond Equivariant Homotopy
Thu, Jan. 25 2pm (Online)	Rep Theory Chelsea Walton (Rice University) View Online:https://cuboulder.zoom.us/j/97927772782 X This talk will be on joint work with Robert Laugwitz and Milen Yakimov (arXiv:2307.14764) that is motivated by obtaining solutions to the quantum reflection equation (qRE). To start, given a braided monoidal category C and C-module category M, we introduce a version of the Drinfeld center Z(C) of C adapted for M. We refer to this category as the "reflective center" E_C(M) of M. Just like Z(C) is a canonical braided monoidal category attached to C, we show that E_C(M) is a canonical braided module category attached to M. We will also discuss the case when C is the category of modules over a quasitriangular Hopf algebra H, and show how quantum K-matrices arise in this setting (thus yielding solutions to the qRE). Reflective centers of module categories and quantum K-matrices
CANCELED Tue, Jan. 30	Kempner Edray Goins (Pomona College) X Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we ``move'' twelve times then we get back to where we started. This is the elementary concept of a monodromy group. In this talk, we give a gentle introduction to a historical mathematical concept which relates calculus, linear algebra, differential equations, and group theory into one neat theory called ``monodromy''. We explore lots of real world applications, including why it’s so easy to get lost in parking garages, and present some open problems in the field. We end the talk with a discussion of how this is all related to solving polynomial equations, such as Abel’s famous theorem on the insolubility of the quintic by radicals. Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy
Tue, Jan. 30 3:30pm (MATH 3…	Topology Sarah Petersen Organizational Meeting
Thu, Feb. 1 2pm (Online)	Rep Theory Thomas Creutzig (University of Alberta) View Online:https://cuboulder.zoom.us/j/97927772782 X Vladimir Kovalchuk constructed a two parameter family of VOA that have an affine sp(2) as subalgebra and in each even positive conformal weight a singlet and at each odd one an sp(2)-triplet. This structure is the third universal family of W-algebras after the W-infinity algebra and its even spin analogue and quotients of one-parameter subfamilies of Vladimir algebras are often realized by cosets of certain W-algebras of orthosymplectic type. Very much like in the W-infinity case and in the even spin case it is expected that there are quotients that are rational and lisse. I will explain that this expectation is indeed true and it is given by a novel family of rational and lisse cosets. This is joint work with Vlad Kovalchuk and Andy Linshaw. A family of rational VOAs as type C cosets.
Thu, Feb. 1 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) X In this talk I will discuss M(A), the multiplier algebra of a general Banach algebra A, as well as some of its properties. I will present a main result that produces an isometric representation of M(A) on a Banach space E whenever A has a contractive approximate identity (cai) and a nondegenerate isometric representation on E. This implies that the multiplier algebra of a "C*-like" L^p-operator algebra is again an L^p-operator algebra. I will then focus on some particular degenerate L^p operator algebras without cai's and say something about their multiplier algebras. Multiplier Algebras of L^p-Operator Algebras
Tue, Feb. 6 1:25pm (MATH 2…	Algebra/Logic Peter Mayr (CU Boulder) View Online:https://cuboulder.zoom.us/j/96896272260 X Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We identify the Fra{\"i}ss{\'e} limit D of the class of finite direct powers of A as a filtered Boolean power of A by the countable atomless Boolean algebra B and show that D also arises as congruence classes of the countable free algebra in the variety generated by A. Further we show that filtered Boolean powers of A by B are $ω$ -categorical, have the small index property, strong uncountable cofinality and the Bergman property. This is joint work with Nik Ruskuc (University of St Andrews). Filtered Boolean powers and their automorphism groups
Tue, Feb. 6 3:30pm (MATH 3…	Topology Juan Moreno X Last semester we saw the category of spectra introduced as the right place to study stable phenomena for spaces. This idea turns out to be incredibly useful largely because spectra behave very much like algebraic objects. We will spend a good part of the talk covering two instances of this: Duality - analogous to the notion of duality for vector spaces is something called Spanier-Whitehead duality for spectra. Localization - analogous to the notion of localizing abelian groups at a prime is something called Bousfield localization of spectra. With the remaining time we will see how these two notions can be used to capture important information about the stable homotopy groups of spheres. In particular we'll talk about a sort of "first approximation" to these groups: the stable image of J. Duality, Localization, and stable homotopy groups of spheres
Wed, Feb. 7 3:30pm (MATH 3…	Math Phys Markus J. Pflaum (CU Boulder) X This is an organizational meeting for the Spring 2024 semester. We will have a few external speakers, talks by graduate students on their research in Mathematical Physics and talks on the semester theme "Noncommutative geometry and topological phases of matter". Organizational Meeting\| Semester Theme: Noncommutative Geometry and Topological Phases of Matter
Thu, Feb. 8 2pm (Online)	Rep Theory Shoma Sugimoto (Tsinghua University) View Online:https://cuboulder.zoom.us/j/97927772782 X The Feigin-Tipunin algorithm is a combinatorial and iterative algorithm introduced by the speaker recently to construct and study log VA(-module)s that have the q-series valued quantum invariant of 3-mfds called homological block introduced by S. Gukov et al. as their characters. The key point is that at each step of the iteration, a geometric representation theory can be used as in the usual Feigin-Tipunin construction, so that the representation theory of the log-VA can be studied without having to examine its complicated algebraic structure. In this talk, after describing the speaker's previous work, it will be explained that if the FT algorithm can be applied to a certain lattice VOA-module, we can construct a log VA-module with the homological block of the (N+2)-Seifert 3-mfd as its character. Feigin-Tipunin algorithm
Thu, Feb. 8 3:35pm (MATH 3…	Probability Jack Morris (Cornell Tech) X How much information do the outputs of language models contain about their inputs? We investigate this problem in two scenarios, recovering text inputs from the outputs of embeddings from sentence embedders and next-token probability outputs from language models. In both cases, our methods are able to fully recover some inputs given just the model output. Inverting Language Models
Fri, Feb. 9 9:05am (Zoom)	Math Edu Lee Roberson & Jen Gensler (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/91244797970 X What we want students to take away from homework assignments and what students actually take away do not always align. To address this issue we will work to understand what meaningful learning is and use this understanding to outline our learning goals for students engaging in homework assignments. Applying this framework, we will evaluate assessment items to determine if they align with our goals and explore strategies for creating homework items that promote meaningful learning. Time permitting, we will discuss the importance of constructive feedback on homework as a component of meaningful student learning. Creating Homework that Promotes Meaningful Learning
Tue, Feb. 13 3:30pm (MATH 3…	Topology Taylor Rogers The Steenrod Algebra and Its Dual
Wed, Feb. 14 3:30pm (MATH 3…	Math Phys Andrew Hamilton (CU Boulder, Astrophysics Department) View Online:https://cuboulder.zoom.us/j/94002553301 (Password: 790356) X The grand unified group Spin(11,1) is motivated by the fact that Spin(10) chirality coincides with Dirac chirality, allowing 10 compact internal dimensions and 3+1 large spacetime dimensions to coexist in a geometry of just 11+1 dimensions. Spin(11,1) admits a 12 dimensional bosonic string theory whose 26 underlying dimensions are compactified to 12 on the 14 dimensional self-dual torus of the SU(8)xSU(8) group. The 10 dimensional geometry is a complex five-fold that becomes a Calabi-Yau five-fold after symmetry breaking to the standard model. The multiverse just got a whole lot bigger. Spin(11,1) and String Theory
Thu, Feb. 15 2pm (Online)	Rep Theory Shigenori Nakatsuka (University of Alberta) View Online:https://cuboulder.zoom.us/j/97927772782 X In physics, the webs of W-algebras are introduced as the vertex algebras associated with the (p, q)-webs of interfaces in the topologically twisted N = 4 super Yang-Mills theory. This class of vertex algebras are generalizations and extensions of the so-called vertex algebras at the corner, or equivalently the affine cosets of hook-type W-algebras in type A. Although not proven yet in general, it has recently been noticed that the webs of W-algebras actually recover the general W-algebras in type A through the ``reduction by stages". In this talk, I will present the first non-trivial examples and some interesting phenomena found in the course both in rational and irrational cases. The talk is based on a joint work with T. Creutzig, J. Fasquel, and A. Linshaw. On the structure of W-algebras in type A
Tue, Feb. 20 1:25pm (MATH 2…	Algebra/Logic John T. Baldwin (University of Illinois at Chicago) View Online:https://cuboulder.zoom.us/j/96896272260 X A $t-(κ,k,s)$ block design is a set of $κ$ elements and a collection of $k$ -element subsets $B$ of $P$ (called blocks) with the property that each $t$ -element subset of $P$ occurs in exactly $s$ blocks. A $k$ -Steiner system is a $2-(κ,k,1)$ system. Using variants of the Hrushovski method we construct infinite block designs and Steiner systems that are a) $ℵ1$ -categorical and with more work b) have $t$ -transitive automorphism groups for prescribed $t$ . The strongly minimal Steiner $k$ -Steiner system (M,R) from Baldwin and Pao (2021) can be `coordinatized' in the sense of Ganter and Werner (1975) by a quasigroup if $k$ is a prime-power. But for the basic construction this coordinatization is never definable in (M,R) by Baldwin (2023). Nevertheless, by refining the construction, if $k$ is a prime power there is a (2,k)-variety of quasigroups which is strongly minimal and definably coordinatizes a Steiner $k$ -system. We compare these structures with Steiner systems given by Fra{\"\i}ss\'{e} constructions by Barbina and Casanovas (2019) and compare versions of the small intersection property for $ℵ0$ -categorical structures and countably saturated structures by Lascar (2002). Infinite combinatorics from finite structures
Tue, Feb. 20 3:30pm (MATH 3…	Topology Elizabeth Tatum (Universität Bonn) X In recent work, Guchuan Li, Sarah Petersen, and I have constructed models for $C2$ -equivariant analogues of the integral Brown-Gitler spectra. In this talk, I will start by introducing the classical Brown-Gitler spectra and some of their applications. After that, I will discuss the $C2$ -equivariant integral Brown-Gitler spectra, as well as the applications we are beginning to study. Equivariant Brown-Gitler spectra
Tue, Feb. 20 4:50pm (MATH 3…	Grad Student Seminar Alex LaJeunesse (University of Colorado) X Algebraic K-theory is a booming field that interacts with many diverse areas of mathematics. It’s universality makes it difficult to understand, but much progress has been made in recent years using a variety of “trace” methods; that is, approximating K-theory by simpler algebraic invariants. In this talk I will introduce algebraic K-theory and the related Hochschild homology, with the ultimate goal of constructing a useful map from the former to the latter. The Dennis Trace and Algebraic K-Theory
Wed, Feb. 21 3:30pm (MATH 3…	Math Phys James Woodcock (CU Boulder, Mathematics Department) Noncommutative Tori
Thu, Feb. 22 2pm (Online)	Rep Theory Ana Ros Camacho (Cardiff University) View Online:https://cuboulder.zoom.us/j/97927772782 X The study and classification of algebra objects in modular tensor categories has a strong motivation from the conformal field theoretical point of view, these objects being related to e.g. full theories [Fuchs-Runkel-Schweigert] and extensions of vertex operator algebras [Huang-Kirillov-Lepowsky, Creutzig-Kanade-McRae for superalgebras]. In this talk, I will present a classification of rigid, Frobenius algebras in the so-called Dijkgraaf-Witten categories, which we achieved using Frobenius monoidal functors. Joint work with Robert Laugwitz and Sam Hannah, based on SIGMA 19 (2023), 075, 42 pages. On the classification of rigid Frobenius algebras in Dijkgraaf-Witten categories
Fri, Feb. 23 9:05am (Zoom)	Math Edu Rebekah Jones (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/91244797970 X We will discuss the process of planning, creating and implementing active learning materials in the classroom. We’ll consider different aspects, including the purpose and style of such activities, and give concrete examples from the calculus sequence at CU. The emphasis of this talk will be on the practical aspects of this process. Developing Effective Active Learning Materials
Fri, Feb. 23 3:30pm (ECCR 2…	Kempner Chad Topaz (Williams College) X Tens of millions of people in the United States have been directly impacted by the criminal justice system, with nearly half the population affected through close familial or social ties. Alongside the direct harm inflicted by the system, an insidious challenge arises: the system's opaque nature makes pinpointing the specific loci of harm complex and elusive. Echoing the words of civil rights pioneer Ida B. Wells, who stated that "the way to right wrongs is to turn the light of truth upon them," this talk will showcase how data science can be harnessed to expose racial injustice. It will feature case studies spanning various scales and stages of the criminal justice system, including policing in the small municipality of Williamstown, Massachusetts; criminal sentencing across all 94 federal district courts; and incarceration at Rikers Island in New York during the COVID pandemic. These examples underscore the pivotal role of data science tools in fostering transparency and advancing justice. Data Science for Criminal and Social Justice
Tue, Feb. 27 1:25pm (MATH 2…	Algebra/Logic Chase Meadors (CU Boulder) View Online:https://cuboulder.zoom.us/j/96896272260 X S4-algebras (or interior algebras) provide semantics for the well-known modal logic S4, and there is a syntactic criterion characterizing when a variety of S4-algebras is locally finite in terms of its "depth" (a classical result of Segerberg and Maksimova). Since the logic MS4 (monadic S4) axiomatizes the one-variable fragment of predicate S4, it is natural to try to generalize the Segerberg--Maksimova theorem to this setting. We discuss several results in this direction. We establish that this theorem naturally extends to a family of subvarieties of MS4 containing, in particular, S4_u (S4 with a universal modality). On the other hand, we provide a translation of varieties of S5_2-algebras into varieties of MS4-algebras of depth 2 which preserves and reflects local finiteness, demonstrating that the problem of characterizing locally finite varieties of MS4-algebras is at least as hard as the corresponding problem for S5_2 (the bimodal logic of two unrelated S5 modalities), a wide-open problem. Finally, we discuss another natural subvariety of MS4 obtained by asserting a monadic analogue of Casari's predicate formula; this subvariety plays a role in obtaining a faithful provability interpretation of monadic intuitionistic predicate logic, and is expected to have a more manageable characterization of local finiteness. Local finiteness in varieties of MS4-algebras
Tue, Feb. 27 2:30pm (MATH 3…	Lie Theory Farid Aliniaeifard (UBC) X We define vertex-colourings for edge-coloured digraphs, which unify the theory of $P$ -partitions and proper vertex-colourings of graphs. Furthermore, we use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and quasisymmetric functions and generating functions of $P$ -partitions. We also discuss the relations between generalized chromatic functions, Schur functions in noncommuting variables, and the well-known Stanley-Stembridge (3+1)-free conjecture. Generalized Chromatic Functions Sponsored by the Meyer Fund
Tue, Feb. 27 3:30pm (MATH 3…	Topology Courtney Hauf X This is look at operads and the definition of a permutative category. Operads and Permutative Categories
Tue, Feb. 27 4:50pm (MATH 3…	Grad Student Seminar Jon Kim (University of Colorado) X Hodge theory provides us with powerful tools for studying the cohomology of smooth manifolds through PDEs. Surprisingly, it has deep connections to complex geometry in studying bidgree differential forms on complex manifolds, specifically complex projective varieties. In this talk, I will introduce Hodge theory on complex manifolds and discuss how these connections from PDEs to complex geometry are made. We will conclude by giving a short proof of the Hodge decomposition via the existence of a Green's operator and showcase some useful consequences. Hodge Theory and The Hodge Decomposition
Wed, Feb. 28 3:30pm (MATH 3…	Math Phys Markus Pflaum (CU Boulder, Mathematics Department) Noncommutative Geometry and the Quantum Hall Effect
Thu, Feb. 29 2pm (Online)	Rep Theory Iván Angiono (Universidad Nacional de Córdoba) View Online:https://cuboulder.zoom.us/j/97927772782 X Due to a celebrated result by Deligne, symmetric tensor categories of moderate growth over (algebraically closed) fields of characteristic zero correspond to categories of representations of affine algebraic supergroups. Once we move to positive characteristic, we need to take into account the Verlinde category Ver_p: Coulembier-Etingof-Ostrik proved recently that every such symmetric tensor category is the one of representations of an algebraic group in Ver_p, under some restrictions. Thus, we wonder how to describe algebraic groups in Ver_p, which in turn correspond to pairs of usual algebraic groups and Lie algebras in Ver_p, as described by Venkatesh. This leads to the question of how to obtain Lie algebras in Ver_p. This talk is based on joint works with J. Plavnik and G. Sanmarco where we look for examples of these Lie algebras. We prove the existence of contragredient Lie algebras in symmetric tensor algebras generalizing Kac-Moody construction of Lie (super) algebras, which at the same time give a description of some examples obtained previously by 'semi simplifying' usual Lie algebras and provide new Lie algebras in Ver_p. Contragredient Lie algebras in symmetric tensor categories.
Thu, Feb. 29 3:35pm (MATH 3…	Probability Jorge Garza Vargas (Caltech) X Classical random matrix theory focuses on the study of highly structured models (e.g. Wigner and Wishart matrices) which are presented as a sequence of random matrices defined for every dimension, whose asymptotic (i.e. as the dimension goes to infinity) spectral properties must be understood in detail. However, modern problems in data and computer science require only a coarser understanding of the random matrices in question, but necessitate nonasymptotic results in settings where the models are less structured and do not necessarily belong to a prescribed sequence of matrices. In this work we provide tools for analyzing the spectral distribution of any self-adjoint noncommutative polynomial evaluated in arbitrary independent unitarily invariant Hermitian random matrices of a fixed dimension. Our results can be interpreted as a quantitative version of Voiculescu's celebrated asymptotic freeness result. This is joint work with Chi-Fang Chen and Joel Tropp. Non-asymptotic Random Matrix Theory for Unitarily Invariant Matrices
Tue, Mar. 5 10:10am (MATH …	Geometry/Analysis Ian Miller (CU Boulder) X The magnetic nonlinear Schrödinger (mNLS) equation is a variant of the well-studied nonlinear Schrödinger equation. In mNLS, identities involving motion are less well-behaved and cause difficulty for establishing blow-up results. Blow-up results have been obtained for mNLS with constant magnetic field. These results relied on the specific structure and symmetry of these potentials. In this talk we establish existence of blow-up solutions for a class of potentials with no prescribed symmetry. Blow-up results for the nonlinear Schrödinger equations with trapping magnetic potentials
Tue, Mar. 5 2:30pm (MATH 3…	Lie Theory Florencia Orosz Hunziker (University of Colorado Boulder) X Modular forms played an important role in the proof (Borcherds 1992) of the Monstrous Moonshine conjecture providing the first fundamental bridge between number theory and representation theory through vertex algebras. In this talk, we will give an overview of several ways in which Vertex algebras can be systematically be used to connect representation theory to number theory. Connections between Representation Theory and Number Theory through vertex algebras
Tue, Mar. 5 3:30pm (MATH 3…	Topology Alexander LaJeunesse X In this talk I will introduce monads and their algebras. Following a discussion of the relationship between monads and adjunctions, we will discover how every operad gives rise to a monad, and with this in hand we will spend some time trying to understand May’s comparison theorem. If time permits, we will conclude by looking at how the monadic bar construction can be used to construct canonical resolutions of algebraic objects. Monads and Operads
Wed, Mar. 6 3:30pm (MATH 3…	Math Phys Ezzeddine El Sai (CU Boulder, Department of Mathematics) Strict Deformation Quantization
Thu, Mar. 7 2pm (Online)	Rep Theory Philip Argyres (University of Cincinnati) View Online:https://cuboulder.zoom.us/j/97927772782 X The local operators of a unitary 4d N=2 SCFT in twisted Schur cohomology form a vertex operator algebra (VOA). By "local operator" we mean one associated with a point in space-time. We show that to every 4d N=2 SCFT there is associated a vertex algebra containing the VOA of local twisted Schur operators as a proper subalgebra. The new vertex operators of this larger vertex algebra are associated with certain extended operators (line, surface, etc.) in twisted Schur cohomology. Though we can compute some partial results in simple SCFTs, the structure of these extended vertex algebras is still largely mysterious. The extended vertex algebra of 4-dimensional N=2 superconformal field theories
Fri, Mar. 8 9:05am (Zoom)	Math Edu Andrew Meier & Harrison Stalvey (University of Colorado Boulder) View Online:https://cuboulder.zoom.us/j/91244797970 X Although we value active learning in the form of student-led activities, we should still make an effort to utilize active learning techniques when we lecture. In this talk we will share strategies to create an engaging and active lecture, and provide examples of ways we can capitalize on students’ engagement through various styles of questioning in a lecture environment. Lecturing for Engagement
Tue, Mar. 12 2:25pm (online)	Algebra/Logic Stefano Fioravanti (Charles University Prague) View Online:https://cuboulder.zoom.us/j/96896272260 X We investigate some applications of a certain technique (that we call Freese's technique), which is a tool for identifying certain lattices as sublattices of the congruence lattice of a given algebra. In particular we gave sufficient conditions for two families of lattices (called the rods and the snakes) to be admissible as sublattices of a variety generated by a given algebra, extending a result of R. Freese and P. Lipparini. On some admissible sublattices of a congruence lattice
Tue, Mar. 12 2:30pm (MATH 3…	Lie Theory Aram Bingham (Colorado School of Mines) X Given a reductive algebraic group G with Borel subgroup B, a spherical variety X is a G-variety such that B acts with finitely many orbits. Well-known examples include toric varieties, flag varieties, symmetric varieties and their embeddings, and so-called “wonderful varieties” which play an important role in the classification of spherical varieties. In many cases, Borel subgroup orbits can be combinatorially parametrized and equipped with poset structure induced by the closure-containment (or Bruhat) order. Shellability is a much-studied property in poset topology which implies that a simplicial complex associated to a poset has the homotopy type of a wedge of spheres. It has been known since the 1980s that Bruhat orders of flag varieties are shellable, and these results have been extended to other related settings more recently. We will discuss some results, open questions, and hunches relating these two areas, based on joint work with Néstor Díaz. SOME SPECULATIONS ON SHELLABILITY AND SPHERICAL VARIETIES Sponsored by the Meyer Fund
Wed, Mar. 13 3:30pm (MATH 3…	Topology J. Peter May (University of Chicago) View Online:https://cuboulder.zoom.us/j/94002553301 (Passcode: 790356) X I defined operads in 1971, and they are ubiquitous. I defined $E∞$ ring spaces and $E∞$ ring spectra soon afterwords. The latter are the starting point of derived algebraic geometry. That was a half century ago. All of the old mathematics seems to be correct. However, answering a question Agnes Beaudry asked me in 2023 has led me to the conclusion that this idiot got the definition of $E∞$ ring spaces conceptually wrong. I will explain what I now think is the right way to think about ring theory operadically. The new theory is very elementary and should also have been understood a half century ago. It leads to an operadic definition of bipermutative categories that generalizes equivariantly and leads in turn to a concrete construction of commutative ring $G$ -spectra in equivariant algebraic $K$ -theory. The talk will focus on the elementary combinatorial foundations. The new theory also leads to many open questions and new directions that I may mention. Operads, Moperads, and Bioperads
Wed, Mar. 13 3:30pm (Math350)	Math Phys J. Peter May (University of Chicago) View Online:https://cuboulder.zoom.us/j/94002553301 (Passcode: 790356) X I defined operads in 1971, and they are ubiquitous. I defined $E∞$ ring spaces and $E∞$ ring spectra soon afterwords. The latter are the starting point of derived algebraic geometry. That was a half century ago. All of the old mathematics seems to be correct. However, answering a question Agnes Beaudry asked me in 2023 has led me to the conclusion that this idiot got the definition of $E∞$ ring spaces conceptually wrong. I will explain what I now think is the right way to think about ring theory operadically. The new theory is very elementary and should also have been understood a half century ago. It leads to an operadic definition of bipermutative categories that generalizes equivariantly and leads in turn to a concrete construction of commutative ring $G$ -spectra in equivariant algebraic $K$ -theory. The talk will focus on the elementary combinatorial foundations. The new theory also leads to many open questions and new directions that I may mention. Operads, Moperads, and Bioperads
Thu, Mar. 14 9am (Online)	Rep Theory Anne Moreau (Paris-Saclay) View Online:https://cuboulder.zoom.us/j/97927772782 On a series of simple affine VOAs at non-admissible level arising from rank one 4D SCFTs
Thu, Mar. 14 4:40pm (MATH 3…	Grad Student Seminar Nicholas Christoffersen (University of Colorado) TBD
Fri, Mar. 15 10am (KOBL 342)	Thesis Defenses Erik Knutsen (CU Boulder) PhD Thesis Defense
Tue, Mar. 19 12pm (Math 350)	Diversity Diversity Committee and Math for All (CU BOULDER) X The Diversity Committee and the Math For All Team are co-organizing a panel on the basics of academic job searches. Whether you are applying for jobs soon or in a few years, we think this information will be helpful. After the panelists share some words of wisdom on certain topics we will have a Q&A session. The panelists and their topics are: Agnès Beaudry (Research Statement Basics). Lee Roberson (Teaching Statement Basics and Teaching Portfolios). Alonso Delfín Ares de Parga (Tips on Searching for a Research-Focused Postdoc position). Rebekah Jones (Tips on Searching for a Teaching-Focused Postdoc position). Academic Job Panel
Tue, Mar. 19 2:30pm (MATH 3…	Lie Theory Dana Ernst (Northern Arizona University) X In this talk, we will discuss the architecture of braid graphs in simply-laced Coxeter systems. It turns out that every reduced expression has a unique factorization as a product of so-called links, which in turn induces a decomposition of the braid graph into a box product of the braid graphs for each link factor. When the Coxeter graph has no three-cycles, each braid graph is a median graph (i.e., for every triple of vertices, there is a unique vertex, called the median, that belongs to shortest paths between each pair). One consequence of this result is that every braid graph can be isometrically embedded into a hypercube. For a special class of reduced expressions, called Fibonacci links, we show that the corresponding braid graphs are Fibonacci cubes. Braid graphs in simply-laced triangle-free Coxeter systems are median Sponsored by the Meyer Fund
Tue, Mar. 19 3:30pm (MATH 3…	Topology Andrew Doumont X We introduce Symplectic Manifolds and some of their fundamental techniques of study with the goal of proving Gromov's Non-squeezing Theorem. Sympletic Topology
Wed, Mar. 20 3:30pm (MATH 3…	Math Phys Robert Maier (University of Arizona and CU Boulder) View Online:https://cuboulder.zoom.us/j/94002553301 (Passcode: 790356) X Single-boson creation and annihilation operators satisfy a canonical commutation relation and generate the Weyl algebra. It is also generated by the noncommuting operators x and D (the derivative with respect to x), acting on any suitable space of functions. An ordering identity in this algebra can be viewed as an element of a two-sided ideal in the free associative algebra generated by x and D. An example of an identity is the one that rewrites a word (a specified product of x's and D's) as a linear combination of normally ordered words: ones in which D's appear to the right of x's. In the relatively easy `single annihilator' case, the coefficients are Stirling numbers, with a combinatorial interpretation. But ordering identities can be far more complicated. We introduce triangles of recursively defined generalized Stirling and Eulerian numbers, and ordering identities in which they appear as coefficients. Some of these number triangles are related by a `binomial transform' operation, but most have no known combinatorial interpretation. Combinatorial Identities in the Weyl Algebra
Thu, Mar. 21 11am (Zoom)	Algebra/Logic Mikhail V. Volkov (Ural Federal University) View Online:https://cuboulder.zoom.us/j/96896272260 X We exhibit several finite monoids each of which is not contained in any variety generated by a finitely based finite semigroup but is contained in a finitely based locally finite variety. The smallest monoid with these properties we found so far has as few as 9 elements. The result solves a 20+ years old problem and has numerous implications for the finite basis problem for finite semigroups. This is joint work with Sergey Gusev (Ekaterinburg, Russia) and Olga Sapir (Beersheba, Israel). Strongly nonfinitely based monoids
Thu, Mar. 21 2pm (Online)	Rep Theory Matthew Rupert (University of Saskatchewan) View Online:https://cuboulder.zoom.us/j/97927772782 X Quantum vertex algebras are deformations of vertex algebras introduced by Etingof and Kazhdan in 1998. They are families of vertex operators with relations deformed by a solution of the quantum Yang-Baxter equation. There is also a dual notion of quantum vertex coalgebras which deform vertex coalgebras. In this talk I will explain how to construct two distinct structures of a quantum vertex coalgebra on the Yangian associated to any simple finite-dimensional complex Lie algebra, and how to induce quantum vertex algebra structures on the dual Yangian. This talk is based on ongoing work with Alex Weekes and Curtis Wendlandt. Constructing Quantum Vertex (Co)-Algebras associated to Yangians
Thu, Mar. 28 2pm (Online)	Rep Theory David Ridout (University of Melbourne) View Online:https://cuboulder.zoom.us/j/97927772782 X Quantum hamiltonian reduction refers to a collection of functors that map the module category of a given affine vertex algebra to those of its associated W-algebras. Some of these functors are reasonably well understood and then the representation theory of the W-algebra is accessible. But some are not. Inverse quantum hamiltonian reduction is a recent discovery that there (sometimes) exist functors in the opposite direction: from a given W-algebra module category to that of another W-algebra, which may be the affine vertex algebra itself. I will give an overview of the simplest example, which connects the module categories of the Virasoro and sl2 minimal model vertex operator algebras. Inverse quantum hamiltonian reduction for beginners.

Main menu

Search

Other ways to search:

Events for November 2023 – March 2024

Probability

Grad Student Seminar

Algebraic Geometry

Rep Theory

Math Phys

Algebra/Logic

Lie Theory

Topology

Math Phys

Algebraic Geometry

Algebra/Logic

Lie Theory

Math Edu

Topology

Math Phys

Grad Student Seminar

Algebraic Geometry

Rep Theory

Kempner

Algebra/Logic

Topology

Grad Student Seminar

Algebraic Geometry

Rep Theory

Functional Analysis

Math Edu

Topology

Grad Student Seminar

Kempner

Algebra/Logic

Topology

Topology

Rep Theory

Kempner

Topology

Rep Theory

Functional Analysis

Algebra/Logic

Topology

Math Phys

Rep Theory

Probability

Math Edu

Topology

Math Phys

Rep Theory

Algebra/Logic

Topology

Grad Student Seminar

Math Phys

Rep Theory

Math Edu

Kempner

Algebra/Logic

Lie Theory

Topology

Grad Student Seminar

Math Phys

Rep Theory

Probability

Geometry/Analysis

Lie Theory

Topology

Math Phys

Rep Theory

Math Edu

Algebra/Logic

Lie Theory

Topology

Math Phys

Rep Theory

Grad Student Seminar

Thesis Defenses

Diversity

Lie Theory

Topology