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Events for the weeks of April 14th – 26th

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Tue, Apr. 16 1:25pm (MATH 2…	Algebra/Logic Piotr Kawalek (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X In 1999, Goldmann and Russell initiated a systematic study of algorithmic complexity of equation satisfiability problems in finite groups. In this talk we present some of the most important historical results on the topic as well as some of the very recent progress. We also consider closely connected problems of satisfiability and equivalence of circuits in finite algebras from congruence modular varieties. Some of the most general results in this area were obtained through relating functions computable by short polynomials in these algebras with classes of bounded-depth modular circuits. We discuss these types of connections, which turn out to be especially useful in tractability proofs. Complexity of Satisfiability and Equivalence Problems in Finite Algebras Sponsored by the Meyer Fund
Tue, Apr. 16 3:30pm (MATH 3…	Topology Ralph Kaufmann (Purdue-University) View Online:https://cuboulder.zoom.us/j/94002553301 X We review the setup of topological invariants as they appear in physics in the interpretation of K-theory. The basic Z-valued invariant can be identified with the first Chern-class. This goes back to the TKNN integers appearing in the quantum Hall effect. More subtle invariants appear in the setting of symmetries. These can be identified as coming from Real K-theory (KR) theory and its shifted cousin, quaternionic K-theory (KQ). We will give a gentle introduction and present the mathematical and condensed matter classification. This is joint work with D. Li and E.B Kaufmann Topological Insulators and K-theory Sponsored by the Meyer Fund
Wed, Apr. 17 3:30pm (MATH 3…	Math Phys Birgit Kaufmann (Purdue-University) View Online:https://cuboulder.zoom.us/j/94002553301 X Starting from a periodic system, one can by means of Bloch theory or discretisation form an effective geometry. In the standard case, this is a bundle over the Brillouin torus, whose sections are the states. More generally, one can consider families of Hamiltonians parameterized over a base. Such geometries can be thought of as classical or C* geometries. In the latter form, they appear via quiver representations. We will present the background and tools for the analysis of these geometries. This is joint work with R. Kaufmann and S. Khlebnikov Effective geometries and their local and global invariants. Sponsored by the Meyer Fund
Thu, Apr. 18 2pm (Online)	Rep Theory Mamoru Ueda (University of Alberta) View Online:https://cuboulder.zoom.us/j/97927772782 X Creutzig-Diaconescu-Ma conjectured that there exists a homomorphism from the shifted affine Yangian to the universal enveloping algebra of an iterated W-algebra. They also conjectured that this homomorphism will induce a resolution of the generalized AGT conjecture. In this talk, I will explain how to construct a homomorphism from the affine Yangian of type A to the universal enveloping algebra of a W-algebra including the non-rectangular W-algebra. I expect that this homomorphism can be extended to the shifted affine Yangian. Affine Yangians and W-algebras
Thu, Apr. 18 3:35pm (MATH 3…	Probability Andrew Campbell (ISTA) X A universality of local eigenvalue statistics of Hermitian random matrices has been the subject of immense investigation over the past couple decades resulting in the now well established principle that local eigenvalue statistics are determined only by the symmetry class of the matrix (i.e. real symmetric vs complex Hermitian) and the shape of the local eigenvalue density. For example, generically at the edge of the spectrum the eigenvalue density of random matrices exhibits square-root decay, leading to the local eigenvalue statistics falling into the famous Tracy--Widom universality class. For non-Hermitian matrices substantially less is known, with full universality in the bulk and at the edge for a random matrix X with centered independent identically distributed entries (or IID matrix) established only quite recently. While this is quite a substantial accomplishment, it is nowhere near the generality available for Hermitian matrices. In this talk we will consider the edge statistics of a deformed IID matrix A+X, where A is some deterministic deformation of the IID matrix X. By using matrices with Gaussian entries as a middle step for comparison we will see that this model has implications for many important non-Hermitian random matrix models. This is based on joint work with Giorgio Cipolloni, Laszlo Erdos, and Hong Chang Ji. At the edge of deformed non-Hermitian matrices.
Fri, Apr. 19 2:30pm (MATH 3…	Geometry/Analysis Leandro Lichtenfelz (Wake Forest University) X The Euler equations of hydrodynamics, which model ideal fluid flows on some region $M$ , admit a beautiful description as geodesic equations on the group of volume-preserving diffeomorphisms of $M$ , as first shown by V. Arnold. A major difficulty in studying the geometry of this group is the fact that it is infinite-dimensional, so a natural idea is to try to approximate it in some sense by a finite-dimensional model. One such model was constructed by Zeitlin, based on a quantization scheme developed earlier by Hoppe. In this talk, I will give an overview of Zeitlin's model, and then describe some aspects related to its geometry, in particular conjugate points. This is joint work with Stephen Preston and Alice Le Brigant. Conjugate points on Lie groups and Zeitlin's model of hydrodynamics Sponsored by the Meyer Fund
Tue, Apr. 23 12pm (MATH 350)	Topology Topology Day : Kyle Ormsby (Reed College) X Model structures underpin the modern enterprise of abstract homotopy theory and provide a convenient framework in which we can pass from one notion of sameness (isomorphism) to a weaker one (weak equivalence). Despite their fundamental nature, model structures have historically been studied en masse or applied in specific cases, and very little is known about the totality of model structures on a given category. Homotopical combinatorics is an emerging field that remedies this situation by studying the enumerative combinatorics and structural properties of model structures on finite lattices. Specialized to a finite chain, we find rich connections with Catalan combinatorics, including (intervals in) the Tamari and Kreweras lattices. I will introduce the audience to model structures and sketch homotopical combinatorics as it currently stands, including the surprising assist its development received from equivariant infinite loop space theory. Counting model structures Sponsored by the Meyer Fund
Tue, Apr. 23 1pm (MATH 220)	Probability David Renfrew (Binghamton University) X We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this singularity depends on the relative positions of the zero submatrices. We provide a classification of all possible singularities and determine the exponent in the density blow-up. Singularities in the spectrum of random block matrices
Tue, Apr. 23 1:25pm (online)	Algebra/Logic Paolo Marimon (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X We classify the operations which are minimal above the clone generated by a permutation group G acting on a set. Rosenberg (1986) showed that when G is trivial there are only five types of minimal operations. We show that for most permutation groups there are only three types of minimal operations. More generally, we carry such classification for any permutation group and specify the behaviour of the minimal operations on tuples with two or more elements in the same orbit. Our results are especially helpful for the study of constraint satisfaction problems on omega-categorical structures, where we improve and generalise results of Bodirsky and Chen (2007), and answer some questions of Bodirsky (2021). This is joint work with Michael Pinsker. Minimal operations over permutation groups
Tue, Apr. 23 2:30pm (MATH 3…	Lie Theory Thomas Creutzig (University of Alberta) X An affine Lie algebra is a central extension of the loop algebra of a finite dimensional Lie algebra. Certain modules, the vacuum modules at any complex level k, of the affine Lie algebra carry themselves an interesting algebraic structure, namely that of a vertex operator algebra (VOA). The representation theory of affine VOAs is rather rich, e.g. suitable categories of modules form ribbon categories and there are exciting connections to geometry, quantum groups, physics and much more. I want to give an overview on the state of the art of this area. Representation Theory of Affine VOAs Sponsored by the Meyer Fund
Tue, Apr. 23 3:30pm (MATH 3…	Topology Topology Day: Ping Xu (Penn State) X Dg manifolds are a useful geometric notion which unifies many important structures such as homotopy Lie algebras, foliations and complex manifolds. In this talk, we describe a Duflo-Kontsevich type theorem for dg manifolds. The Duflo theorem of Lie theory and the Kontsevich theorem regarding the Hoschschild cohomology of complex manifolds can both be derived as special cases of this Duflo--Kontsevich type theorem for dg manifolds. This is a joint work with Hsuan-Yi Liao and Mathieu Stienon. Duflo-Kontsevich type theorem for dg manifolds
Wed, Apr. 24 3:30pm (MATH 3…	Math Phys Howy Jordan (CU Boulder, Department of Mathematics) Infinite Dimensional Control Theory
Thu, Apr. 25 11:15am (MATH …	Algebraic Geometry Daniel Bragg (Utah) TBD Sponsored by the Meyer Fund
Thu, Apr. 25 12:20pm (Math …	Noncomm Geometry Dmitry Kaledin (Steklov Math Institute) X It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement". Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view. I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator". How to enhance categories, and why Sponsored by the Meyer Fund
Thu, Apr. 25 12:20pm (MATH …	Algebraic Geometry Dmitry Kaledin (Steklov Math Institute) X It has become accepted wisdom by now that when you localize a category with respect to a class of morphisms, what you get is not just a category but a category "with a homotopical enhancement". Typically, the latter is made precise through the machinery of "infinity-categories", or "quasicategories", but this is quite heavy technically and not really optimal from the conceptual point of view. I am going to sketch an alternative technique based on Grothendieck's idea of a "derivator". How to enhance categories, and why (Cross listed with Non-commutative Geometry) Sponsored by the Meyer Fund

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