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Events for the weeks of November 9th – 21st

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Tue, Nov. 11 12:10pm (MATH …	Kempner Gregory Berkolaiko (Texas A&M) X Quantum chaos is the study of signatures of chaotic dynamics at the quantum level. The objects of study include the energy (eigenvalue) or wavefunction (eigenfunction) statistics. Nodal fluctuations belong to the second class; they express deviations of the number of zeros (or nodal domains) of the eigenfunction from its expected value. We will discuss the nodal fluctuations in a particular model, discrete Schroedinger operators on graphs. The conjecture is that the nodal fluctuations are always Gaussian, in the appropriate limit and after appropriate normalization. While the conjecture has been established in some classes of graphs, it is mostly wide open. We will review recent progress in this area which combines many different approaches: Morse Theory, Random Matrices, Spectral Graph Theory and Algebraic Geometry. Universality of nodal fluctuations: from quantum chaos to algebraic geometry
Tue, Nov. 11 1:25pm (online)	Algebra/Logic George Metcalfe (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X This talk will be about idempotent semifields, which, from a purely algebraic perspective are just lattice-ordered groups formulated in a restricted language with the group multiplication, neutral element, and lattice-join operation. We will see that although countably infinitely many equational theories of lattice-ordered groups have a finite equational basis, no non-trivial equational theory of idempotent semifields has this property. On the other hand, as in the case of lattice-ordered groups, there are continuum-many equational theories of classes of idempotent semifields. Finally, we will relate the problem of deciding equations in the class of idempotent semifields to the problem of deciding if there exists a right order on a free group satisfying a given finite set of inequalities, and show that these problems are, respectively, co-NP-complete and NP-complete. This is joint work with Simon Santschi. Equational Theories of Idempotent Semifields
Tue, Nov. 11 1:30pm (MATH 3…	Homotopy Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Tue, Nov. 11 1:30pm (MATH 3…	Topology Itamar Mor (University of Illinois Urbana-Champaign) X The lower central series is a classical device to deform a group into an abelian group, or in fact into a Lie algebra. In the 60s, Curtis and Rector used this to define a version of the unstable Adams spectral sequence. I'll describe a categorification of this construction in the spirit of synthetic spectra, which gives a way to deform a space into an animated Lie algebra. Many classical constructions in unstable homotopy theory may be deformed in this way: for example, I will discuss how this may be used to relate the EHP spectral sequence to Curtis' algebraic EHP spectral sequence, which can essentially be computed by machine. The synthetic EHP sequence
Tue, Nov. 11 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X We will describe the bounded width portion of the CSP dichotomy theorem. In particular, we will explain what bounded width CSPs are, and present the proof by Barto and Kozik that CSPs whose polymorphism algebras have WNUs for all but finitely many arities, have bounded width. Bounded width CSPs
Tue, Nov. 11 2:30pm (MATH 3…	Lie Theory Peter Brooksbank (Bucknell University) X Tensors have roughly as many definitions and notations as there are fields that use them. Nevertheless there is some broad agreement on the sort of information one might wish to extract from a tensor given by an array of numbers. One common goal is to change the ambient reference frame in order to reveal some internal structure. For instance, one might wish to know if, by a suitable change of basis, the nonzero entries of the array can be made to cluster in some prescribed manner. In this talk I will discuss clustering techniques whose origins lie in computational algebra and show they can be adapted to tensors that occur in the real world. The algorithms that result from this algebraic perspective have certain advantages—such as provable efficiency and reproducibility—and they can detect cluster patterns that elude existing methods. This is a report on joint work with Martin Kassabov and James Wilson. Clustering algorithms for tensors: an algebraic approach Sponsored by the Meyer Fund
Wed, Nov. 12 4:30pm (MATH 3…	Algebraic Geometry Zhijia Zhang (NYU) X Abstract: The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces. Broadly speaking, a G-variety is a variety X carrying an action of a group G. The group can act via automorphisms of X or via Galois actions if the base field is non-closed. There are close connections, as well as drastic differences between these two types of actions from the perspective of birational geometry. In this talk, I will explore these similarities and differences with a focus on equivariant unirationality of (not only) Fano threefolds. This is joint work with Yuri Tschinkel and Ivan Cheltsov. Title: Equivariant unirationality of Fano threefolds - Note the unusual time and date Sponsored by the Meyer Fund
Thu, Nov. 13 3:35pm (MATH 3…	Grad Student Seminar Jon Kim (CU Boulder) X A moduli space is a parameter space where each point represents some mathematical object. For algebraic geometers, these objects are usually geometric, and moduli spaces help us see how these geometric objects deform and detect their "stability". In this GSS talk, I will give a short survey on the development of moduli spaces in algebraic geometry and provide examples on constructing these moduli spaces. The main result will be showcasing how the moduli space of acute triangles is closely related to the moduli space of elliptic curves. What even is a moduli space?
Tue, Nov. 18 1:25pm (MATH 2…	Algebra/Logic Simon Santschi (University Bern) View Online:https://cuboulder.zoom.us/j/96896272260 X Lattice-ordered pregroups (l-pregroups) are exactly the involutive residuated lattices where addition and multiplication coincide. Among them, for every positive integer n, the n-periodic l-pregroup F_n(Z) of n-periodic order-preserving functions on the integers plays an important role in understanding distributive l-pregroups and also n-periodic ones. We give a finite axiomatization of the variety generated by F_n(Z). On the way we also obtain some more general results about periodic l-pregroups and we characterize the finitely subdirectly irreducibles of the variety generated by F_n(Z). Joint work with Nick Galatos. Axiomatizing small varieties of periodic l-pregroups
Tue, Nov. 18 2:30pm (MATH 2…	Grad Algebra/Logic Khizar Pasha (CU Boulder) X Continuation of last week's talk. Bounded width CSPs, 2
Tue, Nov. 18 2:30pm (MATH 3…	Lie Theory Mandi Schaeffer-Fry (DU) X The McKay Conjecture (now a theorem due to Cabanes--Späth) says that there is a bijection between irreducible characters of a finite group G with degree not divisible by p and the corresponding set for the normalizer of a Sylow p-subgroup. Several Galois refinements of this Conjecture exist, positing that the bijection should be compatible with fields of values. I'll discuss joint work with Lucas Ruhstorfer, in which we complete the proof of the original of these Galois refinements, proposed by Isaacs--Navarro in 2002. I'll also discuss several consequences, giving additional local-global properties in the character theory of finite groups. The Isaacs--Navarro Galois Conjecture
Tue, Nov. 18 3:30pm (MATH 3…	Topology Rick TBD
Wed, Nov. 19 4:40pm (MATH 3…	Grad Student Seminar Basia Klos (CU Boulder) X Does that question keep you up at night? If yes, you're in luck - in this talk, we'll define these algebraic objects, which are ubiquitous in the representation theory of infinite-dimensional Lie algebras and also appear in number theory and physics. We'll give a friendly example of a VOA and might even mention why you should care. What even is a vertex operator algebra?
Thu, Nov. 20 11:15am (MATH …	Algebraic Geometry Jon Kim X In 2024, Schock constructed several KSBA compactifications of the moduli space of cubic surfaces. More precisely, he considered pairs consisting of a cubic surface and a boundary divisor given by the sum of the 27 lines, all with the same weight value in the interval (1/9, 1] and provided a finite wall-and-chamber decomposition and described the weighted stable pairs parameterized by the moduli spaces in each chamber. In this talk, I will describe recent work where I provide a similar finite wall-and-chamber decomposition for KSBA compactifications where we weight one “heavy” line with weight b, and the other 26 lines uniformly with weight c. Moduli of (b,c)-weighted stable marked cubic surfaces
Thu, Nov. 20 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X Orbit-breaking in topological dynamical systems was introduced by Ian Putnam in his study of the C-algebras associated to Cantor minimal systems. By breaking an orbit at a single point, Putnam was able to construct all simple unital AF algebras as subalgebras by way of a Cantor minimal system. Since then, orbit-breaking algebras have been used to construct dynamical models for many stably finite “classifiable” C-algebras, most notably the Jiang–Su algebra. In this talk I will highlight these results and also discuss recent work-in-progress with Robin Deeley and Ian Putnam, where we generalize orbit-breaking for a homeomorphism to the setting of a continuous, surjective, local homeomorphism, allowing for purely infinite constructions. Orbit breaking and C*-algebras Sponsored by the National Science Foundation

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