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Events for November 2024 – March 2025

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Thu, Mar. 13 5pm	Functional Analysis Jordan Watts (University of Central Michigan) TBA
Fri, Nov. 1 10:10am (Math …	Math Edu Justin Barhite X We will explore two alternatives to traditional percentage-based grading schemes: standards-based grading and specifications-based grading. Both aim to provide clear measures of student progress that are more directly tied to learning objectives, and to give students ample opportunity to revise work in response to feedback. We will discuss the benefits and trade-offs of each approach, as well as some practical tips based on the experiences of several instructors implementing these methods in a wide variety of courses at the University of Kentucky. Alternative Grading
Fri, Nov. 1 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson X We discuss properties of commutators for algebras in congruence modular varieties. The commutator in congruence modular varieties
Tue, Nov. 5 1:25pm (online)	Algebra/Logic Gergo Gyenizse (University of Szeged, Hungary) View Online:https://cuboulder.zoom.us/j/96896272260 X A variety is Hobby-McKenzie if it satisfies an idempotent Mal’tsev condition that fails in semilattices. Such varieties form a Mal’tsev class which resembles that of Taylor varieties: the idempotent condition can be chosen to be a set of linear identities in two variables. For locally finite varieties, this class contains precisely the varieties omitting TCT types 1 and 5. In this talk, we provide a characterization of general (not necessarily locally finite or idempotent) Hobby-McKenzie varieties based on their compatible 3-ary relations. As a consequence, we prove that these varieties form a prime filter in the interpretability lattice of varieties. We also propose a nice characterization that depends instead on the compatible digraphs of the variety, but which is only proven to be correct in the locally finite case. Joint work with B. Bodor, M. Maróti and L. Zádori On general Hobby-McKenzie varieties
Tue, Nov. 5 3:30pm (MATH 3…	Topology Taylor Rogers X This semester we have introduced chromatic homotopy theory and the modern formulation of algebraic K-theory. In this talk, we will discuss chromatic redshift, a recently proven result that describes a way in which chromatic homotopy theory and algebraic K-theory interact. This interaction is an important ingredient in the recent disproof of the longstanding telescope conjecture. Chromatic Redshift
Thu, Nov. 7 3:35pm (MATH 3…	Probability Curtis Grant (Northwestern) X Metastability is a phenomenon widely believed to hold for Markov chains associated with spin glass models. Roughly, for a complex energy landscape, one should have a decomposition into wells, and the corresponding dynamics tracking which well the original Markov chain is in should be asymptotically Markovian. We will provide an overview of known results for spin glass dynamics, and then explain recent results with Reza Gheissari on metastability for heavy-tailed spin glasses. Metastability in Heavy Tailed Spin Glass Dynamics
Fri, Nov. 8 2:30pm (MATH 2…	Grad Algebra/Logic Peter Mayr X We discuss properties of commutators in congruence modular varieties. Basic properties of commutators
Tue, Nov. 12 11am (MATH 350)	Number Theory Number Theorists (CU) X The faculty from the number theory group will each give a brief overview of what we do for research. Open House
Tue, Nov. 12 1:25pm (Math 3…	Geometry/Analysis Gregory Berkolaiko (Texas A&M) X In this overview talk we will explore a variational approach to the problem of Spectral Minimal Partitions (SMPs). The problem is to partition a domain or a manifold into k subdomains so that the first Dirichlet eigenvalue on each subdomain is as small as possible. We expand the problem to consider Spectral Critical Partitions (partitions where the max of the Dirichlet eigenvalues is experiencing a critical point) and show that a locally minimal bipartite partition is automatically globally minimal. Extensions of this result to non-bipartite partitions, as well as its connections to counting nodal domains of the eigenfunctions and to a two-sided Dirichlet-to-Neumann map defined on the partition boundaries, will also be discussed. The talk is based on joint papers with Yaiza Canzani, Graham Cox, Bernard Helffer, Peter Kuchment, Jeremy Marzuola, Uzy Smilansky and Mikael Sundqvist. Spectral minimal partitions: local vs global minimality
Tue, Nov. 12 1:25pm (online)	Algebra/Logic Paolo Marimon (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a theorem of Rosenberg says that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen. Building on these results, we answer some questions of Bodirsky related to infinite-domain constraint satisfaction problems (CSPs). This is joint work with Michael Pinsker. Minimal operations over permutation groups
Tue, Nov. 12 3:30pm (Online)	Topology Thomas Brazelton (Harvard University) View Online:https://cuboulder.zoom.us/j/93758128989 X Moved to online https://cuboulder.zoom.us/j/93758128989 In this talk we'll touch on how an Euler class valued in equivariant homotopical bordism can reveal conserved symmetries in the solutions to equivariant enumerative problems. We apply this idea in joint work with C. Bethea to compute bitangents to symmetric plane quartics where we will see that homotopical techniques directly reveal patterns which are not obvious from a classical moduli perspective. We will also discuss ongoing work with S. Raman, in which we initiate a study of Galois groups of symmetric enumerative problems, leveraging tools from Hodge theory and computational numerical analysis. Equivariant enumerative geometry
Thu, Nov. 14 11:15am (MATH …	Algebraic Geometry Jonathan Wise TBA
Thu, Nov. 14 2:30pm (MATH 3…	Functional Analysis Karen Strung (Institute of Mathematics of the Czech Academy of Sciences) X One of the most dramatic recent advances in operator algebras is the classification of separable, unital, simple, nuclear C-algebras which are Jiang–Su stable and satisfy the UCT. With this abstract classification theorem in hand, we are left with questions about which ”naturally occurring” C-algebras are covered by the theorem. By “naturally occurring” I mean operator algebraic models of various mathematical structures. These have long played an important role, as they allow one to use a well-stocked toolkit consisting of both algebraic and analytic equipment to study such various mathematical objects. An example of this is the relationship between topological dynamical systems and C-algebras. In this talk I will discuss examples of classifiable C-algebras given by various constructions arising from topological dynamical systems. Classifiable C*-algebras from topological dynamics Sponsored by the Simons Foundation
Fri, Nov. 15 10:10am (Math …	Math Edu Maggie Reardon and Emily Montelius X Student skills are a vital component of teaching first-year courses. Focusing on developing skills which make it easier to succeed in the university setting will benefit students in your classroom and beyond. In this talk we will present easy to implement methods to help students learn skills for preparing for class, engaging during class, reviewing recent material, and synthesizing semester long concepts. Additionally, we will discuss how to identify students struggling in these areas and how to implement interventions. Incorporating student skills in your classroom
Fri, Nov. 15 2:30pm (MATH 2…	Grad Algebra/Logic Peter Mayr X We characterize abelian algebras in congruence modular varieties. Abelian algebras
Tue, Nov. 19 1:25pm (online)	Algebra/Logic Max Hadek (Charles University Prague) View Online:https://cuboulder.zoom.us/j/96896272260 X An algebra is called minimal Taylor if its clone satisfies a non-trivial minor condition, but no proper subclone does so. Recently, Barto, Brady, Bulatov, Kozik and Zhuk initiated the systematic study of minimal Taylor algebras, intending to build a unified theory to understand the complexity of constraint satisfaction problems. They conjecture that every minimal Taylor algebra is finitely related, which we disprove by giving a counterexample. This result can be interpreted as follows: there is an infinite sequence of tractable finite domain CSPs, such that every CSP harder than all problems in the sequence, is already NP-complete. A non-finitely related minimal Taylor algebra
Tue, Nov. 19 2:30pm (Math 3…	Lie Theory Spencer Daugherty (CU Boulder) X The q,t-Catalan numbers can be described elegantly in terms of pairs of statistics on Dyck paths: area and bounce, or area and dinv. Mahonian permutation statistics, such as coinversion, disorder, and the sorting index, are some of the most thoroughly studied statistics on permutations. Using bijective methods, we prove new expressions of the q,t-Catalan numbers over subsets of permutations in terms of at least one Mahonian statistic. In the process, we develop new Catalan subsets of permutations, new bijections from Dyck paths to these subsets, and new permutation statistics. Mahonian Statistics and the q,t-Catalan Numbers
Tue, Nov. 19 3:30pm (MATH 3…	Topology Andrew Doumont X We will construct Lagrangian Floer homology. Time permitting, we will also discuss Fukaya categories and the homological mirror symmetry conjecture. Lagrangian Floer Homology
Wed, Nov. 20 1:30pm (MATH 3…	Kempner Rodrigo Ribeiro (Denver University) X Networks are everywhere, from social media platforms to intricate systems in nature. But how do we study and understand them? Different fields like computer science, math, and statistics offer their own tools and views. In this talk, we'll explore how these areas approach network analysis and how mathematicians formalize intuition and results from other areas. The talk will cover joint works with Rémy Sanchis (UFMG), Roberto I. Oliveira (IMPA) and Caio Alves (Oak Ridge National Lab). Interdisciplinary Perspectives on Network Analysis: A Confluence of Computer Science, Mathematics, and Statistics
Thu, Nov. 21 2pm (CSU)	Algebraic Geometry Carl Lian (Tufts Univerisity) X Let Gr(k,n) be the Grassmannian of k-planes in C^n. The standard torus action on C^n induces a torus action on Gr(k,n), whose orbits encode interesting combinatorial and geometric invariants. I will describe an explicit degeneration of the “generic” torus orbit closure into a union of Richardson varieties (intersections of two Schubert varieties). This gives a new proof of a formula of Berget-Fink for the Chow class of this subvariety of X, and the technique has further (but not yet fully realized) applications in enumerative geometry. The method also works for the variety of full flags in C^n, giving a new proof of an earlier result of Anderson-Tymoczko. Via the toric moment map, the combinatorial shadow of this degeneration is a polyhedral decomposition of the permutohedron due to Harada-Horiguchi-Masuda-Park. Time-permitting, I will mention some ongoing work with Grace Chen extending this story to type B. Degenerations of torus orbits
Tue, Dec. 3 1:15pm (Math 3…	Functional Analysis Peter Haskell (Virginia Tech University) View Online:Zoom link to follow X Jeff Fox and I met in 1983. We were intrigued by Kasparov's elegant and powerful bivariant K-theory, and we dared hope it would allow us to use Jeff's background in representation theory and mine in topology to prove cases of the Baum-Connes and Connes-Kasparov conjectures. The depth of the challenges posed by those conjectures was greater than we first imagined, but, largely due to Jeff's knowledge of representation theory, we did make a contribution to the area. We also proved some representation-multiplicity index theorems for transversally elliptic operators. These results illustrated K-theory's ability to extract representation-theoretic integer-valued invariants from group C*-algebras. Other work we did involved index theory for singular spaces, pushing inspiration from Riemann-Roch theorems in directions that involved enough analysis to suggest roles for spectral invariants. I learned much mathematics and much about how to do mathematics from Jeff. Working with him, I got to know one of the kindest, most generous people I have ever met. My collaboration with Jeff Fox: Mathematical and personal connections formed as products of Kasparov's bivariant K-theory
Tue, Dec. 3 3:30pm (MATH 3…	Topology Alexander LaJeunesse TBD
Wed, Dec. 4 3:30pm (Math350)	Math Phys Andrew Doumont (CU Boulder) Gromov-Witten Invariants
Thu, Dec. 5 11:15am (MATH …	Algebraic Geometry Daniel Lyness TBA
Thu, Dec. 5 2pm (Zoom)	Algebraic Geometry Nicola Tarasca (Virginia Commonwealth University) View Online:https://cuboulder.zoom.us/j/97927772782 TBA
Thu, Dec. 5 2pm (Online)	Rep Theory Nicola Tarasca (Virginia Commonwealth University) View Online:https://cuboulder.zoom.us/j/97927772782 TBA
Thu, Dec. 5 2:30pm (MATH 3…	Functional Analysis Levi Lorenzo and Maggie Reardon (CU Boulder) X There will be two 25-minute talks. Abstract (Levi Lorenzo): K-theory is the generalized cohomology theory that has proven incredibly effective at classifying C- algebras. In this talk, we discuss its dual homology theory, K-homology. K-homology and K-theory admit a bilinear pairing to the integers, called the index pairing, which allows one to learn about K-theory using K-homology and vice versa. In general, this pairing is very difficult to compute; however, if a Calgebra admits a dense subalgebra on which its K-homology is finitely summable, Connes has equipped us with a more computable formula. Given a smooth manifold, M, of dimension n, the K-homology of is finitely summable on for In this way, the summability also sees the dimension of the manifold. It is natural to ask whether similar results hold in the noncommutative setting. Towards this end, Connes showed that the irrational rotation algebras have uniformly summable K-homology. The irrational rotation algebras are examples of crossed product algebras arising from minimal actions on a topological space. In my work, I study other noncommutative algebras and ask the same question. For example, we make the space a Cantor Set and examine the K-homology of crossed products arising from minimal actions on it. In this talk, we discuss progress in such directions. Abstract (Maggie Reardon): Matui’s HK-conjecture proposes a relationship between the homology groups of a nice enough groupoid and the $K$ -theory of the associated reduced $C$ -algebra. The conjecture is not true in general and there are a number of counterexamples. However, the conjecture holds for certain classes of groupoids including AF groupoids. Putnam introduced a new class of groupoids in the paper titled “Some classifiable groupoid $C$ -algebras with prescribed $K$ -theory”. These new groupoids are related to AF groupoids and this prompts a natural question: does this new class of groupoids satisfy the HK-conjecture? Finitely Summable K-homology and the HK-conjecture for certain groupoids constructed by Putnam
Fri, Dec. 6 10:10am (MATH …	Math Edu Rebecca Machen DBER
Wed, Dec. 11 4:45pm (MATH 3…	Grad Student Seminar Howy Jordan (CU Boulder) X TBD Stratified Spaces
Thu, Dec. 12 11:15am (MATH …	Algebraic Geometry Matthew Watson TBA
Thu, Dec. 12 2pm (Online)	Rep Theory Michael Lau (Université Laval) View Online:https://cuboulder.zoom.us/j/97927772782 TBA
Tue, Feb. 18 12pm (MATH 350)	Algebraic Geometry Mihnea Popa (Harvard) X TBD TBD Sponsored by the Meyer Fund
Tue, Mar. 11 12:10pm (MATH …	Kempner Edmund Harriss (University of Arkansas) TBA
Thu, Mar. 20 2:30pm (MATH 3…	Functional Analysis Laura Scull (Fort Lewis College) TBA

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