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Events for August – December

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Tue, Aug. 20 3pm (MATH 350)	Topology Sabrina Pauli (TU Darmstadt) X Enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions. A famous problem in this area is counting plane rational curves of degree d passing through 3d-1 given points. Tropical geometry has been a powerful tool in tackling enumerative geometry problems, notably marked by Mikhalkin's correspondence theorem. This theorem translates the count of plane curves into the count of their tropical counterparts, for which there are elegant solutions using only combinatorics. Results from A1-homotopy theory allow to ask questions in enumerative geometry over arbitrary base fields, not just algebraically closed ones, and still get meaningful answers, leading to a new area called A1-enumerative geometry. In the talk I will give an introduction to A1-enumerative geometry and explain how tropical geometry can be used to solve problems in this area. Tropical methods in A1-enumerative geometry Sponsored by the Meyer Fund
Tue, Aug. 20 3pm (MATH 350)	Algebraic Geometry Sabrina Pauli (TU Darmstadt) X Enumerative geometry is the branch of algebraic geometry concerned with counting numbers of solutions to geometric questions. A famous problem in this area is counting plane rational curves of degree d passing through 3d-1 given points. Tropical geometry has been a powerful tool in tackling enumerative geometry problems, notably marked by Mikhalkin's correspondence theorem. This theorem translates the count of plane curves into the count of their tropical counterparts, for which there are elegant solutions using only combinatorics. Results from A1-homotopy theory allow to ask questions in enumerative geometry over arbitrary base fields, not just algebraically closed ones, and still get meaningful answers, leading to a new area called A1-enumerative geometry. In the talk I will give an introduction to A1-enumerative geometry and explain how tropical geometry can be used to solve problems in this area. Tropical methods in A1-enumerative geometry
Thu, Aug. 22 2:30pm (MATH 2…	Functional Analysis Tomasz Maszczyk (University of Warsaw) X Under the technical condition of separability of some topological space of cohomology, we show that the Godbillon-Vey number of a foliation of codimension one on a compact orientable 3-fold is topologically rigid if and only if the foliation admits a projective transversal structure. Here by the rigidity of the Godbillon-Vey number we mean that it is constant under the infinitesimal singular deformations of the foliation, and a foliation admits a transversal projective structure whenever it can be glued from the level sets of locally defined functions related by fractional linear transition maps. Title: Foliations with rigid Godbillon-Vey class
Thu, Aug. 29 2:30pm (Math 3…	Functional Analysis PIOTR M. HAJAC (IMPAN, Warsaw, Poland) X In 2006, Katsura discovered optimal conditions for morphisms of topological graphs to contravariantly induce morphisms between their C-algebras. We use these morphisms in the special case of discrete topology (usual directed graphs) to extend the well studied theory of unions of graphs to one-injective pushouts of graphs. Our main result is a pushout-to-pullback theorem that yields a one-surjective gauge equivariant pullback of graphs C-algebras, which suits the Mayer-Vietoris six-term exact sequence in K-theory and applications to noncommutative topology. To exemplify our theorem, first we vastly generalize the old concept of a derived graph to obtain locally derived graphs. Then we use locally derived graphs, which provide us with a very rich class of non-injective graph homomorphisms satisfying Katsura's conditions, to construct pushouts satisfying the assumptions of our pushout-to-pullback theorem. (Based on joint work with Mariusz Tobolski.) LOCALLY DERIVED GRAPHS AND GAUGE EQUIVARIANT PULLBACKS OF GRAPH C*-ALGEBRAS
Tue, Sep. 3 3:30pm (MATH 3…	Topology All Organizational Meeting
Wed, Sep. 4 4:45pm (MATH 3…	Grad Student Seminar Nicholas Christoffersen (CU Boulder) X In this introductory talk, we'll aim to understand how C*-algebras and probability theory come together to form free probability, and explain how it describes certain classes of random matrices in the large-dimension limit. Note that this talk will contain free probability, free groups, and free pizza. An Introduction to Free Probability
Thu, Sep. 5 11:15am (MATH …	Algebraic Geometry Algebraic geometry group X The algebraic geometry group will talk a bit about their research. Algebraic geometry open house
Thu, Sep. 5 2:30pm (MATH 3…	Functional Analysis Andrzej Sitarz (Jagiellonian University, Poland) X I will review the construction of spectral functionals for finitely summable spectral triples, which in the classical, commutative case, provide metric, Einstein and torsion tensors. Further, I will discuss examples of these functionals over several well-known spectral triples, including spin manifolds, Hodge-de Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and the quantum SU(2) group. Based on a series of joint papers with Ludwik Dabrowski and Pawel Zalecki. Spectral Functionals
Tue, Sep. 10 1:25pm (MATH 2…	Algebra/Logic Keith Kearnes (CU) View Online:https://cuboulder.zoom.us/j/96896272260 X My goal will be to explain why a locally finite variety V has the property that its finitely generated projective algebras are free if and only if (1) the finite, nontrivial members of V are E-minimal and (2) if V has a pseudoconstant term, then V also has a constant term. Locally finite varieties whose finitely generated projectives are free
Tue, Sep. 10 2:30pm (MATH 3…	Lie Theory faculty organizers X We give an introduction to the faculty of the seminar and their research areas. ALT seminar open house
Tue, Sep. 10 3:30pm (MATH 3…	Topology Faculty Open House
Wed, Sep. 11 3:30pm (Math350)	Math Phys Gregory Berkolaiko (Texas A&M University) X The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises in diverse areas of mathematical physics. Among the particular motivations for this talk are the Floquet-Bloch decomposition of the Schrödinger operator on a periodic structure, nodal count statistics of eigenfunctions of quantum graphs, conical points in potential energy surfaces in quantum chemistry and the minimal spectral partitions of domains. In each of these problems one seeks to identify and/or count the critical points of the eigenvalue with a given label (say, the third lowest) over the parameter space which is often known and simple, such as a torus. Classical Morse theory is a set of tools connecting the number of critical points of a smooth function on a manifold to the topological invariants of this manifold. However, the eigenvalues are not smooth due to presence of eigenvalue multiplicities or ``diabolical points''. We rectify this problem for eigenvalues of generic families of finite-dimensional operators. The ``diabolical contribution'' to the ``Morse indices'' of the problematic points turns out to be universal: it depends only on the multiplicity and the relative position of the eigenvalue of interest and not on the particulars of the operator family. Using tools such as Clarke subdifferential and stratified Morse theory of Goresky--MacPherson, we express the ``diabolical contribution'' in terms of homology of Grassmannians of ppropriate dimensions. Based on a joint work with Igor Zelenko (TAMU). Berkolaiko, G., Zelenko, I. Morse inequalities for ordered eigenvalues of generic self-adjoint families. Invent. math. (2024). Morse theory for eigenvalues of self-adjoint families
Wed, Sep. 11 4:45pm (MATH 3…	Grad Student Seminar Daniel Lyness (CU Boulder) X Poincaré Duality is an extremely powerful tool in Geometry and Topology. In this talk, I will briefly introduce Singular, De Rham and Dolbeault Cohomology and explore the theorems relating these different theories. The I will give and compare the appropriate duality statement in each case. Hopefully there will be time at the end to do some calculations and see these results in action! This talk will be most suited to those with some familiarity with singular homology/cohomology and differential forms, but I intend to present the material in such a way that everyone can get something out of it! Cohomology, Duality and Eduroam
Thu, Sep. 12 11:15am (MATH …	Algebraic Geometry Adrian Neff X Given a nodal genus one curve and a proper subcurve of genus one, we will construct a contraction that collapses the subcurve to a genus one singularity. We will do this by first introducing residues for curves over local artinian rings and "twists" of these residues by tropical data from the curve, then we will use these residues to explicitly construct the contraction. Residues and contractions of genus one curves
Thu, Sep. 12 12:30pm (MATH …	Kempner Dr. Pamela E. Harris (University of Wisconsin-Milwaukee) X What is mathematical research? How does a mathematician find problems to work on? How does one build mathematical collaborations? In this talk, I will share my journey to research mathematics, what it entails, how I have developed new research ideas, and how I have found my place within the mathematical community. Mathematical topics of discussion will include lattice point visibility, parking functions, and a connection between vector partition functions and juggling. No prior mathematical background on these topics is expected nor assumed as we will introduce all the needed concepts from first principles. All that is needed is the willingness to wonder and ask the question: “what happens if…? How to choose your own mathematical adventures
Thu, Sep. 12 2:30pm (MATH 3…	Functional Analysis Robin Deeley (CU Boulder) X I will introduce some of the basic ideas involved in the Baum-Connes conjecture. Also, this will be an organizational meeting where we plan the other talks on this subject. We will be following https://arxiv.org/abs/1703.10912. The Baum-Connes conjecture
Thu, Sep. 12 3:35pm (MATH 3…	Probability Janos, Kyle & Sean (CU Boulder) X Janos, Kyle and Sean will talk about their current research and what it's like to work in the probability group. The talks will be informal and there will be plenty of time for questions. Probability Open House
Tue, Sep. 17 1:25pm (MATH 2…	Algebra/Logic Nik Ruskuc (University of St Andrews) View Online:https://cuboulder.zoom.us/j/96896272260 X The height of a (finite) lattice L is the size of a maximum chain in L. Cameron, Solomon and Turull (1989) showed that the height of the subgroup lattice of the symmetric group S_n is given by \lceil 3n/2 \rceil - b(n), where b(n) is the number of 1s in the binary expansion of n. The analogue of S_n for semigroups is the full transformation semigroup T_n. Cameron, Gadoleau, Mitchell and Perese (2017) established an accurate asymptotic formula for the height of the subsemigroup lattice of T_n. But the subgroup lattice of a group G can be viewed from a different angle: it is (isomorphic to) the lattice of right (or left) congruences of G.(And one-sided congruences of a monoid are in a 1-1 correspondence with cyclic transformation representations of S.) In this talk I will introduce a general method which gives a lower bound for the height of the lattices of one- or two-sided congruences of an arbitrary semigroup, and under certain additional conditions gives the exact values. I will apply this theory to obtain the height for the lattices of right and left congruences of T_n, as well as for many other natural semigroups of transformations, partitions and matrices. This is joint work with Matthew Brookes, James East, Craig Miller and James Mitchell. Heights of congruence lattices of semigroups Sponsored by the Meyer Fund
Tue, Sep. 17 2:30pm (MATH 3…	Lie Theory Spencer Daugherty (CU) X The quasisymmetric functions, QSym, are generalized for a finite alphabet A by the colored quasisymmetric functions, QSym_A, in partially commutative variables. Their dual, NSym_A, generalizes the noncommutative symmetric functions, NSym, through a relationship with Hopf algebras of trees. We define a new pair of dual bases that generalize the immaculate and dual immaculate bases of QSym and NSym. We use tableaux combinatorics and creation operators in their definitions, and we also present results on the Hopf algebra structure, skew functions, and multiplication rules. We then define a new Hopf algebra Sym_A, contained within QSym_A, that is isomorphic to the symmetric functions, Sym, when A is an alphabet of size one. Its graded dual, PSym_A, is the commutative image of NSym_A and also generalizes Sym. In addition to defining generalizations of the classic bases of the symmetric functions to Sym_A and PSym_A, we describe multiplication, comultiplication, and the antipode in terms of a basis for both algebras. Colored Schur-like bases and generalizations of the symmetric functions
Tue, Sep. 17 3:30pm (MATH 3…	Topology Taylor Rogers X Chromatic homotopy theory studies the stable homotopy category (in particular, the stable homotopy groups of spheres) by means of the chromatic filtration. This filtration reveals global structure in the stable homotopy category that would be difficult to see otherwise. In this first talk, we will discuss some motivation for this filtration and introduce some tools necessary for its description and systematic study. An Introduction to Chromatic Homotopy Theory I
Wed, Sep. 18 3:30pm (Math350)	Math Phys Andrew Waldron (University of California at Davis) X In this talk we will explain why contact geometry is in some sense an optimal description of classical mechanics. Then we will explain how to quantize both strict and regular contact structures. Time permitting we will also discuss classical measurement theory for models defined on supermanifolds. Contact Geometry, Quantization and Super Measurement Theory Sponsored by the Meyer Fund
Wed, Sep. 18 5pm (Math 350)	MathClub Rebekah Jones X We'll talk about the physical and mathematical principles that enable soap bubbles and soap films to exist in certain geometric configurations and not in others. We'll also talk about some of the areas of math that grew from the study of these problems, in particular, calculus of variations and geometric measure theory. The Geometry of Soap Bubbles
Thu, Sep. 19 11:15am (MATH …	Algebraic Geometry Jonathan Wise TBA
Thu, Sep. 19 2:30pm (MATH 3…	Functional Analysis Frederic Latremoliere (Denver University) X ABSTRACT: The spectral propinquity is a distance over the class of metric spectral triples, up to unitary equivalence. It is constructed as a special form of the propinquity between compact quantum metric spaces, itself rooted in the work on the Gromov-Hausdorff distance and its noncommutative analogues, in the more general framework of Rieffel's work in noncommutative metric geometry. In this talk, we wish to present the spectral propinquity and discuss various properties and examples of convergence in the sense of this metric: for instance, we will discuss how the spectrum of Dirac operators is continuous with respect to the spectral propinquity, and how various spectral triples on quantum tori, quantum solenoids, and Bunce-Deddens algebras are limits of other spectral triples. The spectral propinquity
Thu, Sep. 19 3:35pm (MATH 3…	Probability Mei Yin (University of Denver) X We give a survey into parking functions, concentrating in particular on the probabilistic and combinatorial aspects. Joint work with multiple collaborators: Irfan Durmi\'{c}, Alex Han, Pamela E. Harris, Rodrigo Ribeiro; Richard Stanley; Stephan Wagner. Parking functions: probabilistic and combinatorial
Thu, Sep. 19 4:45pm (MATH 3…	Grad Student Seminar Ezzeddine El Sai (CU Boulder) X The Yang–Mills existence and mass gap problem is one of the Millennium Prize problems and a central problem in mathematical physics. In this talk, we will discuss the statement of the problem and unravel what it means. We will also discuss connections with geometry, analysis, and probability. The Yang–Mills existence and mass gap
Tue, Sep. 24 11am (MATH 350)	Number Theory Travis Morrison (Virginia Tech) X Computing the endomorphism ring of a supersingular elliptic curve is the central hard problem in isogeny-based cryptography. In this talk, we will present an algorithm for computing inseparable endomorphisms of a given supersingular elliptic curve. The algorithm requires low storage and is easy to parallelize, and conditional on the Generalized Riemann Hypothesis, terminates in O~(p^(1/2)) bit operations, matching the time complexity of generic algorithms. Unlike generic algorithms, the algorithm produces endomorphisms which generate quadratic orders with predictable discriminants; this allows us to prove arithmetic properties (such as being Gorenstein or Bass) of the quaternionic orders generated by endomorphisms produced by our algorithm. Let P denote the 2-sided ideal of inseparable endomorphisms of a supersingular elliptic curve E in characteristic p. Then our algorithm outputs endomorphisms contained in P. We prove that two calls to our algorithm for computing inseparable endomorphisms produces a generating set for a Bass suborder of the endomorphism ring. I'll discuss a heuristic argument that the expected number of calls required to produce a generating set for Z+P, the unique index p suborder of index p in End(E), is bounded by a constant, independent of p. This is joint work with Fuselier, Iezzi, Kozek, and Namoijam and began at the first Rethinking Number Theory workshop. Computing supersingular endomorphism rings using inseparable endomorphisms
Tue, Sep. 24 1:10pm (MATH 3…	Kempner Travis Morrison (Virginia Tech) X A useful feature of elliptic curve cryptography is the ability to "hash into" the set of public keys: a user can easily compute a uniformly random public key in a way so that no one (not even the user!) knows the corresponding private key. It is not known whether isogeny-based cryptography enjoys this functionality. In isogeny-based cryptosystems, a private key is an isogeny from a fixed public supersingular elliptic curve, and the corresponding public key is the codomain of that isogeny, another supersingular elliptic curve. Public keys can be thought of as vertices in the supersingular isogeny graph, and private keys are random walks (beginning at the fixed public curve) in that graph. Whether one can "hash into" the supersingular isogeny graph is an open question: there is no known method for quickly computing a random supersingular elliptic curve that does not also provide, as a byproduct, enough information to easily find a path from that curve to the fixed public base curve. This byproduct is the ring of endomorphisms of the supersingular elliptic curve: there is no known efficient algorithm for computing the endomorphism ring, and computing endomorphism rings is exactly as hard as path-finding in isogeny graphs. There are isogeny-based cryptosystems that can only be securely instantiated given a single supersingular elliptic curve with unknown endomorphism ring - a supersingular curve you can trust. In this talk, I will discuss a practical, distributed protocol for computing a supersingular elliptic curve with unknown endomorphism ring. The main ingredient in this protocol is another protocol, a proof of knowledge, that proves knowledge of a secret isogeny. We show this proof of knowledge is statistically zero-knowledge (the protocol does not reveal anything other than the fact that the prover knows the secret information). To prove that our proof of knowledge is statistically zero-knowledge, we introduce isogeny graphs with level structure and prove that these graphs are Ramanujan graphs: random walks mix as rapidly as possible. In this talk, I will discuss isogeny-based cryptography at a high level and explain our distributed protocol and proof of knowledge. I will then explain why the Ramanujan-Peterrson conjecture implies that our isogeny graphs with level structure have the Ramanujan property, and hence why our proof of knowledge is statistically zero-knowledge. This is based on joint work with Basso, Codogni, Connolly, De Feo, Fouotsa, Lido, Panny, Patranabis, and Wesolowski. (NOTE SPECIAL TIME) Supersingular curves you can trust
Tue, Sep. 24 1:25pm (Math 2…	Algebra/Logic Charlotte Aten (CU Boulder) View Online:https://cuboulder.zoom.us/j/96896272260 X I first met Walter Taylor in 2018 at the Algebras and Lattices in Hawai'i conference. He presented his result from the previous year that there exist 2-dimensional simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice. He also asked whether similar examples exist for higher-dimensional simplicial complexes. I will present an n-dimensional analogue of Taylor's book-spaces and show that they are similarly topologically modular-but-not-distributive. There will be pictures. Higher-dimensional book-spaces
Tue, Sep. 24 2:30pm (MATH 3…	Lie Theory Juan Villarreal (CU) X This talk is for general audience. We will start with some basics definitions and results of finite dimensional Lie algebras. Then we will extend these results to infinite dimensions finding an amazing! relation with the theory of modular forms. Finally, if time permits, I will mention some modern results relating finite and infinite dimensional algebras with symplectic singularities. These relations are very interesting! "Symplectic singularities are the Lie algebras of the 21st century" (A. Okounkov) Representation theory of infinite dimensional Lie algebras
Tue, Sep. 24 3:30pm (MATH 3…	Topology Agnès Beaudry X This talk is a continuation of last week's talk. We will discuss the spectrum of the stable homotopy category, introducing the Morava K-theories K(n), the role of v_n self-maps and other central localizations of this category. An Introduction to Chromatic Homotopy Theory II
Wed, Sep. 25 3:30pm (Math350)	Math Phys Amanda Young (University of Illinois) X We discuss the bulk gap for a truncated 1/3-filled Haldane pseudopotential for the fractional quantum Hall effect in the cylinder geometry. In the case of open boundary conditions, a lower bound on the spectral gap (which is uniform in the volume and particle number) accurately reflects the presence of edge states, which do not persist into the bulk. A uniform lower bound for the Hamiltonian with periodic boundary conditions is also obtained. Both of these bounds are proved by identifying invariant subspaces to which spectral gap and ground state energy estimating methods originally developed for quantum spin Hamiltonians are applied. Customizing the gap technique to the invariant subspace, however, we are able to avoid the edge states and establish a more precise estimate on the bulk gap in the case of periodic boundary conditions. The same approach can also be applied to prove a bulk gap for the analogously truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. This is based off joint work with S. Warzel. A bulk gap in the presence of edge states for a truncated Haldane pseudopotential Sponsored by the Meyer Fund
Wed, Sep. 25 4:45pm (MATH 3…	Grad Student Seminar Alex LaJeunesse (CU Boulder) X Modern algebraic topology is largely centered around the field of stable homotopy theory. In this field we study spectra, which are sort of like chain complexes of spaces. I plan to motivate spectra via generalized cohomology theories, and then explore the analogy between stable homotopy theory and homological algebra as deeply as time will allow. Brave New Algebra
Thu, Sep. 26 11:15am (Math …	Algebraic Geometry Dawei Chen (Boston College) X Multiscale differentials arise as limits of holomorphic differentials with prescribed orders of zeros on nodal curves. In this talk, I will explain a beautiful conjecture, initially proposed by Ranganathan—Wise and further elaborated upon by Battistella—Bozlee, which concerns contraction of multiscale differentials to Gorenstein singularities level by level. Differentials and Singularities Sponsored by the Simons Foundation
Thu, Sep. 26 2:30pm (MATH 3…	Functional Analysis Alonso Delfín (CU Boulder) An introduction to Hilbert C*-modules
Fri, Sep. 27 10am (Math 350)	Math Edu Rebekah Jones X We will discuss potential topics, speakers and modality for the Seminar on Undergraduate Math Education this semester. All those interested in attending SUME are welcome. SUME Open House
Fri, Sep. 27 2:30pm (MATH 2…	Grad Algebra/Logic Faculty X The foundations group will talk about its research. Foundations open house
Tue, Oct. 1 1:15pm (MATH 3…	Geometry/Analysis Ian Miller (University of Colorado Boulder) X We consider focusing nonlinear Schr\"odinger equations, which are mass supercritical and energy subcritical. For these equations, given initial data which has mass and energy below ground state initial data, a classification between blow up and global existence is known. However for initial data above the ground state, behavior is only known for special cases. In this talk we discuss the impact of angular momentum on long time behavior of solutions and introduce some new global and blow up solutions. New global and blowup solutions for nonlinear Schrodinger equations above the ground state
Tue, Oct. 1 2:30pm (MATH 3…	Lie Theory Richard Green (CU) X A root system for a simply laced finite Weyl group is a discrete collection of vectors in Euclidean space on which the group acts transitively. In some cases, the set of maximal sets of orthogonal positive roots has the structure of a graded partially ordered set, known as a quasiparabolic set. The talk will describe the rich combinatorial structure of these partially ordered sets. This is joint work with Tianyuan Xu (University of Richmond). Quasiparabolic sets and orthogonal bases of roots
Tue, Oct. 1 3:30pm (MATH 3…	Topology Sylvia Maher X An infinity category is a category equipped with some notion of homotopy, allowing us to transport parts of classical homotopy theory to a more abstract setting. In this talk I will introduce infinity categories through the language of simplicial sets and give an overview of some of the basic definitions and constructions that arise when studying infinity categories. An Introduction to Infinity Categories
Wed, Oct. 2 3:30pm (Math350)	Math Phys Howy Jordan (CU Boulder) X Algebraic Quantum Field Theories are formulated by giving axioms on a C*-algebra valued cosheaf on the open subsets of Minkowski space. This dependence on an a priori specified spacetime is the subject of debate. Here we begin investigations into one possibility for removing this dependence. The fundamental idea is to attempt to derive a spatial locale equivalent to the open sets on Minkowski space from families of observables. In this talk, we outline the basic structures and describe some initial steps towards realizing this program. Towards Spatiality of the Spacetime Locale
Wed, Oct. 2 4:45pm (MATH 3…	Grad Student Seminar Mateo Muro (CU Boulder) X Pending Mal'cev Algebras are the only Algebras
Thu, Oct. 3 11:15am (MATH …	Algebraic Geometry Jon Kim X We will showcase the classification of algebraic surfaces by Kodaira dimension followed by an introduction to the minimal model program using surfaces as a guiding example. Classification of Algebraic Surfaces and the Minimal Model Program
Thu, Oct. 3 2pm (Online)	Rep Theory Gaywalee Yamskulna (llinois State University) View Online:https://cuboulder.zoom.us/j/97927772782 X In this talk, I will explore the algebraic properties of an $ℕ$ -graded vertex algebra associated with Gorenstein rings. Through this framework, I will demonstrate how these vertex algebras offer a natural bridge to the shifted theory of vertex algebras of the CFT type. On the algebraic structure of $N$-Graded Vertex Algebras $V=\oplus_{n=0}^{\infty}V_n$ when $V_0$ is a Gorenstein ring and Their Relation to vertex algebras of CFT-Type.
Thu, Oct. 3 2:30pm (MATH 3…	Functional Analysis Darwin Tallana (CU Boulder) Unbounded operators and the Dirac operator on the circle
Fri, Oct. 4 2:30pm (MATH 2…	Grad Algebra/Logic Charlotte Aten X Commutator Theory was generalized from groups to general algebras in the 1980s and quickly became one of the main tools for structure theory of algebras. This Fall we'll work through the book Commutator Theory by Freese and McKenzie. This talk is an introduction to the basic objects of general algebra. Algebras, lattices, varieties
Mon, Oct. 7 4:45pm (MATH 2…	Grad Student Seminar Colin Jackson (CU Boulder) X In this talk, we will see how far we can take the question in the title. We will start with some simpler results, and move on to the prime number theorem, discussing error terms and conjectures, and continue this to primes in arithmetic progression. To finish, we will immerse ourselves in everyone’s favorite sporting event, prime number races. How many prime numbers are there really?
Tue, Oct. 8 12pm (online)	Algebra/Logic Sebastian Meyer (TU Dresden, Germany) View Online:https://cuboulder.zoom.us/j/96896272260 X We want to study the class of all finite structures together with the preorder given by primitive positive constructions as it plays an important role in the theory of constraint satisfaction problems. It is also equivalent to the homomorphism poset of the polymorphism minion of the structure, which is the right generalization of endomorphism monoid/ring in this context. It turns out that the first two layers of this order consist of a single equivalence class each, while the third layer consists of infinitely many points, represented by the transitive tournament on three vertices and structures in one-to-one correspondence with all finite simple groups. Finite simple groups in the primitive positive constructability poset
Tue, Oct. 8 2:30pm (Math 3…	Lie Theory John McHugh (University of Denver) X The "extended tensor product" is a relatively new operation in the representation theory of finite groups which generalizes both the familiar tensor product of representations over the ground field as well as the tensor product of bimodules. It was introduced in 2008 by Serge Bouc and studied extensively by Robert Boltje and Philipp Perepelitsky in the early part of this decade. I will attempt to motivate and explain the definition of the extended tensor product. If I am successful I will go on to discuss new results in the theory of modular representations of finite groups that are proved using the extended tensor product construction. The material will be presented in the most elementary ways possible: a potential audience member should only know what a finite group is and what an action of a finite group on a finite set looks like. The Extended Tensor Product Sponsored by the Meyer Fund
Tue, Oct. 8 3:30pm (MATH 3…	Topology Courtney Hauf X Born of Grothendieck’s brain, K-theory started as a way to discuss isomorphism classes of objects that live above some object of interest (in his case, vector bundles over algebraic manifolds). Today, K-theory can be an ambiguous term due to the various attempts to construct (higher) K-theory. In this talk we will look at the history of K-theory, discussing the motivations that led to its many variations and ways that K-theory has been used in various areas of mathematics (and physics!). [Will not require background.] Algebraic K-Theory I: Where did we come from? Where did we go?
Wed, Oct. 9 3:30pm (Math350)	Math Phys Rebecah Deans (CU Boulder) Introduction to Spencer Cohomology
Thu, Oct. 10 11:15am (MATH …	Algebraic Geometry Jon Kim X We will continue the talk from last week starting by classifying algebraic surfaces via Kodaira dimension. Classification of Algebraic Surfaces and the Minimal Model Program II
Thu, Oct. 10 2pm (Online)	Rep Theory Harshit Yadav (University of Alberta) View Online:https://cuboulder.zoom.us/j/97927772782 Rigidity of vertex tensor categories.
Thu, Oct. 10 2:30pm (MATH 3…	Functional Analysis Levi Lorenzo (CU Boulder) K-theory for C*-algebras
Fri, Oct. 11 2:30pm (MATH 2…	Grad Algebra/Logic Mateo Muro X We present the characterization of congruence modular varieties with Day terms. Congruence modular varieties
Mon, Oct. 14 4:45pm (MATH 3…	Grad Student Seminar Jon Kim (CU Boulder) X A cubic surface is defined to be a surface that is defined as a vanishing set of cubic polynomials. In 1849, Cayley and Salmon showed that there are exactly 27 lines on a smooth cubic surface. Through the introduction of new tools in algebraic geometry in the 20th century, a more streamlined proof has been made. Namely, by introducing linear systems and blow-ups, this talk will showcase how we can get these 27 lines. Linear Systems, Blow-ups, and Cubic Surfaces
Tue, Oct. 15 1:25pm (online)	Algebra/Logic Roman Fellner (TU Wien, Austria) View Online:https://cuboulder.zoom.us/j/96896272260 X Given a finite set of oriented graphs F, the F-free orientation problem is the following decision problem. Given a finite input graph, is there an orientation of its edges such that the resulting directed graph omits every member of F. If the set F consists of tournaments (i.e. complete oriented graphs), Bodirsky and Guzmán-Pro have recently established that this computational problem exhibits a complexity dichotomy: it is either solvable in polynomial time or NP-complete. I will explain how the F-free orientation problem can be viewed as the constraint satisfaction problem (CSP) of an omega-categorical template, making it amenable to universal algebraic methods. In particular I will demonstrate how the recently developed technique of "smooth approximations", provides a shorter algebraic proof of the complexity dichotomy for the graph orientation problem. Graph orientation problems with forbidden tournaments
Tue, Oct. 15 3:30pm (MATH 3…	Topology Courtney Hauf X After decades of development, we reached a construction of algebraic K-theory that checked all the boxes: Waldhausen’s S-construction. Extending this construction to oo-categories, we can (nicely) discuss the algebraic K-theory of (ring) spectra, spaces, and more. In this talk we will see the S-construction applied to oo-categories and discuss some of the ways we can utilize algebraic K-theory of oo-categories. [Will volley off the ideas Sylvia presented for oo-categories.] Algebraic K-Theory II: Where are we now?
Wed, Oct. 16 3:30pm (Math350)	Math Phys Tomoyuki Arakawa (RIMS, Kyoto) X Symplectic singularities, introduced by Beauville, appear in various aspects of representation theory. Additionally, symplectic singularities arise in the context of quantum field theory, particularly in the Higgs and Coulomb branches of three-dimensional theories, as well as in the Higgs branches of four-dimensional theories. Furthermore, the 4D/2D duality proposed by Beem et al. identifies vertex algebras as invariants for superconformal four-dimensional theories. It has been suggested that the Higgs branch of four-dimensional theories can be reconstructed as the associated variety of vertex algebras. As a result, all vertex algebras arising from four-dimensional theories are believed to be chiral quantizations of symplectic singularities. In this lecture, we will discuss such vertex algebras and their representation theory. Symplectic singularities and vertex algebras
Wed, Oct. 16 3:30pm (MATH 3…	Lie Theory Tomoyuki Arakawa (Research Institute for Mathematical Sciences, Kyoto University) X Symplectic singularities, introduced by Beauville, appear in various aspects of representation theory. Additionally, symplectic singularities arise in the context of quantum field theory, particularly in the Higgs and Coulomb branches of three-dimensional theories, as well as in the Higgs branches of four-dimensional theories. Furthermore, the 4D/2D duality proposed by Beem et al. identifies vertex algebras as invariants for superconformal four-dimensional theories. It has been suggested that the Higgs branch of four-dimensional theories can be reconstructed as the associated variety of vertex algebras. As a result, all vertex algebras arising from four-dimensional theories are believed to be chiral quantizations of symplectic singularities. In this lecture, we will discuss such vertex algebras and their representation theory. Symplectic singularities and vertex algebras Sponsored by the Meyer Fund
Thu, Oct. 17 11:15am (MATH …	Algebraic Geometry Jon Kim X We continue the talk from last week starting with Mori's cone theorem. Introduction to the Minimal Model Program III
Thu, Oct. 17 2:30pm (MATH 3…	Functional Analysis James Woodcock (CU Boulder) KK-theory part 1
Fri, Oct. 18 10:10am (MATH …	Math Edu Christopher Mellott (CU Boulder's Office of Student Conduct & Conflict Resolution) X A presentation on CU's Honor Code and Student Code of Conduct. The presenters will describe the resolution process after an honor code violation is submitted and talk about the most common types of honor code violations, with time for questions at the end. Honor Code Training Workshop
Fri, Oct. 18 2:30pm (MATH 2…	Grad Algebra/Logic Nick Jamesson X We introduce commutators for general algebras. Commutators
Fri, Oct. 18 4pm (MATH 220)	Geometry/Analysis Siddhant Agrawal (University of Colorado Boulder) X We consider the 2D incompressible Euler equation on a bounded simply connected domain. We give sufficient conditions on the domain so that for all bounded initial vorticity, the weak solutions are unique. Our sufficient conditions allow us to prove uniqueness for a large subclass of $C1,α$ domains and convex domains. Previously uniqueness for general bounded initial vorticity was only known for $C1,1$ domains with possibly a finite number of acute angled corners. The fundamental barrier to proving uniqueness below the $C1,1$ regularity is the fact that for less regular domains, the velocity near the boundary is no longer log-Lipschitz. We overcome this barrier by defining a new change of variable which we then use to define a novel energy functional. This is joint work with Andrea Nahmod. Uniqueness of the 2D Euler equation on rough domains
Tue, Oct. 22 12:10pm (MATH …	Kempner Daniel Martin (PhD '20) (Clemson) X “Lattice problems” drew significant interest from cryptographers in the late 90s. The belief was (and still is) that they offer an easy way to encrypt information that comes with a hard-to-hack guarantee. The popularity of lattice problems continued to rise in subsequent decades, and today they are the darlings of so-called post-quantum cryptography. This talk will show you what the fuss is all about. We will explore how lattice-based encryption works, what advantages it has over other systems, and how it invites the algebraic number theorist to the world of cryptography. No prior understanding of cryptography or number theory is necessary. Lattices and number theory in modern cryptography
Tue, Oct. 22 1pm (MATH 350)	Number Theory Colby Brown (UC Davis) X The Markoff graphs modulo p were proven by Chen (2024) to be connected for all but finitely many primes, and Baragar (1991) conjectured that they are connected for all primes, equivalently that every solution to the Markoff equation modulo p lifts to a solution over Z. In this talk, we provide an algorithmic realization of the process introduced by Bourgain, Gamburd, and Sarnak to test whether the Markoff graph modulo p is connected for arbitrary primes. Our algorithm runs in o(p^(1+epsilon)) time for every epsilon > 0. We demonstrate this algorithm by confirming that the Markoff graph modulo p is connected for all primes less than one million. Finally, we discuss other approaches to decomposing the Markoff graph, with possible applications to determining its spectral properties. Navigating the Markoff graph computationally
Tue, Oct. 22 1:25pm (Online)	Algebra/Logic Dylene Agda Souza de Barros (Universidade Federal de Uberlandia, Brasil) View Online:https://cuboulder.zoom.us/j/96896272260 X The notion of half-homomorphism between two groups is trivial, but it is an interesting subject when we drop the associativity law. In this talk, we will discuss some properties of half-homomorphism between two loops, paying special attention to some Bol loops and code loops. On half-homomorphisms of some types of Loops
Tue, Oct. 22 2:30pm (MATH 3…	Lie Theory UhiRinn Suh (Seoul National University) X Classical W-algebras, which are reductions of enveloping algebra of affine Lie algebras, have been studied in connection with Hamiltonian integrable equations. By quantization method of Hamiltonian reduction called BRST cohomology, one can get (quantum) W-algebras which are algebraic structures in Toda field theories. Moreover, conjecturally, W-algebras can be embedded in supersymmetric field theories by considering supersymmetric W-algebras obtained by supersymmetric analogue of BRST. In this talk, I will try to avoid technical details but explain basic ideas of the constructions of classical/quantum W-algebras and supersymmetric W-algebras. For last 10 mins, I will also introduce recent results related to supersymmetric W-algebras. Supersymmetry in W-algebras theory Sponsored by the Meyer Fund
Tue, Oct. 22 3:30pm (MATH 3…	Topology Alexander LaJeunesse X Over the past two weeks we have followed the development of algebraic K-theory as a tool in homotopy theory, from Quillen's original definition for ordinary rings to the modern perspective in terms of infinity-categories. In this talk we will survey a number of tools that have been developed to compute algebraic K-theory, in particular topological Hochschild homology and topological cyclic homology in the case of ring spectra. Along the way, we will aim to connect each of these tools to the recent computations of K(Z/p^n) by Antieau-Krause-Nikolaus. Computations in Algebraic K-Theory
Wed, Oct. 23 3:30pm (Math350)	Math Phys Ezzeddine El Sai (CU Boulder) The mass gap problem in Yang-Mills theory
Wed, Oct. 23 4:45pm (MATH 3…	Grad Student Seminar Matt Watson (CU Boulder) X A moduli space is a geometric space whose points parametrize some collection of geometric spaces. It is a classic result that we can construct a moduli space for 1-dimensional complex tori as the quotient $H/SL(2,Z)$ . We will review this construction and discuss how to repackage it in the language of cohomology. Equipped with this new way of viewing the moduli of complex tori, we will give a rough outline of how one might be able to use Hodge theory to construct a moduli space in some more general situations. To aid in your understanding, donuts will be provided. The Moduli Space of Complex Tori: or How I Learned to Stop Worrying and Love Hodge Theory
Thu, Oct. 24 11:15am (MATH …	Algebraic Geometry Jon Kim X We will finish explaining the minimal model program for surfaces and introduce minimal models of higher dimensional varieties. In particular, we will discuss how singularities can arise when contracting external rays in higher dimensions and how we should expand our category of minimal models to account for these singularities. Introduction to the Minimal Model Program IV (Final part)
Thu, Oct. 24 2pm (Online)	Rep Theory Lea Beneish (University of North Texas) View Online:https://cuboulder.zoom.us/j/97927772782 X We ascertain properties of the algebraic structures in towers of codes, lattices, and vertex operator algebras (VOAs) by studying the associated subobjects fixed by lifts of code automorphisms. In the case of sublattices fixed by subgroups of code automorphisms, we identify replicable functions that occur as quotients of the associated theta functions by suitable eta products. We show that these lattice theta quotients can produce replicable functions not associated to any individual automorphisms. Moreover, we show that the structure of the fixed subcode can induce certain replicable lattice theta quotients and we provide a general code theoretic characterization of order doubling for lifts of code automorphisms to the lattice-VOA. Finally, we prove results on the decompositions of characters of fixed subVOAs. This talk is based on joint work with Jennifer Berg, Eva Goedhart, Hussain M. Kadhem, Allechar Serrano López, and Stephanie Treneer. Replicable functions arising from code-lattice VOAs fixed by automorphisms
Thu, Oct. 24 2:30pm (Zoom)	Functional Analysis A. Sitarz (Moved to Zoom) (Jagiellonian University, Poland) View Online:https://cuboulder.zoom.us/j/92986030547 Meeting ID: 929 8603 0547 X Carla Farsi is inviting you to a scheduled Zoom meeting. Join Zoom Meeting https://cuboulder.zoom.us/j/92986030547 Meeting ID: 929 8603 0547 Starting from the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. An example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus gives all connections compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori is found, which arise from the base-space Dirac operator and a suitable connection. Based on a joint work with Ludwik Dabrowski. Noncommutative circle bundles and new Dirac operators
Fri, Oct. 25 2:30pm (Math 3…	Diversity Adriana Salerno (Bates College) X In this talk, I will show you a glimpse of one of the most exciting facets of research in modern number theory: arithmetic geometry. We will start with a (gentle) introduction to this area of research through some familiar examples. Then we will move on to a not so familiar example where we count solutions of equations mod p. I will end by answering two of the oldest and most mystifying questions in mathematics: how does this work fit into the bigger picture, and who cares? A circular tale: an introduction to arithmetic geometry
Mon, Oct. 28 4:45pm (MATH 3…	Grad Student Seminar Sylvia Maher (CU Boulder) X What do the trace of a matrix, the cycle type of a permutation, and the Euler characteristic of a CW complex have in common? In this talk I will investigate the key categorical properties of the trace of a matrix and show how we can generalize this idea to talk about 'traces' in other contexts. The universal property of the trace
Tue, Oct. 29 1:25pm (Online)	Algebra/Logic Matt Evans (Washington & Jefferson College) View Online:https://cuboulder.zoom.us/j/96896272260 X Introduced in the 1960's, BCK-algebras are the algebraic semantics of BCK-logic. Like with many algebraic structures, there is a natural way to associate a topological space to a BCK-algebra; we call this space the spectrum. In this talk I'll recall what is known about spectra of commutative BCK-algebras before asking: what happens when we drop the assumption of commutativity? The discussion will close with a conjecture about spectra of finite BCK-algebras. On spectra of BCK-algebras
Tue, Oct. 29 2:30pm (MATH 3…	Lie Theory Jen Gensler (CU) X Supercharacter theory is a construction that condenses the representation theory of an algebraic structure, hopefully without losing too much information about its representation theory while gaining combinatorial data. Nonnesting supercharacter theory considers the normal supercharacter theory of normal subgroups of UT_n associated to nonnesting set partitions or, equivalently, Dyck paths. In this talk I will define supercharacter theory and work through a motivating example leading into a discussion of results on the nonnesting supercharacter theory of UT_n. Nonnesting Supercharacter Theory
Tue, Oct. 29 3:30pm (MATH 3…	Topology Yang Hu (New Mexico State University) X The orthogonal/unitary calculus of Weiss is a framework of studying functors from vector spaces to topological spaces. Each such functor has an associated Taylor tower — a tower of fibrations whose layers are infinite loop spaces. When applied to the functor BO(-) or BU(-), Weiss calculus provides a "custom-made" resolution for the classifying spaces, allowing for the program of enumerating unstable vector bundles with stable calculations. In this talk, we present old and new enumeration results along this program and discuss, if time allows, an equivariant version of the story. This talk contains joint work with Hood Chatham and Morgan Opie, and work in progress with Prasit Bhattacharya. Bundle-counting with calculus
Thu, Oct. 31 11:15am (MATH …	Algebraic Geometry Sebastian Casalania-Martin TBA
Thu, Oct. 31 2pm (Online)	Rep Theory Justine Fasquel (University of Melbourne) View Online:https://cuboulder.zoom.us/j/97927772782 X W-algebras are vertex algebras obtained form quantum Hamiltonian reductions of an affine vertex algebra. These reductions are naturally upgraded to functors from the category of modules over the affine vertex algebras to the category of the modules over the corresponding W-algebras. However, they are difficult to control in general. Recently, two approaches have been developed to improve our understanding of the functors. One consists in spitting the functor into small pieces that are easier to deal with (partial reductions), the other aims to reverse the quantum Hamiltonian reduction procedure (inverse Hamiltonian reductions). In this talk, I will discuss about recent advances in these complementary approaches. The talk is based on recent papers with T. Creutzig, A. Linshaw and S. Nakatsuka and with Z. Fehily, E. Fursman and S. Nakatsuka Partial and inverse Hamiltonian reductions for W-algebras
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

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