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Events for May – September 2024

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May. 01, 2024 3:30pm (MATH 3…	Math Phys Howy Jordan (CU Boulder, Department of Mathematics) Infinite Dimensional Control Theory
May. 02, 2024 11:15am (MATH …	Algebraic Geometry Luca Schaffler (Universita Roma Tre) X Given the moduli space of hyperplanes in projective space, V. Alexeev constructed a family of compactifications parametrizing stable hyperplane arrangements with respect to given weights. In particular, there is a toric compactification that generalizes the Losev–Manin compactification for the moduli of points on the line. We study the first natural wall crossing that modifies this compactification into a non-toric one by varying the weights. In particular, we prove that in dimensions two the wall crossing corresponds to blowing up at the identity of the dense torus of the generalized Losev–Manin space. As an application, we show that any Q-factorialization of this blow-up is not a Mori dream space for a sufficiently high number of lines. This is joint work in progress with Patricio Gallardo. An explicit wall crossing for the moduli space of hyperplane arrangements Sponsored by the Meyer Fund
May. 02, 2024 12:15pm (Math …	Algebraic Geometry Farbod Shokrieh (University of Washington) X I will describe some connections between arithmetic of abelian varieties, non-archimedean/tropical geometry, and combinatorics. For example, we give formulas for (non-archimedean) canonical local heights in terms of tropical geometry. Our formulas extend classical computations of local height functions due to Néron (involving Néron models) and, in the case of elliptic curves, due to Tate (involving Bernoulli polynomials). Based on joint work with Robin de Jong. Canonical local heights and tropical theta functions Sponsored by the Simons Foundation
May. 02, 2024 3:35pm (MATH 3…	Probability Vishesh Jain (University of Illinois at Chicago) X Markov chains provide a natural approach to sample from various distributions on the independent sets of a graph. For the uniform distribution on independent sets of a given size $k$ in a graph, perhaps the most natural Markov chain is the so-called ``down-up walk''. The down-up walk, which essentially goes back to the foundational work of Metropolis, Rosenbluth, Rosenbluth, Teller and Teller on the Markov Chain Monte Carlo method, starts at an arbitrary independent set of size $k$ , and in every step, removes an element uniformly at random and adds a uniformly random legal choice. Davies and Perkins showed that there is a critical $k = α(Δ)n$ such that it is hard to (approximately) sample from the uniform distribution on independent sets for the class of graphs $G$ with $n$ vertices and maximum degree at most $Δ$ . They conjectured that for $k$ below this critical value, the down-up walk mixes in polynomial time. I will discuss a resolution of this conjecture, which additionally shows that the down-up walk mixes in (optimal) time $OΔ(nn)$ . Based on joint work with Marcus Michelen, Huy Tuan Pham, and Thuy-Duong Vuong. Optimal mixing of the down-up walk on fixed-size independent sets
May. 07, 2024 10am (MATH 350)	Lie Theory Lucas Gagnon (York University) X A long-standing conjecture of Stanley and Stembridge asks whether certain symmetric function invariants of graphs are “e-positive,” i.e. expand positively in the basis of elementary symmetric functions. Efforts to resolve Stanley—Stembridge have raised the wider question of whether other symmetric functions are e-positive, particularly for symmetric invariants of other interesting objects. This talk will describe an instance of e-positivity arising in the study of modules of the unipotent upper triangular groups over a finite field. I use a collection of novel module homomorphisms to prove e-positivity, and these maps implicate a well-known algorithm from the study of Iwahori—Hecke algebras. Throughout, I will connect these results to previously known connections between the unipotent upper triangular group and symmetric functions in non commuting variables. Positivity in unipotent symmetric function invariants and Hecke traces Sponsored by the Meyer Fund
May. 07, 2024 12:10pm (MATH …	Kempner Luis David Garcia Puente (Colorado College) X Let G be a finite, connected graph. An arithmetical structure on G is an assignment of positive integers to the vertices such that, at each vertex, its label divides the sum of the labels at adjacent vertices (counted w/ multiplicity). Arithmetical structures naturally generalize the notion of the Laplacian matrix of a graph. They also appear in the context of arithmetical geometry. In this talk, I will present a general introduction to the topic, we will focus on the combinatorics of arithmetical structures on certain graph families including some counting results that relate arithmetical structures on a path graph and Catalan numbers. We will also discuss some results about the associated finite Abelian group of an arithmetical structure. What is an arithmetical structure? Sponsored by the Meyer Fund
Jun. 27, 2024 5pm (MATH 220)	Probability Stanislav Volkov (Lund University) X I will present some generalizations of the one-dimensional forest fire model with ignition occurring only at zero, which was analyzed in particular by Volkov (2009). In more recent work, we allow the rates at which the trees grow to depend on their location, and the fire can spread using long-range connections. We establish that the expected time required for the fire to reach a site at a distance $x$ from the origin is at most of the order $log x)log 2 + o(1)$ . The talk is based on a recent joint paper with Mikhail Menshikov (Durham) and the late Francis Comets (Paris). Generalized one-dimensional forest fire model
Aug. 20, 2024 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
Aug. 20, 2024 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
Aug. 22, 2024 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
Aug. 29, 2024 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
Sep. 03, 2024 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)	Math Club 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

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