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Events for September 2018 – January 2019

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Sep. 20, 2018 5pm (Math 350)	Carly Matson & Krisztina Dearborn X Brief overviews of suggested timelines for preparing for a career in academia or in industry will be given and a variety of resources will be shared. An informal Q&A about the hiring process in academia will be held with Dr. Robin Deeley. Timeline for preparing for a career while in graduate school
Oct. 18, 2018 5pm (Math 220)	Cat Wilson (Career Services) X Cat Wilson is the Graduate Student Career Development Advisor at Career Services. She will present on what kind of information to include on your CV or resume, what language to use, and how to use formatting to your advantage. Tea and snacks will be served. Academic CV vs Industry Resume: Tips for Both
Oct. 04, 2018 5pm (Math 350)	Krisztina Dearborn X Join us to practice introducing yourself at a career fair or your research elevator pitch in a stress-free, low-stakes environment. Then (if applicable) print off copies of your current resume, walk over to the Fall Technology Career Fair at the UMC (11am-4pm) with confidence, and put your practice to use. Career Fair Introductions and Research Elevator Pitches
Sep. 27, 2018 5pm (Math 350)	Cat Wilson, Carly Matson, & Krisztina Dearborn X Cat Wilson, Graduate Student Career Development Advisor from Career Services, will join us to briefly introduce herself. Afterwards, there will be an informal workshop on application materials (CV, resume, website, etc). Note: Cat will not stay for this part of the seminar. Use this time to seek feedback from peers. We will share tips, templates, and discuss any other relevant topics. Cat Wilson introduction and workshop on application materials
Sep. 04, 2018 10am (MATH 350)	Geometry/Analysis Chi Hin Chan (National Chiao Tung University, Taiwan) X In this talk, we will talk about a recent work, in which we establish the existence of a stationary linear-Stokes flow in an exterior domain of a hyperbolic plane. We assume the no-slip boundary condition and the finite Dirichlet norm condition. Thus, we give the antithesis of the Stokes paradox in the hyperbolic setting. We will indicate why our method also leads to a nontrivial Navier-Stokes flow in an exterior domain of the hyperbolic plane under the same condition. This is a joint work with Magdalena Czubak. About the antithesis of the Stokes Paradox on the hyperbolic plane Sponsored by the Meyer Fund
Sep. 04, 2018 11am (MATH 350)	Number Theory Hanson Smith (CU Boulder) X The talk will be concerned with motivating and presenting the following result: Consider an elliptic curve $E$ over a number field $K$ and let $𝔭$ be a prime of $𝒪_{K}$ lying above a prime $p$ of $ℤ$ . Suppose $E$ has supersingular reduction at $𝔭$ . Fix a positive integer $n$ and define $L$ to be a minimal extension of $K$ such that $E(L)$ has a point of exact order $p^{n}$ . If $𝔭$ is unramified over $p$ , then $L/K$ is an extension of degree $p2n-p2n-2$ that is totally ramified over $𝔭$ . If $𝔭$ is ramified over $p$ , then $(pn)$ still properly divides $L:Q]$ . Using the stronger bound, one can show that sporadic points on the modular curve $X1(pn)$ cannot correspond to elliptic curves that are supersingular at $𝔭$ with $𝔭$ unramified over $p$ . These methods generalize to $X1(N)$ with $N$ composite. Ramification in the Division Fields of Elliptic Curves and an Application to Sporadic Points on Modular Curves
Sep. 04, 2018 1pm (MATH 350)	Ulam D. Kaledin X Enhanced, or infty-categories are proving to be a useful working tool in many areas of homological algebra, but their definitions in current use are quite cumbersome and depend on hardcoded arbitrary choices. I will try to give a brief overview of the area, explain why it is indeed useful for real-life mathematics, and then present a somewhat more invariant approach to the subject based on Grothendieck's idea of a "derivator". On the notion of an enhanced category
Sep. 04, 2018 3pm (Math 350)	Algebraic Geometry David Holmes (University of Leiden) X It is well-known that the Abel-Jacobi map does not extend over the boundary of the moduli space of stable marked curves. We approach this problem by making (logarithmic) blowups of the moduli space, constructing a `universal’ resolution of the indeterminacies of the Abel-Jacobi map. After considering some elementary examples, we will show how to apply this construction to the problem of compactifying the double ramification cycle, and show that the resulting compactification is compatible with various conjectures and formulae in the literature. Extending the Abel-Jacobi map Sponsored by the Meyer Fund
Sep. 04, 2018 4pm (MATH 350)	Topology Markus Pflaum (CU Boulder) K-homology
Sep. 05, 2018 4:03pm (MATH 3…	Grad Student Seminar Lucas Gagnon (CU Boulder) X A $q$ -analog of a theorem or formula is a generalization involving a parameter $q$ so that $q → 1$ gives the original result. The $q$ -binomial coefficient, or Gaussian binomial coefficient is a well known example, generalizing a large number of the properties of binomial coefficients in surprising and interesting ways. We will motivate this analogy by briefly reviewing the properties of the binomial coefficient, and then define and discuss the $q$ -binomial, touching on topics relating to finite fields, non-commutative geometry, and lattice paths. Time permitting, the talk will end with a fun application of the $q$ -binomial coefficient to the game SET. q-Analogs and the q-Binomial
Sep. 11, 2018 1pm (MATH 350)	Ulam D. Kaledin X This is a continuation of my talk on Sep. 4. although it should be understandable by itself. I will give a precise derivator-style definition of an enhanced category and explain the main points of the theory. On the notion of an enhanced category, II
Sep. 11, 2018 1pm (MATH 220)	Peter Mayr X Constraint Satisfaction Problems (CSP) include a wide variety of classical decision problems, like satisfiability of Boolean formulas, colorability of graphs, solvability of systems of linear equations,... and real-life problems, like scheduling, database queries. The Dichotomy Conjecture by Feder & Vardi states that every CSP is either solvable in polynomial time or NP-complete. It has just been verified independently by Bulatov and by Zhuk using two different algebraic approaches. We give an introduction to CSP, the algebraic formulation of the Dichotomy Conjecture and, time permitting, a broad overview of Zhuk's algorithm. See https://arxiv.org/abs/1704.01914 More details of the solution will be filled in throughout the semester. Constraint Satisfaction Problems
Sep. 11, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) X The concept of a Cofinality Spectrum Problem (CfSP) was introduced recently by M. Malliaris and S. Shelah (J. Amer. Math. Soc., 2016), and was used to obtain spectacular results in model theory and set theoretic topology. In model theory the Malliaris-Shelah results on CfSPs shed new light on Keisler’s order -- a notion from the 1960’s to classify first order theories. In set theoretic topology these results were used to prove that the cardinals p and t related to the continuum are equal (in ZFC), although for decades, this equality was expected to be independent of ZFC. Overview of the Malliaris--Shelah paper, Part 1
Sep. 11, 2018 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between groups. A supercharacter theory is a framework for simplifying the character theory of a finite groups, while ideally not losing all important information. This talk examines one such theory that straddles the gap between retaining valuable group information while reducing the above questions to more combinatorial lattice constructions. Joint with Aliniaeifard. The structure of normal lattice supercharacter theories
Sep. 11, 2018 3pm (MATH 350)	Algebraic Geometry Zheng Zhang (CU Boulder) X The period map is a powerful tool for studying moduli spaces, and has been applied successfully to abelian varieties, K3 surfaces, cubic threefolds/fourfolds, and hyper-Kahler manifolds. However, for some interesting moduli problems (e.g. moduli spaces for pairs of varieties) there might be no obvious way to construct periods. Joint with R. Laza and G. Pearlstein, we construct a period map for cubic pairs consisting of a cubic threefold and a transverse hyperplane using a variation of the construction by Allcock, Carlson and Toledo (which allows us to encode a cubic pair as a “lattice polarized” cubic fourfold). The main result is that the period map induces an isomorphism between a GIT model of the moduli of cubic pairs and the Baily-Borel compactification of some locally symmetric domain. On the moduli space of pairs consisting of a cubic threefold and a hyperplane
Sep. 11, 2018 3pm (MATH 220)	Topology Sam Nariman (Northwestern University) Topology Seminar Pretalk Sponsored by the Meyer Fund
Sep. 11, 2018 4pm (MATH 350)	Topology Sam Nariman (Northwestern University) X There are at least three different approaches to construct characteristic invariants of a flat symplectic bundle. Reznikov generalized Chern-Weil theory for finite dimension Lie groups to the infinite dimensional group of symplectomorphisms. He constructed nontrivial invariants of symplectic bundles whose fibers are diffeomorphic to complex projective spaces. Kontsevich used formal symplectic geometry to build interesting classes that are not yet known to be nontrivial. For surface bundles whose holonomy groups preserve the symplectic form, Kotschick and Morita used the flux homomorphism to construct many nontrivial stable classes. In this talk, we introduce infinite loop spaces whose cohomolgy groups describe the stable characteristic invariants of symplectic surface bundles. As an application, we give a homotopy theoretic description of Kotschick and Morita's classes and prove a result about codimension 2 foliations that implies the nontriviality of KM classes. On the moduli space of flat symplectic surface bundles Sponsored by the Meyer Fund
Sep. 12, 2018 4pm (MATH 350)	Grad Student Seminar Leo Herr (CU Boulder) X Schemes and Varieties have a reputation for being somewhat challenging to become familiar with. Is it too late to recall their original geometric intuition? No! We'll see a handful of down-to-earth examples of varieties encoded by cones in, say 3-d real space. Maybe we'll get to resolution of singularities or Stanley's Theorem. Toric Varieties and Convex Geometry
Sep. 13, 2018 11am (Math 220)	SPORT Graduate Internship (NSA) X The SPORT program at the National Security Agency (NSA) offers graduate students the opportunity to apply their academic knowledge in a stimulating professional environment. As a SPORT intern you will work closely with full time Operations Research analysts applying academic and technical skills to challenging, real-world problems. Internships are paid and are 12 weeks in duration (May-August). Applications accepted September 1st through October 31st. Summer Program for Operations Research Technology at NSA
Sep. 18, 2018 10am (MATH 350)	Geometry/Analysis Yuhao Hu (University of Colorado, Boulder) Geometry of Backlund transformations Sponsored by the Meyer Fund
Sep. 18, 2018 1pm (MATH 220)	Peter Mayr X We discuss several classical reductions between CSPs over finite constraint languages. In particular we show that each constraint language may be replaced by the singleton expansion of its core. Further the complexity of CSP(Gamma) is determined by the variety generated by its polymorphism algebra. CSP reductions
Sep. 18, 2018 2pm (Math 350)	Lie Theory Julianne Rainbolt (Saint Louis University) X Let $\tilde{G}$ denote a connected reductive algebraic group defined over an algebraically closed field of characteristic $p > 0$ . Let $F : \tilde{G} \to \tilde{G}$ be a Frobenius endomorphism. Let $G$ be the finite group of Lie type which is the fixed points of $F$ . Let $B$ be an $F$ -stable Borel subgroup of $\tilde{G}$ and let $T$ be an $F$ -stable maximal torus of $\tilde{G}$ contained in $B$ . Let $N = NG(T)$ . Denote the Weyl group of $G$ by $W = NF/TF$ . The element $\overset{\cdot}{w}$ will denote a preimage of $w ∈ W$ with respect to the natural surjection from $N^{F}$ to $W$ . The double cosets $B^{F} \overset{\cdot}{w} B^{F}$ are called the Bruhat cells of $G$ . An element $x ∈ G$ is called regular if the dimension of its centralizer is minimal. In this talk, we will discuss necessary and sufficient conditions for Bruhat cells to contain only regular elements. Furthermore, we will investigate Bruhat cells that contain both regular and nonregular elements but have cosets consisting entirely of regular elements. Cosets and Double Cosets Containing only Regular Elements Sponsored by the Meyer Fund
Sep. 18, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Overview of the Malliaris--Shelah paper, Part 2
Sep. 19, 2018 4pm (MATH 350)	Grad Student Seminar Andrew Campbell (CU Boulder) X The distribution of eigenvalues of random matrices is a central idea in random matrix theory. Universality is a phenomenon which holds for a wide class of random variables, usually motivated by normal random variables. We will look at Wigner's famous semicircle law, the circular law, the elliptic law, and results on the distributions of eigenvalues on the unit circle for probability measures on compact matrix groups. No prior knowledge on probability or random matrix theory will be assumed. Pictures will be included. Universality, Eigenvalues of Random Matrices, and Circles
Sep. 20, 2018 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X I will discuss joint work with Magnus Goffeng and Allan Yashinski on the construction of non-zero projections in certain C-algebras. To begin, the case of continuous trace C-algebras will be discussed. The results in this case lead to a natural conjecture for more general type I C*-algebras. However, as will be outlined via explicit examples, even in the case of Fell algebras the question of the existence of non-zero projections is quite subtle. On the existence of projections in Fell algebras
Sep. 21, 2018 12pm (MATH 350)	Ulam Roman Bezrukavnikov (MIT) X I will review old results (joint with I. Mirkovic and D. Rumynin) on localization theory for representations of semi-simple Lie algebras and then discuss recent results and conjectures extending them to more general contexts, emphasizing relation to derived algebraic geometry. Modular representations and geometry
Sep. 25, 2018 11am (MATH 350)	Number Theory Robert Hines (CU Boulder) X We consider approximation of vectors $z∈ F⊗R≅Rr×Cs$ by elements of a number field $F$ and construct examples of badly approximable vectors. These examples come from compact subspaces of $SL2(OF) SL2(F⊗R)$ naturally associated to (totally indefinite, anisotropic) $F$ -rational binary quadratic and Hermitian forms, a generalization of the well-known fact that quadratic irrationals are badly approximable over $ℚ$ . Examples of badly approximable vectors over number fields
Sep. 25, 2018 1pm (MATH 220)	Peter Mayr X We show that if a constraint language does not have a WNU polymorphism, then its CSP is NP-complete. Then we discuss various kinds of local consistency checks and in particular (2,3)-minimal instances. CSP hardness and bounded width
Sep. 25, 2018 1pm (MATH 350)	Ulam V. Baranovsky (UC Irvine) X Let (X, w) be a complex projective manifold with a holomorphic symplectic form w. Assume for simplicity that the space of holomorphic 2-forms on X is one-dimensional. Then it is known that (symplectic) deformations of the pair (X, w) are described by the Beauville-Bogomolov quadric Q in the second complex cohomology H2(X, C). The goal of the talk is to understand Q in terms of algebraic deformation theory and the fact that the Koszul bracket on the de Rham complex of X is homotopy abelian. Joint work with D. Kaledin. L-infinity morphisms and the Beauville-Bogomolov quadric
Sep. 25, 2018 2pm (MATH 350)	Lie Theory Michael Strayer (University of North Carolina at Chapel Hill) X R.M. Green axiomatically defined full heaps and used them to build minuscule-like representations of many affine Kac-Moody algebras. Two other classes of colored posets, namely minuscule and d-complete posets, have also been used in many applications to Lie theory; for instance, they correspond to “dominant minuscule” elements of Kac-Moody Weyl groups. We present new poset coloring properties that unify the above three classes of colored posets and characterize various Kac-Moody (sub)algebra representations. These include the full heap representations of Green, the minuscule representations of semisimple Lie algebras, and Demazure modules of dominant minuscule Weyl group elements. We will give the classifications of colored posets satisfying the two most important sets of these properties. Minuscule Kac-Moody settings unified by new poset coloring properties Sponsored by the Meyer Fund
Sep. 25, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The regular and good ultrapowers, Part 1
Sep. 25, 2018 3pm (Math 350)	Algebraic Geometry Leo Herr (University of Colorado, Boulder) X We will introduce a variant of Gromov-Witten Theory for log smooth curves, and compare invariants of a product of log smooth varieties with the invariants of each. To make this possible, we will give brief introductions to both Gromov-Witten Theory (curve counting) and Log Geometry. This variant of the theory originated in the work of M. Gross and B. Siebert, and we offer a new perspective on it, accompanied by new theorems. The Log Gromov-Witten Product Formula
Sep. 25, 2018 4pm (MATH 350)	Topology Robin Deeley (CU Boulder) X I will begin with a discussion on the basic properties of C-algebras with an emphasis on examples. Next the notions of essentially self-adjoint and essentially normal operator will be defined and relationship between these operators and K-homology with be developed. The talk will very much be an introduction and hence accessible to a wide audience. An introduction to C-algebras and K-homology
Sep. 26, 2018 4pm (MATH 350)	Grad Student Seminar Mark Pullins (CU Boulder) X Finite groups equipped with a sharply 2-transitive action have a useful, and simple, geometry associated to them. The geometry allows us to write the finite group as a semi-direct product and recover the structure of a near-field. In this talk, we examine the case of infinite groups with sharply 2-transitive actions. We will use the involutions to study the group, demonstrate how to construct a near field or near domain, and sketch a recent construction of an infinite sharply 2-transitive group that does not split. The Geometry of Sharply 2-Transitive Groups
Sep. 27, 2018 2pm (MATH 350)	Functional Analysis Robin Deeley (CU Boulder) X Smale spaces are a class of dynamical system defined by Ruelle to axiomatize properties of the basic sets of an Axiom A diffeomorphism. I will introduce Smale spaces by presenting three natural examples in detail. From a Smale space one can construct a number of C-algebras; each is obtained from an equivalence relation. These algebras will be discussed both in general and in the three aforementioned examples. Much of this talk is based on Ian Putnam's paper "C-algebras from Smale spaces". An introduction to Smale space C*-algebra
Oct. 02, 2018 11am (MATH 350)	Number Theory Number Theory Lab Meeting X We will have a Number Theory Lab Meeting. Mark Coffey has volunteered to speak briefly (on analytic topics, with an eye toward recent news events). All with an interest in number theory are welcome to attend. Number Theory Lab Meeting
Oct. 02, 2018 1pm (MATH 220)	Peter Mayr X We describe the (2,3)-minimal algorithm as the first reduction step in Zhuk's algorithm. CSP local consistency
Oct. 02, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The regular and good ultrapowers, Part 2
Oct. 02, 2018 4pm (MATH 350)	Topology Jon Belcher Pseudodifferential Operators and Symbols
Oct. 04, 2018 12pm (MATH 350)	Ulam B. Tsygan (Northwestern University) X We will show that the p-adically completed periodic cyclic complex of a differential graded algebra over Z is a homotopy crystal, i.e. such complexes are canonically (up to all higher homotopies) isomorphic for any two algebras that are the same modulo p. Periodic cyclic complex as a homotopy crystal. Sponsored by the Meyer Fund
Oct. 04, 2018 12pm (Math 350)	Noncomm Geometry Boris Tsygan (Northwestern University) X We will show that the p-adically completed periodic cyclic complex of a differential graded algebra over Z is a homotopy crystal, i.e. such complexes are canonically (up to all higher homotopies) isomorphic for any two algebras that are the same modulo p. Periodic cyclic complex as a homotopy crystal. Sponsored by the Meyer Fund
Oct. 04, 2018 2pm (MATH 350)	Functional Analysis Alexander Mundey (University of Wollongong) X Given a homeomorphism of a space X the associated crossed product of C(X) by the integers encodes the dynamics. However, if we are given multiple self-mappings of X it becomes less clear what the natural dynamical C-algebra to associate is. In this talk I will introduce Cuntz-Pimsner algebras, which can be thought of as a crossed product by a C-correspondence. I will explain how they can be used to encode the dynamics of certain multivariable dynamical systems, and how the K-theory of these algebras captures certain dynamical features. This talk is based primarily on Kajiwara and Watatani's work on C*-algebras associated to iterated function systems, but also relates to the work of Davidson, Katsoulis, and others on tensor algebras for multivariable dynamics. Multivariable dynamics and Cuntz-Pimsner algebras
Oct. 04, 2018 4pm (Math 350)	Noncomm Geometry Dan Freed (University of Texas at Austin) X There are many mathematical problems in which we can trade symmetry information for a parametrized family, and then extract information from the geometry of that family. In this talk we focus on this equivariance-to-families principle in differential geometry, where in joint work with Mike Hopkins we use abstract homotopy theory to develop a mathematical theory. We then describe some applications to equivariant Chern-Weil theory and to the geometry of families of Dirac operators. (An application to condensed matter physics is the subject of a talk on Friday in the physics department.) The Equivariance-to-Families Principle
Oct. 09, 2018 11am (MATH 350)	Number Theory Daniel Martin (CU Boulder) X Continued fractions have been used since the late 19th century to produce rational approximations to complex numbers, but they are nonexistent outside of the five Euclidean imaginary quadratic fields. In this talk we will produce a tool that creates continued fractions in any imaginary quadratic field. We will also find applications of this tool to Bianchi group presentations and integral circle packings. The geometry of imaginary quadratic fields
Oct. 09, 2018 12:10pm (MATH …	Kempner Bram Mesland (Max Planck Institute for Mathematics Bonn) X Kasparov's KK-theory is a bivariant homology theory for C*-algebras providing a general framework for index theory. Cycles for the theory come from the abstract analogue of a first-order differential operator. After an exposition of the theory for non-specialists, I will discuss some recent results. These include analytic properties of self-adjoint operators, applications of KK-theory in the theory of arithmetic manifolds and automorphic forms and the physics of topological insulators. KK-theory in geometry and physics
Oct. 09, 2018 1pm (MATH 220)	Peter Mayr X We describe the second step of Zhuk's algorithm for solving CSP that combines local consistency methods and quotient algebras. CSP irreducibility
Oct. 09, 2018 2pm (MATH 350)	Lie Theory Farid Aliniaeifard (CU Boulder) X The concept of Hopf algebras originated from the theory of algebraic groups and algebraic topology in the mid 20th century and now it has many application in algebraic combinatorics. Also, the notion of a Hopf monoid in the monoidal category of linear species was introduced by Aguiar and Mahajan, and they show the great importance of this concept in algebraic combinatorics with examples that show many combinatorial objects have Hopf monoid structures. Hopf structures have numerous applications in many other mathematical branches, and now it is a familiar concept in representation theory as the class functions or superclass functions of some tower of groups have Hopf structures where representation theoretic functors give the product and coproduct. In this talk, we give a brief introduction to normal lattice supercharacter theories, and then we construct a Hopf structure by using these supercharacter theories. (With Nat Thiem and Shawn Burkett) Normal lattice supercharacter theories and Hopf structures
Oct. 09, 2018 2pm (MATH 220)	Michael Wheeler (CU Boulder) The existence of good ultrafilters
Oct. 09, 2018 3pm (MATH 350)	Ulam D. Kaledin X While deformation quantization first appeared in physics and/or differential geometry, there is actually a purely algebraic version of the story, and it has quite a lot of applications (for example, to algebraic geometry of symplectic singularities in the sense of Beauville). I will give a general introduction to the subject. I will mostly follow my old papers with Bezrukavnikov, but I will also present some newer results. Deformation quantization in algebraic geometry
Oct. 09, 2018 3pm (MATH 350)	Algebraic Geometry Dmitry Kaledin (Steklov Math Institute Moscow and University of Colorado) X While deformation quantization first appeared in physics and/or differential geometry, there is actually a purely algebraic version of the story, and it has quite a lot of applications (for example, to algebraic geometry of symplectic singularities in the sense of Beauville). I will give a general introduction to the subject. I will mostly follow my old papers with Bezrukavnikov, but I will also present some newer results. Deformation quantization in algebraic geometry
Oct. 09, 2018 4pm (MATH 350)	Topology Cherry Ng The Atiyah-Jänich Theorem and Kuiper's Theorem
Oct. 10, 2018 4pm (MATH 350)	Grad Student Seminar Leo Herr (CU Boulder) X If n is odd, a square can't be dissected into n triangles of equal area! Proof from "the book;" only known proof uses p-adics and valuations. We'll introduce some of this stuff with an eye towards tropical geometry. Accessible to anybody. Sperner Colorings, Triangles, and p-adics
Oct. 11, 2018 2pm (MATH 350)	Functional Analysis Bram Mesland (Max Planck Institute for Mathematics Bonn) X In this talk I will discuss several examples of spectral triples for C-algebras that arise as "noncommutative boundaries" of commutative dynamical systems. The examples concern Cuntz-Krieger algebras, crossed products of Kleinian groups by their limit sets and transverse groupoid C-algebras of a Delone sets. The common theme for these spectral triples is that they carry non-trivial K-homological content, they are not finitely summable, and their operators formally resemble the logarithm of the Laplacian on R^n. The latter admits a representation as a singular integral operator, the expression for which makes sense in the context of metric measure spaces. The talk selects from joint works with C. Bourne, M. Goffeng and M.H. Sengun Spectral triples and noncommutative boundaries Sponsored by the Meyer Fund
Oct. 11, 2018 3pm (MATH 220)	Functional Analysis Elizabeth Gillaspy (University of Montana) X Higher-rank graphs ( $k$ -graphs) are category theoretic objects which can also be viewed as generalizations of directed graphs. In order to better understand the C*-algebras associated to $k$ -graphs, Kumjian, Pask, and Sims introduced two cohomology theories for $k$ -graphs. Using ad hoc methods, Kumjian, Pask, and Sims showed that the $i$ th categorical and cubical cohomology groups of a $k$ -graph are isomorphic for $i ≤ 2$ . This talk presents recent joint work with Jianchao Wu, in which we show that for all $i \in \Z$ the $i$ th cubical and categorical homology and cohomology groups of any $k$ -graph are isomorphic. This proves a conjecture posed by Kumjian, Pask, and Sims in 2015, and also uncovers more structural information about the categorical (co-)homology groups. Our first proof of this result relies on the topological realization of a $k$ -graph (as defined by Kaliszewski, Kumjian, Quigg, and Sims) and the reformulation of categorical cohomology using $Λ$ -modules, as introduced by Gillaspy and Kumjian. Time permitting, we will also present our more computational second proof, which gives an explicit formula for passing between cubical and categorical (co-)cycles. Cubical and categorical (co-)homology for k-graphs Sponsored by the Meyer Fund
Oct. 16, 2018 10am (MATH 350)	Geometry/Analysis Sema Salur (University of Rochester) X Let $N2n$ be a smooth symplectic manifold equipped with a closed, nondegenerate differential 2-form $ω$ . An $n$ -dimensional submanifold $L^{n}$ of $N2n$ is called Lagrangian if the restriction of $ω$ to $L$ is zero. Lagrangian submanifolds and their deformations have important applications in symplectic geometry and mathematical physics. In partciular, they play a role in establishying the correspondence between “Calabi-Yau mirror pairs” in string theory. In this talk we first study the deformations of (special) Lagrangian submanifolds and then extend the theory to “Lagrangian Type” submanifolds inside $G2$ manifolds. If time permits, we will also discuss relations between $G2$ and contact structures. Deformation Theory of Calibrated Submanifolds Sponsored by the Meyer Fund
Oct. 16, 2018 12pm (MATH 350)	Geometry/Analysis Catherine Searle (Wichita State University) X The classification of compact Riemannian manifolds with positive or non-negative sectional curvature is a long-standing problem in Riemannian geometry. One successful approach has been the introduction of symmetries, and an important first case to understand is that of continuous abelian symmetries. In recent work with Escher, we obtained an equivariant diffeomorphism classification of closed, simply-connected non-negatively curved Riemannian manifolds admitting an isotropy-maximal torus action, with implications for the Maximal Symmetry Rank Conjecture for non-negatively curved manifolds. I will discuss joint work with Escher and Dong, that builds on this work to extend the classification to those manifolds admitting an almost isotropy-maximal action. Torus actions, maximality, and non-negative curvature Sponsored by the Meyer Fund
Oct. 16, 2018 12:10pm (MATH …	Kempner Geometry and Analysis Day TBA
Oct. 16, 2018 1pm (MATH 220)	Peter Mayr X We discuss the third step in Zhuk's algorithm where constraints are replaced by all their weaker constraints. CSP weaker relations
Oct. 16, 2018 2pm (MATH 350)	Lie Theory Mandi Schaeffer-Fry (MSU) X Galois automorphisms act naturally on the irreducible characters of a finite group. But, it is in general a difficult problem to describe this action, say, in terms of known parameters for the characters of a given group. We discuss this problem in the case of finite symplectic and special orthogonal groups. This is joint work with Jay Taylor. Galois Actions and Classical Groups
Oct. 16, 2018 3pm (MATH 350)	Geometry/Analysis James P. Kelliher (UC Riverside) X We say that the regularity of a function in $ℝ^{d}$ is \textit{striated} if it has higher regularity along certain hypersurfaces than it does in directions normal to those hypersurfaces. In the context of active transport equations, we say that striated regularity is propagated if such regularity is maintained as both the scalar and the hypersurfaces are transported by the flow map for the velocity field. (Being active scalars, the velocity field at time $t$ is a function of the scalar at time $t$ , making the underlying PDE nonlinear.) We first discuss briefly the transport of vorticity by the 2D Euler equations. Two simplifying properties of these equations are that the transport is by a divergence-free vector field, and the transport equations related to the hypersurfaces are pure transport. We outline how the propagation of striated regularity was first established for the 2D Euler equations in a landmark 1991 result of Jean-Yves Chemin. We place Chemin's approach and subsequent approaches by later authors in a larger framework that we then apply to a seemingly very similar active transport equation: the aggregation equation with Newtonian potential (the inviscid form of a limiting case of the Keller-Segel equation). Such equations lack, however, the two simplifying properties of the 2D Euler equations. We explain how we overcome these difficulties to obtain the propagation of the regularity of level sets of the active scalar, a restricted form of propagation of striated regularity. This extends a recent result of Bertozzi, Garnett, Laurent, and Verdera for patch boundary regularity for the aggregation equation. This is joint work with Hantaek Bae of Ulsan National Institute of Science and Technology (UNIST). Striated regularity for a class of active transport equations Sponsored by the Meyer Fund
Oct. 17, 2018 4pm (MATH 350)	Grad Student Seminar Andrew Campbell (CU Boulder) X In this talk we will use characters on the unitary group to describe properties of the trace and eigenvalues of random unitary matrices. We will use the group structure of U(n) to take questions about random matrices and rephrase them as questions on the inner product of class functions and thus characters. Little to no knowledge of probability will be assumed. This talk is based on the work of Persi Diaconis ad Mehrdad Shahshahani. Characters and Random Unitary Matrices
Oct. 18, 2018 2pm (MATH 220)	Functional Analysis Valentin Deaconu (University of Nevada at Reno) X I will recall the definition of a $C$ -correspondence and of the Cuntz-Pimsner algebra. I will discuss group actions on $C$ -correspondences and crossed products. I will illustrate with examples related to graphs and to vector bundles. Symmetries of Cuntz-Pimsner algebras
Oct. 18, 2018 3pm (MATH 350)	Probability Ke Wang (Hong Kong University of Science and Technology (HKUST)) X In this talk, we consider the matrix model Y=S+X where S is a low-rank deterministic matrix, representing the signal, and X is a random noise. It is a central task in high dimensional data analysis to understand how the spectral properties of S are altered with a small random perturbation. We give a precise description of the limiting distribution of the angles between the outlier singular vectors of Y with their counterparts, the leading singular vectors of S. It turns out that the limiting distribution depends on the structure of S and the distribution of X, and thus it is non-universal. This talk is based on a joint work with Zhigang Bao and Xiucai Ding. Limiting distribution of outlier singular vectors of low-rank matrices with additive random noise
Oct. 23, 2018 1pm (MATH 220)	Steven Weinell (CU) X In 2001, Andrei Bulatov generalized the binary commutator operation on a general algebra to an n-ary commutator operation. In a simple algebra higher commutators may only be the congruence 0 or 1. I have shown that for any natural number, n>1, we can construct an algebra with the n-ary commutator [1, ..., 1] = 1 while the (n+1)-ary commutator [1, ..., 1, 1] = 0. In this talk I will present the construction in the case where n=2. Controlling Higher Commutators in a Simple Algebra
Oct. 23, 2018 1pm (MATH 350)	Ulam D. Kaledin X I will give a short overview of the technique of "formal geometry", with its applications to deformation quantization of algebraic varieties and to characteristic classes. Then I will show how the moduli space of quantizations can be described in terms of certain characteristic classes of symplectic algebraic varieties introduced by Rozansky and Witten (joint work in progress with V. Baranovsky). Formal geometry, Fedosov quantization and Rozansky-Witten classes
Oct. 23, 2018 2pm (MATH 220)	Mark Pullins (CU) X I will talk about a recent construction of Rips, Segev and Tent, which solves a longstanding problem. A sharply 2-transitive group without a nontrivial abelian normal subgroup.
Oct. 23, 2018 3pm (MATH 350)	Algebraic Geometry Xiaolei Zhao (UC Santa Barbara) X It is a classical result of Beauville and Donagi that Fano varieties of lines on cubic fourfolds are hyper-Kahler. More recently, Lehn, Lehn, Sorger and van Straten constructed a hyper-Kahler eightfold out of twisted cubics on cubic fourfolds. In this talk, I will explain a new approach to these hyper-Kahler varieties via moduli of stable objects on the Kuznetsov components, and further generalizations. An application towards the study of 0-cycles on these hyper-Kahler varieties will also be discussed. This is based on a joint work with Chunyi Li and Laura Pertusi. Twisted cubics on cubic fourfolds and stability conditions Sponsored by the Meyer Fund
Oct. 23, 2018 4pm (MATH 350)	Topology Markus Pflaum Characteristic Classes
Oct. 24, 2018 4pm (MATH 350)	Grad Student Seminar Cherry Ng (CU Boulder) X The Kervaire Invariant is an invariant of 4n+2 dimensional manifolds which measures the similarities between a manifold and a sphere of the same dimension. The Kervaire Invariant problem concerns the Kervaire Invariant of all manifolds of a given dimension, and has been solved in every dimension save for 126. We will begin with an accessible description of the Kervaire Invariant and the Kervaire Invariant problem, and then discuss the Kervaire Invariant problem from the perspective of algebraic topology and homotopy theory. The Kervaire Invariant Problem
Oct. 25, 2018 2pm (MATH 350)	Functional Analysis Karen Strung (Radboud Universiteit) X Now that the classification of infinite dimensional simple separable unital C-algebras with finite nuclear dimension and which satisfy the UCT is complete, it becomes an interesting question to determine the range of the invariant for certain naturally-occurring subclasses. I will discuss joint work in progress with Robin Deeley and Ian Putnam that considers this question for the C-algebras arising from groupoids associated to minimal dynamical systems. In particular, I will discuss dynamical constructions which realize certain prescribed Elliott invariants. C*-algebras of minimal dynamical systems and related groupoids with prescribed K-theory Sponsored by the Meyer Fund
Oct. 30, 2018 11am (MATH 350)	Number Theory Jeff Achter (CSU) X The set of abelian varieties over a given field is naturally partitioned into isogeny classes. If the field is finite, then so is each isogeny class. I'll explain several different ways of thinking about the cardinality of such a class, including a new, explicit product formula recently (developed jointly with Ali Altug, Luis Garcia and Julia Gordon). The size of an isogeny class
Oct. 30, 2018 1pm (MATH 220)	Jordan Dubeau Set Theory, Model Theory, Group Theory
Oct. 30, 2018 2pm (MATH 220)	Jordan Dubeau Set Theory, Model Theory, Group Theory
Oct. 30, 2018 4pm (MATH 350)	Topology Katharine Adamyk Homotopy Theoretic K-Homology and the Bott Spectrum
Oct. 31, 2018 4pm (MATH 350)	Grad Student Seminar Robert Hines (CU Boulder) X jk, I ain't talking 'bout none of that, but it does sound ~spooky. I'll (probably) be describing a moduli space for planar polygons, i.e. how to take the square root of a polygon. We should be able to give a reasonable answer to the (ill-posed) question, "What's the probability that a triangle is obtuse?" Costumes encouraged! Free candy (which coincidentally shares many properties with pizza)! n-Skeleta, the Monster, Killing forms, and the ghosts of departed quantities...
Nov. 06, 2018 11am (MATH 350)	Number Theory Christelle Vincent (University of Vermont) X The shape of a number field is an invariant which refines the discriminant. In this talk we present Piper H's PhD thesis on the equidistribution of shapes of S_3-, S_4-, and S_5-number fields when they are ordered by discriminant. We then discuss joint work that is in progress on the joint distribution of the shapes of a field and its resolvent. This talk will be accessible to anyone who knows some Galois theory as well as the definition of a number field and its ring of integers. On the equidistribution of the shape of certain number fields
Nov. 06, 2018 1pm (MATH 220)	Election Day! Vote!
Nov. 06, 2018 2pm (MATH 350)	Lie Theory Henry Kvinge (CSU) X First formally defined by Borodin and Olshanski, a coherent system on a graded graph is a sequence of probability measures which respect the action of certain down/up transition functions between graded components. In one common example of such a construction, each measure is the Plancherel measure for the symmetric group and the down transition function is induced from the restriction functor. In this talk we will show how to generalize the above framework to the case of any free Frobenius tower where we no longer assume that our algebras are semisimple. In particular, we describe two coherent systems on graded graphs defined via representation theory of a tower of algebras and connect one of these systems to a family of central elements of the tower. When the algebras are not semisimple, the resulting coherent systems reflect the duality between simple modules and indecomposable projective modules. Coherent systems of probability measures on graphs for representations of free Frobenius towers Sponsored by the Meyer Fund
Nov. 06, 2018 2pm (MATH 220)	Election Day! Vote!
Nov. 06, 2018 3pm (MATH 350)	Algebraic Geometry Jeff Achter (CSU) X Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients. I'll use recent advances in the theory of K3 surfaces to construct arithmetic period maps which explain these uniformizations. Arithmetic moduli for lattice-polarized K3 surfaces, or, Three views of six points Sponsored by the Meyer Fund
Nov. 06, 2018 4pm (MATH 350)	Topology Alex Mundey Dirac operators
Nov. 07, 2018 4pm (MATH 350)	Grad Student Seminar Jonathan Quartin (CU Boulder) X The Inverse Galois Problem is easily stated— “does every finite group occur as the automorphism group of some finite Galois extension of $ℚ$ ” While this is still unsolved, if we replace $ℚ$ by $C(t)$ , the statement is true. The proof of this fact highlights an interesting boundary between Algebra and Geometry. In this talk, I will discuss Complex manifolds and Covering spaces—two of the key ingredients that go into the proof. A geometric approach to a 200 year old problem in Algebra
Nov. 08, 2018 3pm (MATH 350)	Probability Indrajit Jana (Temple) X In this talk, we discuss about a CLT for the linear eigenvalue statistics of non-Hermitian random band matrices. Let $X$ is a random matrix with iid entries, and $λ1,λ2,. . . .,λn$ be it's eigenvalue. Define the linear eigenvalue statistics $L(f)=f(λ1)+. . . +f(λn)$ . Rider, and Silverstein '06 had shown that the unscaled and centered $L(f)-E[L(f)]$ with analytic $f$ converges to a Gaussian distribution. The variance of the limiting distribution is completely determined by the test function $f$ only. We extend that result for non-Hermitian random band matrices. In case of band matrices, the linear eigenvalue statistics needs to be scaled properly. In addition, the variance of the limiting Gaussian distribution depends on the test function, as well as the growth rate of the bandwidth. Linear eigenvalue statistics of non Hermitian random band matrices
Nov. 13, 2018 1pm (MATH 350)	Ulam Markus Pflaum (CU Boulder) X The inertia space of a compact Lie group action or, more generally, of a proper Lie groupoid, has an interesting singularity structure. Unlike the quotient space of the group action, respectively the groupoid, the inertia space cannot be stratified by orbit types, in general. In this talk, we explain this phenomenon. We also indicate a connection between the inertia space and the non-commutative geometry of the underlying groupoid in terms of basic relative Grauert-Grothendieck forms on the inertia space. We finally pose a conjecture about the Hochschild homology of the convolution algebra of the transformation groupoid of a compact Lie group action. The talk is based on joint work with with C. Farsi and Ch. Seaton (singularity theory of inertia groupoids) and with H. Posthuma and X. Tang (Grauert-Grothendieck forms and Hochschild homology of convolution algebras). Inertia groupoids and a conjecture on the Hochschild homology of the convolution algebra of a compact Lie group action
Nov. 13, 2018 1pm (MATH 220)	Peter Mayr (CU) X We discuss Rosenberg's classification of maximal clones on finite sets and its consequences for the structure of finite algebras with WNU. CSP maximal clones
Nov. 13, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Cofinality Spectrum Problems, Part 1: A motivating example by Malliaris and Shelah
Nov. 13, 2018 3pm (MATH 350)	Algebraic Geometry Gregory Pearlstein (Texas A&M University) X The theory of normal functions and the Hodge conjecture have their origin in the study of algebraic cycles by Lefschetz and Poincare. I will sketch the history of the subject and discuss some of my recent work on singularities of normal functions to the Hodge conjecture and the zero locus of a normal function to a conjectural filtration of Bloch and Beilinson. Normal Functions and the Hodge Conjecture Sponsored by the Meyer Fund
Nov. 14, 2018 3pm (Math350)	Math Phys Magdalena Lottner On causal fermionic systems, continued
Nov. 14, 2018 4pm (MATH 350)	Grad Student Seminar André Davis (CU Boulder) X Did you know that one can deduce the irrationality of nth roots of 2 from Fermat's last theorem? Or that Cayley's theorem (every group is isomorphic to a subgroup of a symmetric group) follows as a special case of the Yoneda lemma? In this lighthearted talk we will prove a multitude of theorems using unconventional techniques. The only criteria is that the proof must be short, beautiful, and unexpected. We will end with a proof from THE BOOK. Swatting Flies With a Sledgehammer
Nov. 15, 2018 2pm (MATH 350)	Functional Analysis Ulrik Enstad (University of Oslo) X In time-frequency analysis, some of the central objects of study are Gabor frames. A sequence consisting of time-frequency translates $e2π i ω tη(t-x)$ of a single function $η$ in $L2(R)$ is called a Gabor system. The Balian-Low theorem, a fundamental theorem about Gabor systems, implies that for sufficiently nice $η$ , Gabor systems can never be orthonormal bases. A solution to this is to settle with (Gabor) frames, which can be overcomplete in general. The theory of Gabor frames is available in $L2(G)$ for any locally compact abelian group $G$ , but has so far been investigated mostly for ``elementary'' groups such as $ℝ$ , $ℤ$ , $𝕋$ , $Z/(n)$ and products of these. As first discovered by F. Luef, Gabor frames in $L2(G)$ are related to M. Rieffel's Heisenberg modules over twisted group $C*$ -algebras. In this talk I will show how the Balian-Low theorem, which concerns $L2(R)$ , might or might not generalize to $L2(G)$ , and that the answer depends on the structure of certain Heisenberg modules, or equivalently, certain line bundles associated to $G$ . I will also present joint work with Luef and M. Jakobsen on the existence of Gabor frames in $L2(G)$ , with $G$ being either the adeles over the rationals or the group $ℝ \times ℚ_{p}$ .? Gabor frames, Heisenberg modules and vector bundles
Nov. 15, 2018 3pm (MATH 350)	Probability Lu Wei (University of Michigan-Dearborn) X Quantum bipartite model is a standard model in describing the interaction of a physical object and its environment for different quantum systems. We wish to understand the degree of entanglement of such systems as measured by von Neumann entropy via its exact moments. The problem of computing the moments of von Neumann entropy was first considered by Don Page in 1994, where a formula for the first moment was conjectured. Page’s conjecture was proved independently by a number of works in the years followed. Recently, an expression for the second moment was conjectured by Vivo, Pato, and Oshanin, which was subsequently proved by us last year. In this talk, we will first review the computations for the first two moments. We will then show how our approach can be extended to obtain the third moment and beyond. Moments of von Neumann Entropy of Quantum Bipartite Systems: Results in Progress and in Perspectives
Nov. 27, 2018 11am (MATH 350)	Number Theory Özlem Ejder (CSU) X The points on the modular curve X_1(n) (roughly) classifies the pairs (E,P) up to isomorphism where E is an elliptic curve and P is a point of order n on E. We call a closed point x on X_1(n) sporadic if there are only finitely many closed points of degree at most deg(x); hence classifying sporadic points on X_1(n) is closely related to determining the torsion subgroups of elliptic curves over a degree d field. When d=1 or 2, Mazur and Kamienny's work show that there are no sporadic points of degree d on X_1(n). In this talk, I will discuss that the sporadic j-invariants of bounded degree is finite. This is joint with A. Bourdon, Y. Liu, F. Odumudu and B. Viray. Sporadic points on modular curves
Nov. 27, 2018 12:10pm (MATH …	Kempner Xudong Chen (CU Boulder) X Ensemble control deals with the problem of using a finite number of control inputs to simultaneously steer a large population (in the limit, a continuum) of individual control systems. As a dual, ensemble estimation deals with the problem of using a finite number of measurement outputs to estimate the initial state of every individual system in the (continuum) ensemble. We introduce in the talk a novel class of ensembles of nonlinear control systems, termed distinguished ensemble systems. Every such system has two key components, namely a set of finely structured control vector fields and a set of co-structured observation functions. In the first half of the talk, we demonstrate that the structure of a distinguished ensemble system can significantly simplify the analysis of ensemble controllability and observability. Moreover, such a structure can be used as a principle for ensemble system design. In the second half of the talk, we address the issue about existence of a distinguished ensemble system for a given manifold. We will focus on the case where the state space of every individual control system is an arbitrary semi-simple Lie group or its homogeneous space. Structure Theory for Ensemble Control and Estimation of Nonholonomic Systems
CANCELED Nov. 27, 2018	Ulam Erik van Erp (Dartmouth College) X This is joint work with Robert Yuncken. We developed a coordinate-free geometric definition and a unified approach to various pseudodifferential calculi. The starting point of the construction is the identification of an appropriate groupoid, which is a purely geometric object. These groupoids are suitable adaptations of Connes' tangent groupoid. We show how, once the appropriate groupoid has been constructed, the details of the calculus are developed on its foundation. Our construction recovers the classical pseudodifferential calculus as well as, for example, the Heisenberg calculus (on contact manifolds) and its generalizations (to filtered manifolds). A groupoid approach to Pseudodifferential calculi
Nov. 27, 2018 1pm (MATH 220)	Peter Mayr X We discuss the final steps in Zhuk's algorithm: reductions for absorbing subuniverses, centers, polynomially complete quotients and linear quotients. CSP linear quotients 1
Nov. 27, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Cofinality Spectrum Problems, Part 2: A motivating example by Malliaris and Shelah
Nov. 27, 2018 3pm (MATH 350)	Topology Paul Lessard X The simplex category, the category of finite totally ordered sets, is a strict test category, meaning that there exists a product preserving Quillen equivalence between simplicial sets, presheaves on the simplex category, and "nice topological spaces". It is not clear however how the combinatorics of the simplex category relate to spectra, the objects which represent cohomology theories for spaces. All the well known models of spectra, Adams spectra, symmetric spectra, L-spectra, etc. may or do use simplicial sets as their presentation for spaces, but only one almost forgotten model, Kan's semisimplicial spectra of 1963 leverage the combinatorics of the simplex category for elegance and insight. We will begin by asking why the simplex category is a strict test category and why the the category of globes is not. We will then then develop a strict test category, the theta category of Joyal, and construct an elegant suspension functor for cellular sets, presheaves on the category theta. We will then present a conjectured new model of spectra based on this category which recovers the best aspects of Kan's semisimplicial spectra. We will also comment on how this model of spectra may provide a universal algebraic lens to the distinction between stable and unstable homotopy theory. A Cellular Suspension Functor for a New Presentation of Spectra
Nov. 27, 2018 4pm (MATH 350)	Topology Andrew Stocker Analytic K-homology
Nov. 28, 2018 3pm (Math350)	Math Phys Daniel Spiegel Symmetries in QFT and Bargmann's theorem
Nov. 28, 2018 4pm (MATH 350)	Grad Student Seminar Mark Pullins (CU Boulder) X Groups of finite Morley rank can be viewed as infinite groups equipped with a notion of dimension. In this talk, we’ll enter the subject rapidly via the axiomatic definition introduced by Borovik, discuss some of the major tools used to study these groups (using only very basic model theory), and present current avenues of research along with major obstructions. Recent study has involved tools inspired by finite group theory, algebraic geometry, Lie groups, and model theory - so there should be something of interest to (almost) everyone! A Brief Survey of Groups of Finite Morley Rank
Nov. 29, 2018 12pm (Math 350)	Jun Hong X As we all know, the secret to giving a Good Talk is to not give a Bad Talk. Jun Hong has volunteered to give an example of what not to do. While the mathematics will be correct, in 20 minutes Jun will strive to leave us bored, annoyed, and more confused on the subject than before we came in. We will then discuss what happened and workshop ideas for avoiding some of the most common pitfalls. Improve your presentation skills: Workshop on how to avoid giving a bad seminar talk
Dec. 04, 2018 1pm (MATH 220)	Peter Mayr CSP linear quotients 2
Dec. 04, 2018 2pm (MATH 220)	Agnes Szendrei (CU Boulder) Cofinality Spectrum Problems, Part 3
Dec. 04, 2018 2pm (MATH 350)	Lie Theory Spencer Gerhardt (CSU) X Let $C1,…,Ce$ be conjugacy classes of a simple algebraic group $G(k)$ defined over a sufficiently large field $k$ . We consider the following question: what are necessary and sufficient conditions for the existence of a tuple $(x_1,\ldots,x_e)\in C_1\times\ldots\times C_e$ such that $\langle x_1,\ldots,x_e\rangle$ is Zariski dense in $G(k)$? A solution to this problem has several applications, including generic stabilizers in linear representations of algebraic groups, and random generation of finite groups of Lie type. Results and outstanding cases are discussed. Some work in this talk is joint with Robert Guralnick and Tim Burness. Topological generation of algebraic groups and applications
Dec. 04, 2018 4pm (MATH 350)	Topology Robin Deeley The Atiyah-Singer index theorem a la Paul Baum
Dec. 05, 2018 4pm (MATH 350)	Grad Student Seminar Sangman Lee (CU Boulder) X Cantor's pairing function is a well-known bijection used in his proof that rational numbers are denumerable. We will have a brief survey on Cantor's pairing function and discuss open problems on this topic (just not to look too simple). During the talk, we will have some fun with a math puzzle regarding paring functions and, more importantly, a cat. We will also explore what happens if we generalize the puzzle: Cantor's cat will dance on a donut, a ball, and a Möbius strip. Playing with Cantor's Cat
Dec. 06, 2018 3pm (MATH 220)	Topology Prasit Bhattacharya (The University of Virginia) X Connective topological modular form $t m f$ has led to a lot of important calculations in chromatic homotopy theory. One of the key features of $t m f$ is that its cohomology as a module over Steenrod algebra $A$ is isomorphic to $A//A(2)$ , where $A(2)$ is a subalgebra of A generated by $Sq1, Sq2, Sq4$ . On the other hand, $P21= Sq4 Sq2 + Sq2 Sq4$ is an exterior element of $A(2)$ . For any A-module $K$ one can define a chain complex where the action of $P21$ acts as a differential and its homology is the Margolis homology $M(K, P21)$ . The calculation $P21$ Margolis homology is not straightforward as the action do not follow Leibniz rule. In this talk, we will develope a new technique that will allow us to calculate $P21$ Margolis homology. In particular we will give a complete answer for $P21$ Margolis homology of $t m f^{\land r}$ . The P_2^1 Margolis homology of the connective topological modular form.
Dec. 11, 2018 10am (Math 350)	Geometry/Analysis Taylor Klotz (CU Boulder) X Given a nonlinear control system with symmetry one might want to ask if there is a related system that is linearizable and whose solutions can be used to construct solutions to the original nonlinear system. One ad hoc technique is to attempt to add additional differential equations to the system and hope for a new linearizable system. This is currently known as Dynamic Feedback Linearization. In a different direction, if we assume the nonlinear system has symmetries then one can form a smaller system via a quotient by the symmetries. If this system is linearizable then its solutions can be used to construct solutions to the original system. This talk will explore recent work on the connection between these two solution methods and how the latter sheds light on a potential theory of the former. Cascade Linearization and Dynamic Feedback Linearization of Control Systems with Symmetry
Dec. 11, 2018 11am (MATH 350)	Number Theory Dan Stroock (MIT and CU) Continued Fractions and Pell's Equation
Dec. 11, 2018 12:10pm (MATH …	Kempner Florian Pfender (CU Denver) X The flag algebra method is a technique recently developed by Razborov, and it has revolutionized parts of extremal combinatorics. The method draws from the theory of graph limits, analysis, probability and optimization. We will quickly present the fundamental ideas and then show a number of diverse applications. Somewhat counter intuitively, one can even use it to show statements about relatively small graphs, and we will show how it can be used to find new bounds on graph Ramsey numbers. joint work with B. Lidicky Semidefinite programming in extremal graph theory -- advances on the flag algebra method
Dec. 11, 2018 1pm (MATH 220)	Peter Mayr CSP linear quotients 3
Dec. 11, 2018 2pm (MATH 220)	Trevor Jack (CU Boulder) X Given generators for finite transformation semigroups and finite matrix semigroups, we will give explicit polynomial time algorithms for finding all of the left and right identities for the generated semigroups. Computing Left and Right Identities in a Semigroup
Dec. 13, 2018 3pm (MATH 350)	Probability Tulasi Ram Reddy (New York University, Abu Dhabi) X We consider the primary Brownian loop soup (BLS) layering vertex fields and show the existence of the fields in smooth bounded domains for a suitable range of parameters $β$ 's. To show this at a fixed cutoff, we use Kahane's theory of Gaussian multiplicative chaos. On the other hand, when the cutoff is removed, we use Weiner-Ito chaos expansion to establish that the $λ-β2$ limit as the intensity $λ$ of the BLS diverges and $β$ goes to 0 such that $λβ2$ is constant, is a complex Gaussian multiplicative Chaos. ( Based on joint work with F. Camia, A. Gandolfi and G. Peccati) Gaussian multiplicative chaos limit of the Brownian loop soup Poisson layering fields.
Jan. 22, 2019 12:10pm (MATH …	Kempner Zhouli Xu (MIT) X Based on work of Kervaire-Milnor, Browder, and Hill-Hopkins-Ravenel, Guozhen Wang and I recently proved that the 61-sphere has a unique smooth structure, and it is the last odd dimensional case: The only odd dimensional spheres that have a unique smooth structure are the ones in dimensions 1, 3, 5 and 61. The proof is a computation of stable homotopy groups of spheres. In recent work with Dan Isaksen and Guozhen Wang, we developed a new method that can be used to compute stable homotopy groups of spheres in a much more effective way than known ones. This new method uses motivic homotopy theory, which was introduced by Morel and Voevodsky to study algebraic geometry. Smooth structures on spheres, stable homotopy groups of spheres, and motivic homotopy theory
Jan. 22, 2019 3pm (MATH 350)	Topology Danny XiaoLin Shi (Harvard University) X We show that Lubin-Tate spectra at the prime $2$ are Real oriented and Real Landweber exact. The proof is an application of the Goerss--Hopkins--Miller theorem to algebras with involution. For each height $n$ , we compute the entire homotopy fixed point spectral sequence for $E_{n}$ with its $C2$ -action by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $C2$ -fixed points. Then, I will talk about the slice spectral sequence of a $C4$ -equivariant spectrum. This spectrum is a variant of the detection spectrum of Hill--Hopkins--Ravenel and is very closely related to the height 4 Lubin--Tate theory. Real Orientations of Lubin-Tate Spectra
Jan. 22, 2019 4pm (MATH 350)	Topology Zhouli Xu (MIT) X A fundamental problem in 4-dimensional topology is the following geography question: "which simply connected topological 4-manifolds admit a smooth structure?" After the celebrated work of Kirby-Siebenmann, Freedman, and Donaldson, the last uncharted territory of this geography question is the "11/8-Conjecture''. This conjecture, proposed by Matsumoto, states that for any smooth spin 4-manifold, the ratio of its second-Betti number and signature is least 11/8. Furuta proved the ''10/8+2''-Theorem by studying the existence of certain Pin(2)-equivariant stable maps between representation spheres. In this talk, we will present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariants. In particular, we improve Furuta's result into a ''10/8+4''-Theorem. Furthermore, we show that within the current existing framework, this is the limit. This is joint work with Mike Hopkins, Jianfeng Lin and XiaoLin Danny Shi. The geography problem on 4-manifolds: 10/8 + 4
Jan. 23, 2019 4pm (MATH 350)	Grad Student Seminar Sebastian Bozlee (CU Boulder) X Injective modules are important objects in homological algebra and algebraic geometry. We will give the standard definition, then we will show that there is an alternative, more concrete characterization resembling the definition of an algebraically closed field. Injective modules are algebraically closed
Jan. 24, 2019 12:10pm (MATH …	Kempner Sooran Kang (Chung-Ang University) X Quantization is known as a way of constructing (noncommutative) quantum mechanical system from (commutative) classical mechanical system, mathematically forming operators from ordinary functions. The word `` quantize'' means ``discretize'' and we discuss where it came from by reviewing the motivation and background of quantum mechanics. Then we discuss mathematical formulation of (deformation) quantizations and introduce two $C*$ -algebras, noncommutative two tori and quantum Heisenberg manifolds, which are main examples of Rieffel's strict deformation quantizations. We also introduce noncommutative (or quantum) Yang-Mills theory developed by Connes and Rieffel on noncommutative tori, and then review some of the results of Yang-Mills connections on noncommutative two tori and quantum Heisenberg manifolds if we have time. Introduction to deformation quantizations and noncommutative Yang-Mills theory
Jan. 24, 2019 2pm (MATH 350)	Functional Analysis Palle Jorgensen (University of Iowa) X The study of representations of higher rank-graph algebras, and related non-commutative structures, is of interest in its own right. It is also part of wider themes of analysis of non-commuting geometries. The talk will focus on systems that arise in such applications as representation theory, symbolic dynamics, sub-band filters from signal processing and wavelet analysis. We shall give an account of joint results, with many co-authors, on the use of representations of the Cuntz relations O_N, and their generalizations, Cuntz-Krieger, higher-rank, etc. Related applications include a class of filter problems used in the analysis of fractals, and in geometric measure theory. By their nature, these representations reflect intrinsic self-similarity; and thus serve ideally to encode sub-bands, and more generally iterated function systems (IFSs), their dynamics, and their associated measures. At the same time, these representations offer a new harmonic analysis of signals. A key analytic tool will be classes of “transfer operators,” arising in such diverse areas as symbolic dynamics, analysis of Markov processes, and their associated path-space measures. The role of path-space and path-space measures in symbolic dynamics, in multi-resolutions (such as generalized wavelets), and in representation theory Sponsored by the Meyer Fund
Jan. 28, 2019 3pm (Math 350)	Ulam Piotr M. Hajac (CU Boulder / IMPAN) X We define an admissible decomposition of a graph E into subgraphs E_1 and E_2, and consider the intersection graph Fas a subgraph of both E_1 and E_2. We prove that, if the graph E is row finite and its decomposition into the subgraphs E_1 and E_2 is admissible, then the graph C-algebra C(E) of E is the pullback C-algebra of the canonical surjections from C(E_1) and C(E_2) onto C(F). Pullbacks of graph C*-algebras from admissible pushouts of graphs
Jan. 29, 2019 11am (MATH 350)	Number Theory Antoine Marmat and Nikolay Moshchevitin (Univ. Graz and Moscow State Univ.) X We will discuss the problem of optimal inequalities between the ordinary and the uniform Diophantine exponents, for simultaneous approximation as well as for approximation with one linear form. The first result, dealing with approximation to two numbers, was obtained by V. Jarnik in 1940. Quite recently W,M. Schmidt and L. Summerer introduced a new method of Parametric Geometry of Numbers which gave new understanding of related problems. In particular they formulated a conjecture about the optimal bounds between exponents.We will speak about a proof of this conjecture and related topics Uniform and ordinary Diophantine exponents
CANCELED Jan. 29, 2019	Kempner Catherine Sulem (University of Toronto) X The Derivative Nonlinear Schrodinger (DNLS) equation is a long-wave, weakly non-linear model that arises in the context of the Hall magnetohydrodynamic equations for conducting fluids. It was known since the work of Hayashi (1992) that solutions exist globally in time for small initial data but the case of large data remained open. Exploiting the complete integrability of the DNLS equation discovered by Kaup and Newell (1978), we prove global wellposedness for general initial conditions in weighted Sobolev spaces. Furthermore, for initial conditions that support bright solitons (but exclude spectral singularities), we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. This property is usually referred to in the literature as the soliton resolution conjecture. This is a joint work with Robert Jenkins (Colorado State University), Jiaqi Liu (University of Toronto) and Peter Perry (University of Kentucky). Global wellposedness and soliton resolution for the derivative nonlinear Schrodinger equation
Jan. 29, 2019 1pm (MATH 220)	Peter Mayr (CU Boulder) X We show that solvable quotients of subdirect products of perfect groups are nilpotent of arbitrary degree. This answers a question by Derek Holt. Joint work with Keith Kearnes and Nik Ruskuc. Subdirect products of perfect groups
Jan. 29, 2019 2pm (MATH 220)	Michael Wheeler (CU Boulder) X Until recently, the question of whether p < t is consistent with ZFC had been the longest open problem regarding cardinal invariants of the continuum. Malliaris and Shelah proved that p < t is inconsistent and so p = t for all models of ZFC. In these talks we will present a simplified version of Malliaris and Shelah's argument due to Douglas Ulrich. In this first week, we define omega-nonstandard models of ZFC, give some sense of what these models look like, and give a brief outline of the proof that p = t. We will present the basic definitions needed for the argument, and, time permitting, will present the result that "small" types of omega-nonstandard models that are consistently realized in a given pseudofinite set are always realized. p = t via Nonstandard Models of Set Theory, Part 1
Jan. 29, 2019 4pm (MATH 350)	Topology Agnes Beaudry (CU Boulder) X I will give some background on topological field theories with a view towards the Freed-Hopkins-Teleman results on invertible field theories. This will partly be an organizational meeting and talks will be assigned for the rest of the semester. Topological field theories - Intro
Jan. 30, 2019 3pm (Math350)	Math Phys Mike Hermele (University of Colorado, Physics Department) Basics of quantum mechanics from a physicist’s point of view
Jan. 30, 2019 4pm (MATH 350)	Grad Student Seminar Piotr M. Hajac (CU Boulder / IMPAN) X Operator algebras are the language of quantum mechanics just as much as differential geometry is the language of general relativity. Reconciling these two fundamental theories of physics is one of the biggest scientific dreams. It is a driving force behind efforts to geometrize operator algebras and to quantize differential geometry. One of these endeavours is noncommutatvive geometry, whose starting point is natural equivalence between commutative operator algebras (C-algebras) and locally compact Hausdorff spaces. Thus noncommutative C-algebras are thought of as quantum topological spaces, and are researched from this perspective. However, such C-algebras can enjoy features impossible for commutative C-algebras, forcing one to abandon the algebraic-topology based intuition. Nevertheless, there is a class of operator algebras for which one can develop new ("quantum") intuition. These are graph algebras, C*-algebras determined by oriented graphs (quivers). Due to their tangible hands-on nature, graphs are extremely efficient in unraveling the structure and K-theory of graph algebras. We will exemplify this phenomenon by showing a CW-complex structure of the Vaksman-Soibelman quantum complex projective spaces, and how it explains its K-theory. Operator Algebras that One Can See
Jan. 30, 2019 5pm (Math 350)	MathClub Danny Moritz (CU Boulder) X A web through time and space exploring the Geodesic Dome’s historical origins, structural facets, a middle schooler’s construction using Euler Paths, Euler’s formula for polyhedra with two interesting proofs, and extensions into Fullerenes reconsidered with signatures and adjacency matrices. Geodesic Domes, Graph Theory, and Beyond
Jan. 31, 2019 3pm (MATH 350)	Probability Zhen-Qing Chen (University of Washington) X Anomalous diffusion phenomenon has been observed in many natural systems, from the signaling of biological cells, to the foraging behavior of animals, to the travel times of contaminants in groundwater. In this talk, I will first discuss the interplay between anomalous sub-diffusions and time-fractional differential equations, including how they arise naturally from limit theorems for random walks. I will then present some recent results in this area, in particular on the probabilistic representation to the solutions of time fractional equations with source terms. Two-sided estimates on the fundamental solutions will also be given if time permits. Anomalous diffusions and fractional order differential equations

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Events for September 2018 – January 2019

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Lie Theory

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Ulam

Algebraic Geometry

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Functional Analysis

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Number Theory

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Ulam

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Kempner

Ulam

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Topology

Math Phys

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