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Events for June – October 2018

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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. 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
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
Jun. 26, 2018 2pm (MATH 350)	Lie Theory Kento Nakada (Okayama University) X D. Peterson introduced the notion of "minuscule elements" in Weyl groups. This is a generalization of Grassmannian permutations in symmetric groups. This talk introduces minuscule elements, generalized Young diagrams, and their hook formulae. These are generalizations of the ordinary hook formula for Young diagrams. A hook formula for minuscule elements in Weyl groups
Jun. 26, 2018 3pm (MATH 350)	Lie Theory Manabu HAGIWARA (Chiba University) X Insertions and deletions are operations in a model of synchronization errors in coding theory. This talk introduces relations between such operations and mathematics, in particular, minuscule objects of Weyl groups and combinatorics. Algebraic and Combinatorial Aspects of Insertion/Deletion Operations
Jul. 17, 2018 10am (MATH 350)	Geometry/Analysis Peter Vassiliou (Australian National University) X Control systems, typically nonlinear, abound in our daily experience of the world. Mathematically, they can be described by differential equations endowed with functional parameters. The prototypical example is balancing a broomstick on the tip of your finger. A basic problem in control theory is the following. Suppose a control system $\bsy{\o}$ is in state $A$ and you want to ``steer" it to state $B$ . How do you choose the (functional) parameters in the system -- the controls -- in order to achieve this? One oft-used technique is to find a special type of transformation, $T$ , that maps $\bsy{\o}$ to a certain type of universal linear control system called a Brunovsky normal form, $\bsy{\b}$. The trajectories of $\bsy{\b}$ can easily be written down in terms of arbitrary functions of time and their time derivatives after which $T-1$ maps the trajectories of $\bsy{\b}$ to those of $\bsy{\o}$, from which the steering problem can be solved. If we can construct such a solution, $s$ of $\o$, we will say that it is {\em explicitly integrable}. This settles the steering problem for linearizable control systems which form a small subset of control systems of interest. But while every linearizable system is explicitly integrable, the converse is false and for the past few decades there has been a research program underway to characterize the phenomenon of explicit integrability beyond the linearizable case. However it turns out that the Brunovsky normal forms are familiar objects in differential geometry. They correspond to the contact systems on a special class of jet spaces over the real line. In this talk we will explore this geometry to show how to establish explicit integrability for control systems which are intrinsically nonlinear - those that have no linearizing diffeomorphisms. A key ingredient is the invariance of $\bsy{\o}$ under the free and regular action of a Lie group. Symmetry and Geometric Control Theory Sponsored by the Meyer Fund
Jul. 19, 2018 10am (MATH 350)	Geometry/Analysis Peter Vassiliou (Australian National University) X In previous centuries mathematicians sought solutions of differential equations in formula as a matter of course. This approach to the study of differential systems has fallen out of fashion (and possibly favor) as a result of the vast revolutions in analysis and the types of problems requiring solution in the current epoch. Nevertheless a tremendous heritage in this area has been bequeathed to us by previous generations which we have begun to explore only in the last 4 decades or so. This resurgence has produced a fascinating body of mathematics and its applications, such solitons, Poisson geometry, infinite dimensional hamiltonian systems, Backlund transformations; to name a few. One such 19th century topic, Darboux integrability, has been the subject of a number of recent studies which reveal it to have strong geometric content and utility for constructing explicit solutions in formula of certain partial differential equations. However, because Darboux integrability is a comparatively rare phenomenon it is natural to ask if some weaker form of it may exist so as to be of wider applicability while retaining some useful aspects of the original. In this talk I will briefly recall the basic ideas of this form of integrability and then propose a weaked version which will be explored via a few elementary examples. Time permitting we will also explore its application to certain harmonic maps. Hyperbolic Reduction of Partial Differential Equations Sponsored by the Meyer Fund
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 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 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 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 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 3pm (MATH 220)	Topology Sam Nariman (Northwestern University) Topology Seminar Pretalk Sponsored by the Meyer Fund
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 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 220)	Michael Wheeler (CU Boulder) The existence of good ultrafilters
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 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 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 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 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 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 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...

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