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DTSTART;TZID=America/New_York:20200224T160000
DTEND;TZID=America/New_York:20200224T170000
DTSTAMP:20221129T122821
CREATED:20200221T151839Z
LAST-MODIFIED:20200221T151839Z
UID:6164-1582560000-1582563600@math.unc.edu
SUMMARY:Hunter Dinkins - GMA Seminar
DESCRIPTION:Title: Symmetric Functions \nAbstract: The most basic type of symmetric functions appears when studying roots of a polynomial: the coefficients of a polynomial are the elementary symmetric functions of its roots. Much of mathematics was motivated by trying to write down formulas for the reverse relationship. There are many other types of symmetric functions\, which have deep combinatorial and representation theoretic properties. In this talk\, I will provide a tour of some of the basic types of symmetric functions and\, time permitting\, will discuss a neat application of how Schur functions allow us to count 3D partitions.
URL:https://math.unc.edu/event/hunter-dinkins-gma-seminar-2/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20200217T160000
DTEND;TZID=America/New_York:20200217T170000
DTSTAMP:20221129T122821
CREATED:20200213T143323Z
LAST-MODIFIED:20200213T143323Z
UID:6157-1581955200-1581958800@math.unc.edu
SUMMARY:Yiyan Shou - GMA Seminar
DESCRIPTION:Title: Symplectic Toric Orbifolds \nAbstract: Toric varieties are a special class of algebraic T-varieties whose geometry is encoded in convex polytopes. In addition to being interesting in its own right\, toric geometry often serves as a source simple examples where even very abstract geometric concepts manifest in concrete and explicit ways. For example\, the cohomology ring and usual characteristic classes of a smooth complete toric variety admit simple descriptions in terms of the combinatorics of the associated polytope. This talk concerns a subset of toric varieties with extremely mild singularities that appear in both algebraic and differential symplectic geometry. The main result is Delzant’s theorem\, which establishes a correspondence between symplectic toric manifolds and Delzant polytopes. The talk focuses on the differential side of the story\, so no knowledge of algebraic geometry will be assumed. Basic manifold theory will be taken for granted\, but relevant concepts from symplectic geometry will be summarized. While prior knowledge of symplectic geometry and orbifolds would be helpful\, none will be assumed.
URL:https://math.unc.edu/event/yiyan-shou-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20200203T160000
DTEND;TZID=America/New_York:20200203T170000
DTSTAMP:20221129T122821
CREATED:20200130T144102Z
LAST-MODIFIED:20200130T144102Z
UID:6129-1580745600-1580749200@math.unc.edu
SUMMARY:Ben Walker - Applied GMA Seminar
DESCRIPTION:Title: Emergent Clustering from Pairwise Interactions in Polymer Genome Models \nAbstract: The physical organization of chromosomes is known to be vital to cell function. Highly efficient compaction is achieved through various means\, including histones\, loop extrusion\, and crosslinking. Prior work using a polymer bead-chain model of the nucleolus found that rapid crosslinking created multiscale structure\, with pairwise bonds creating clusters creating nucleolar compaction and segregation. I explore this relationship\, revealing the presence of an additional intermediate timescale that maximizes mixing. I present a network approach for leveraging temporal data to identify spatio-temporal clusters in the data. I further consider the problem of finding an effective energy landscape and temperature to explain the clustering dynamics as transmission over energy barriers. Naive averaging of the random crosslinking overestimates the barrier height; I propose an alternative inverse problem approach\, and plan to apply use this technique to obtain estimates of clustering stability in future work.
URL:https://math.unc.edu/event/ben-walker-applied-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191118T160000
DTEND;TZID=America/New_York:20191118T170000
DTSTAMP:20221129T122821
CREATED:20191114T164239Z
LAST-MODIFIED:20191114T164239Z
UID:5907-1574092800-1574096400@math.unc.edu
SUMMARY:Dylan Bruney - GMA Seminar
DESCRIPTION:Title: Data-driven Mesh Optimization for Staggered-grid Lagrangian Hydrodynamics \nAbstract: The Euler equations are used in many industrial applications to model gas dynamics\, but face a multitude of numerical issues. The foremost of which is the development of shock-waves\, at which finite difference schemes produce large errors. One solution is the use of an artificial viscosity; however\, this also necessitates high resolution at the shock interface. For a Lagrangian scheme that tracks the movement of fluid parcels\, we get the benefit of a mesh that naturally adapts to the evolution of the PDE and gives us that necessary resolution\, but we also open up the near limitless number of choices of which fluid parcels to track. The presentation will explore how to choose these nodes in the most numerically cost effective manner.
URL:https://math.unc.edu/event/dylan-bruney-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191111T160000
DTEND;TZID=America/New_York:20191111T170000
DTSTAMP:20221129T122821
CREATED:20191108T154847Z
LAST-MODIFIED:20191108T154847Z
UID:5885-1573488000-1573491600@math.unc.edu
SUMMARY:Hunter Dinkins - GMA Seminar
DESCRIPTION:Title: Bundle up\, it’s cold outside! \nAbstract: Vector bundles are an important part of modern math\, as they provide us with valuable geometric information and allow us to name natural classes in the cohomology of the space over which they live. In this talk\, I will define vector bundles\, provide many examples\, and discuss some of their important properties. Time permitting\, we will also give a gentle and non-rigorous discussion of K-theory. This talk is intended for first and second years who have not had much (if any) exposure to vector bundles.
URL:https://math.unc.edu/event/hunter-dinkins-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191104T160000
DTEND;TZID=America/New_York:20191104T170000
DTSTAMP:20221129T122821
CREATED:20191101T211929Z
LAST-MODIFIED:20191101T211929Z
UID:5866-1572883200-1572886800@math.unc.edu
SUMMARY:Wesley Hamilton - GMA Seminar
DESCRIPTION:Title: Homology: Redux \nAbstract: Topological Data Analysis (TDA) is a relatively recent area of applied topology\, in which tools from algebraic topology are used to understand the topology of data sets. The TDA pipeline is\, in short\, the following: a simplicial complex (to be defined) is associated to the data set\, the persistent homology (to be defined) is computed\, and the collection of birth/death times of topological features/the barcode (to be defined) is reported. During this talk\, we’ll define all of the terms above and see a few instances of TDA in action. In particular\, we’ll see a number of different ways for constructing simplicial complexes (specialized to different types of data)\, how to interpret barcodes\, and finally some results on the statistics of barcodes. No previous TDA or algebraic topology experience is required.
URL:https://math.unc.edu/event/wesley-hamilton-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191029T160000
DTEND;TZID=America/New_York:20191029T170000
DTSTAMP:20221129T122821
CREATED:20191011T171816Z
LAST-MODIFIED:20191011T171816Z
UID:5808-1572364800-1572368400@math.unc.edu
SUMMARY:Wesley Hamilton - Part 2: Optimal Transport and Discrete/Continuum Laplacians - Advanced GMA Seminar
DESCRIPTION:Title: Optimal Transport and Discrete/Continuum Laplacians \nAbstract: In the past 20 years\, spectral methods have shown to be increasingly effective at a wide variety of data analytic problems. These spectral methods usually involve a graph Laplacian constructed from the data points\, which behaves like a discrete version of the familiar (second order differential operator) continuum Laplacian. Since we’re primarily interested in the spectrum of the graph Laplacian\, a natural question is: if we take a denser and denser sampling\, does the spectrum of the graph Laplacian converge to the spectrum of the continuum Laplacian? In this series of lectures\, we’ll see that we do indeed have convergence of the spectrum from the discrete to continuum setting. Moreover\, we’ll see that the graph Laplacian’s eigenvectors also converge (in an appropriate sense) to the continuum Laplacian’s eigenfunctions: the fact that discrete eigenstuff converges to the corresponding continuum eigenstuff is what we call consistency. Lecture 1 will provide an overview of the types of consistency problems that arise and have been studied\, as well as some applications. In lecture 2\, we’ll focus on pointwise convergence results\, including an analysis of the classic Laplacian Eigenmap algorithm and its related constructions. Lecture 3 (and onwards) will take a variational point of view\, using an optimal transport framework to get similar convergence results. This new framework will also let us determine the consistency of other graph operators\, such as the graph cut converging to arclength\, and the graph total variation converging to Dirichlet energy.
URL:https://math.unc.edu/event/wesley-hamilton-part-2-optimal-transport-and-discrete-continuum-laplacians-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191022T160000
DTEND;TZID=America/New_York:20191022T170000
DTSTAMP:20221129T122821
CREATED:20191011T171733Z
LAST-MODIFIED:20191011T171733Z
UID:5806-1571760000-1571763600@math.unc.edu
SUMMARY:Wesley Hamilton - Part 1: Optimal Transport and Discrete/Continuum Laplacians - Advanced GMA Seminar
DESCRIPTION:Title: Optimal Transport and Discrete/Continuum Laplacians \nAbstract: In the past 20 years\, spectral methods have shown to be increasingly effective at a wide variety of data analytic problems. These spectral methods usually involve a graph Laplacian constructed from the data points\, which behaves like a discrete version of the familiar (second order differential operator) continuum Laplacian. Since we’re primarily interested in the spectrum of the graph Laplacian\, a natural question is: if we take a denser and denser sampling\, does the spectrum of the graph Laplacian converge to the spectrum of the continuum Laplacian? In this series of lectures\, we’ll see that we do indeed have convergence of the spectrum from the discrete to continuum setting. Moreover\, we’ll see that the graph Laplacian’s eigenvectors also converge (in an appropriate sense) to the continuum Laplacian’s eigenfunctions: the fact that discrete eigenstuff converges to the corresponding continuum eigenstuff is what we call consistency. Lecture 1 will provide an overview of the types of consistency problems that arise and have been studied\, as well as some applications. In lecture 2\, we’ll focus on pointwise convergence results\, including an analysis of the classic Laplacian Eigenmap algorithm and its related constructions. Lecture 3 (and onwards) will take a variational point of view\, using an optimal transport framework to get similar convergence results. This new framework will also let us determine the consistency of other graph operators\, such as the graph cut converging to arclength\, and the graph total variation converging to Dirichlet energy.
URL:https://math.unc.edu/event/wesley-hamilton-part-1-optimal-transport-and-discrete-continuum-laplacians-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191014T160000
DTEND;TZID=America/New_York:20191014T170000
DTSTAMP:20221129T122821
CREATED:20191011T172823Z
LAST-MODIFIED:20191011T172823Z
UID:5817-1571068800-1571072400@math.unc.edu
SUMMARY:Andrew Ford - Coarse-grained biological simulations: Representing biological systems using molecular dynamics - GMA Seminar
DESCRIPTION:Title: Coarse-grained biological simulations: Representing biological systems using molecular dynamics \nAbstract: At the intersection of biology and data science\, there is a need for simulations of small-scale biological processes. Even as imaging technology continues to improve\, biologists still look to simulations to generate larger amounts of data than experiments alone can provide. Through software packages originally developed for molecular dynamics in physics and chemistry\, mathematicians can model\, simulate\, and analyze functions within the cells of living organisms in order to help biologists gain a greater understanding of the dynamics which underlie them. This talk is intended to provide a background on the usage of molecular dynamics in biological simulations\, and will also cover the usage of these concepts in my own research on chromosome and mucus modeling.
URL:https://math.unc.edu/event/andrew-ford-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191008T160000
DTEND;TZID=America/New_York:20191008T170000
DTSTAMP:20221129T122821
CREATED:20191004T164643Z
LAST-MODIFIED:20191004T164643Z
UID:5772-1570550400-1570554000@math.unc.edu
SUMMARY:Blake Keeler - Part 4: Spectral Asymptotics and the Heat Kernel - Advanced GMA Seminar
DESCRIPTION:Part 4: Spectral Asymptotics and the Heat Kernel. \nAbstract: In this lecture series\, our goal will be to prove a result known as Weyl’s law\, which tells us how the Laplace eigenvalues of a compact manifold are distributed. Since eigenvalues are inherently quite difficult to study\, we will utilize a “back-door” approach via the heat equation. The heat kernel can be constructed using fairly classical techniques\, and much of our time will be spent exploring its properties and using it to develop the spectral theory of the Laplacian. Lecture 1 will cover some preliminary concepts. We begin with a brief overview of the heat equation in Euclidean space\, which will inform our intuition for what we expect on manifolds. We will then extend our notion of the Laplacian to Riemannian manifolds\, which will allow us to write down an associated heat equation. Then\, under the assumption that a fundamental solution to this heat equation exists\, we will be able to show that the Laplacian has discrete spectrum and an associated orthonormal basis of eigenfunctions in L^2(M). In lecture 2\, we will show that the heat kernel exists by actually constructing it. As a consequence of the construction\, we will have an asymptotic expansion of the kernel for small timescales. In lecture 3\, we will connect the heat trace to the distribution of eigenvalues using the Karamata Tauberian theorem\, and Weyl’s law will follow as a straightforward corollary. Time permitting\, we will also discuss some generalizations of Weyl’s law and improvements that can be made in the error term\, as well as some relevant current research.
URL:https://math.unc.edu/event/blake-keeler-part-4-spectral-asymptotics-and-the-heat-kernel-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20191001T160000
DTEND;TZID=America/New_York:20191001T170000
DTSTAMP:20221129T122821
CREATED:20190926T133059Z
LAST-MODIFIED:20190926T133059Z
UID:5740-1569945600-1569949200@math.unc.edu
SUMMARY:Blake Keeler - Part 3: Spectral Asymptotics and the Heat Kernel - Advanced GMA Seminar
DESCRIPTION:Part 3: Spectral Asymptotics and the Heat Kernel. \nAbstract: In this lecture series\, our goal will be to prove a result known as Weyl’s law\, which tells us how the Laplace eigenvalues of a compact manifold are distributed. Since eigenvalues are inherently quite difficult to study\, we will utilize a “back-door” approach via the heat equation. The heat kernel can be constructed using fairly classical techniques\, and much of our time will be spent exploring its properties and using it to develop the spectral theory of the Laplacian. Lecture 1 will cover some preliminary concepts. We begin with a brief overview of the heat equation in Euclidean space\, which will inform our intuition for what we expect on manifolds. We will then extend our notion of the Laplacian to Riemannian manifolds\, which will allow us to write down an associated heat equation. Then\, under the assumption that a fundamental solution to this heat equation exists\, we will be able to show that the Laplacian has discrete spectrum and an associated orthonormal basis of eigenfunctions in L^2(M). In lecture 2\, we will show that the heat kernel exists by actually constructing it. As a consequence of the construction\, we will have an asymptotic expansion of the kernel for small timescales. In lecture 3\, we will connect the heat trace to the distribution of eigenvalues using the Karamata Tauberian theorem\, and Weyl’s law will follow as a straightforward corollary. Time permitting\, we will also discuss some generalizations of Weyl’s law and improvements that can be made in the error term\, as well as some relevant current research.
URL:https://math.unc.edu/event/blake-keeler-part-3-spectral-asymptotics-and-the-heat-kernel-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190930T160000
DTEND;TZID=America/New_York:20190930T170000
DTSTAMP:20221129T122821
CREATED:20190926T185309Z
LAST-MODIFIED:20190926T185309Z
UID:5744-1569859200-1569862800@math.unc.edu
SUMMARY:Bradley Hicks - Hilbert's Third Problem and the Dehn Invariant - GMA Seminar
DESCRIPTION:Title: Hilbert’s Third Problem and the Dehn Invariant \nAbstract: Of Hilbert’s 23 problems posed in 1900 the third was resolved first a year later by Max Dehn. It was settled by Dehn’s construction of an algebraic invariant that detects when two polyhedra are not scissors-congruent to each other. This was just one early example of new algebraic approaches to attack geometric problems. While Dehn’s invariant applied only to polyhedra in 3 dimensional Euclidean space it has been generalized to higher dimensions and to polyhedra in different geometries (Spherical and Hyperbolic)\, and has been connected to ideas in K Theory. For the majority of this talk I will give a laid back presentation of the original question\, its motivation\, and solution by Dehn\, which can be laid out very basically only requiring a familiarity with tensor products of Z-modules. Time permitting I will also show how the problem has been modernized and how the Dehn Invariant is connected to more modern notions.
URL:https://math.unc.edu/event/bradley-hicks-hilberts-third-problem-and-the-dehn-invariant-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190919T160000
DTEND;TZID=America/New_York:20190919T170000
DTSTAMP:20221129T122821
CREATED:20190911T184055Z
LAST-MODIFIED:20190911T184055Z
UID:5705-1568908800-1568912400@math.unc.edu
SUMMARY:Josh Kiers - A survey of the BGG description of cohomology of flag varieties\, with applications\, Part 4 - Advanced GMA Seminar
DESCRIPTION:Part 4: A survey of the BGG description of cohomology of flag varieties\, with applications \nAbstract: In these lectures we will follow the original paper of Bernstein\, Gel’fand\, and Gel’fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology of flag varieties W-equivariantly with certain (sub)quotients of explicit polynomial rings. We will develop the Lie combinatorics necessary to identify (and prove) “good” polynomial representatives with their Schubert class counterparts\, along the way introducing the Bruhat order and the famous divided-difference operators. We will develop an “integration” formula by way of application\, and I will explain how I used this in a crucial way for computer verification of two new instances of the Saturation Conjecture.
URL:https://math.unc.edu/event/josh-kiers-a-survey-of-the-bgg-description-of-cohomology-of-flag-varieties-with-applications-part-4-advanced-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190917T160000
DTEND;TZID=America/New_York:20190917T170000
DTSTAMP:20221129T122821
CREATED:20190909T154404Z
LAST-MODIFIED:20190909T154404Z
UID:5700-1568736000-1568739600@math.unc.edu
SUMMARY:Blake Keeler - Spectral Asymptotics and the Heat Kernel - Advanced GMA Seminar
DESCRIPTION:Title: Spectral Asymptotics and the Heat Kernel. \nAbstract: In this lecture series\, our goal will be to prove a result known as Weyl’s law\, which tells us how the Laplace eigenvalues of a compact manifold are distributed. Since eigenvalues are inherently quite difficult to study\, we will utilize a “back-door” approach via the heat equation. The heat kernel can be constructed using fairly classical techniques\, and much of our time will be spent exploring its properties and using it to develop the spectral theory of the Laplacian. Lecture 1 will cover some preliminary concepts. We begin with a brief overview of the heat equation in Euclidean space\, which will inform our intuition for what we expect on manifolds. We will then extend our notion of the Laplacian to Riemannian manifolds\, which will allow us to write down an associated heat equation. Then\, under the assumption that a fundamental solution to this heat equation exists\, we will be able to show that the Laplacian has discrete spectrum and an associated orthonormal basis of eigenfunctions in L^2(M). In lecture 2\, we will show that the heat kernel exists by actually constructing it. As a consequence of the construction\, we will have an asymptotic expansion of the kernel for small timescales. In lecture 3\, we will connect the heat trace to the distribution of eigenvalues using the Karamata Tauberian theorem\, and Weyl’s law will follow as a straightforward corollary. Time permitting\, we will also discuss some generalizations of Weyl’s law and improvements that can be made in the error term\, as well as some relevant current research.
URL:https://math.unc.edu/event/blake-keeler-spectral-asymptotics-and-the-heat-kernel-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190916T160000
DTEND;TZID=America/New_York:20190916T170000
DTSTAMP:20221129T122821
CREATED:20190916T135117Z
LAST-MODIFIED:20190916T135117Z
UID:5722-1568649600-1568653200@math.unc.edu
SUMMARY:Sam Jeralds - GMA Seminar
DESCRIPTION:Title: Categories\, and Why You Shouldn’t Be Afraid of Them \nAbstract: Developed in the early 1940s\, category theory offers a powerful\, universally applicable set of tools in many fields of mathematics. However\, in part due to its generality and how we discuss it\, category theory can often seem intimidating to the uninitiated. In this casual talk\, designed for those with little to no exposure to the topic\, we will discuss the basic vocabulary and ideas in category theory alongside plentiful examples and applications.
URL:https://math.unc.edu/event/sam-jeralds-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190910T160000
DTEND;TZID=America/New_York:20190910T170000
DTSTAMP:20221129T122821
CREATED:20190905T202503Z
LAST-MODIFIED:20190905T202503Z
UID:5694-1568131200-1568134800@math.unc.edu
SUMMARY:Josh Kiers - A survey of the BGG description of cohomology of flag varieties\, with applications\, Part 3 - Advanced GMA Seminar
DESCRIPTION:Part 3: A survey of the BGG description of cohomology of flag varieties\, with applications \nAbstract: In these lectures we will follow the original paper of Bernstein\, Gel’fand\, and Gel’fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology of flag varieties W-equivariantly with certain (sub)quotients of explicit polynomial rings. We will develop the Lie combinatorics necessary to identify (and prove) “good” polynomial representatives with their Schubert class counterparts\, along the way introducing the Bruhat order and the famous divided-difference operators. We will develop an “integration” formula by way of application\, and I will explain how I used this in a crucial way for computer verification of two new instances of the Saturation Conjecture.
URL:https://math.unc.edu/event/josh-kiers-a-survey-of-the-bgg-description-of-cohomology-of-flag-varieties-with-applications-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190909T160000
DTEND;TZID=America/New_York:20190909T170000
DTSTAMP:20221129T122821
CREATED:20190906T123258Z
LAST-MODIFIED:20190906T123258Z
UID:5697-1568044800-1568048400@math.unc.edu
SUMMARY:Claire Kiers - Rate-induced Tipping in Maps - GMA Seminar
DESCRIPTION:Title: Rate-induced Tipping in Maps \nAbstract: The study of dynamical systems can be divided into two main categories: continuous-time (flows) and discrete-time (maps). Although these types of systems are defined differently\, we look for the same kinds of features in both of them. Rate-induced tipping is one phenomenon that has been well-studied in flows\, and so we might expect a similar thing to happen in maps. In this talk\, I will share my work on defining rate-induced tipping in maps and developing some of the basic theory in that setting. Time-permitting\, we will also look at how results about rate-induced tipping are different between maps and flows\, due to the fundamental differences between these types of systems.
URL:https://math.unc.edu/event/claire-kiers-rate-induced-tipping-in-maps-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190903T160000
DTEND;TZID=America/New_York:20190903T170000
DTSTAMP:20221129T122821
CREATED:20190829T144146Z
LAST-MODIFIED:20190829T144146Z
UID:5674-1567526400-1567530000@math.unc.edu
SUMMARY:Josh Kiers - A survey of the BGG description of cohomology of flag varieties\, with applications - Advanced GMA Seminar
DESCRIPTION:Part 2: A survey of the BGG description of cohomology of flag varieties\, with applications \nAbstract: In these lectures we will follow the original paper of Bernstein\, Gel’fand\, and Gel’fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology of flag varieties W-equivariantly with certain (sub)quotients of explicit polynomial rings. We will develop the Lie combinatorics necessary to identify (and prove) “good” polynomial representatives with their Schubert class counterparts\, along the way introducing the Bruhat order and the famous divided-difference operators. We will develop an “integration” formula by way of application\, and I will explain how I used this in a crucial way for computer verification of two new instances of the Saturation Conjecture.
URL:https://math.unc.edu/event/josh-kiers-advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20190827T160000
DTEND;TZID=America/New_York:20190827T170000
DTSTAMP:20221129T122821
CREATED:20190827T160733Z
LAST-MODIFIED:20190827T160733Z
UID:5668-1566921600-1566925200@math.unc.edu
SUMMARY:Advanced GMA Seminar - Speaker: Josh Kiers - A survey of the BGG description of cohomology of flag varieties\, with applications
DESCRIPTION:Speaker: Josh Kiers \nPart 1: A survey of the BGG description of cohomology of flag varieties\, with applications \nAbstract: In these lectures we will follow the original paper of Bernstein\, Gel’fand\, and Gel’fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology of flag varieties W-equivariantly with certain (sub)quotients of explicit polynomial rings. We will develop the Lie combinatorics necessary to identify (and prove) “good” polynomial representatives with their Schubert class counterparts\, along the way introducing the Bruhat order and the famous divided-difference operators. We will develop an “integration” formula by way of application\, and I will explain how I used this in a crucial way for computer verification of two new instances of the Saturation Conjecture.
URL:https://math.unc.edu/event/advanced-gma-seminar/
LOCATION:metcalf_jason
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181119T160000
DTEND;TZID=America/New_York:20181119T170000
DTSTAMP:20221129T122821
CREATED:20181116T164523Z
LAST-MODIFIED:20181116T164523Z
UID:4905-1542643200-1542646800@math.unc.edu
SUMMARY:Brian Adam\, UNC-Chapel Hill - GMA & Visions Seminar
DESCRIPTION:Title: Building equations one molecule at a time \nAbstract: I work on multiscale models of the cytoskeleton\, a system of proteins that ultimately give biological cells their mechanical properties. At the molecular level\, there is a bewildering amount of complexity\, regulatory feedback\, and redundancy. Making such a system mathematically tractable is a tall order\, but one can start by considering much simpler models of interacting particles. In this talk\, we’ll examine such a simple system composed rigid rods suspended in a fluid from introductory polymer physics/complex fluids. We’ll go through the derivation of the stress tensor for the macroscopic system highlighting the key statistical mechanics ideas and tools that can be used in analyzing more complex systems.
URL:https://math.unc.edu/event/brian-adam-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181112T160000
DTEND;TZID=America/New_York:20181112T170000
DTSTAMP:20221129T122821
CREATED:20181108T185546Z
LAST-MODIFIED:20181108T185546Z
UID:4889-1542038400-1542042000@math.unc.edu
SUMMARY:Blake Keeler\, UNC-Chapel Hill - GMA & Visions Seminar
DESCRIPTION:Title: Diagonalizing the Laplacian – A Tourist’s Guide to Spectral Theory \nAbstract: This talk is aimed at first and second year grad students who are interested in analysis\, or really anyone with a passing curiosity about what analysts do all day besides fiddle with epsilons and deltas. It will be a (hopefully) gentle introduction to some basic notions that we consider in the spectral theory of operators. Spectral theory is motivated by what we know about eigenvalues and eigenvectors for finite dimensional operators\, i.e. matrices. We will be exploring to what extent some of the properties of eigenvalues and eigenvectors of matrices carry over to operators on infinite dimensional spaces. In particular\, we will examine the notion of diagonalizing an operator in a “basis of eigenvectors\,” whatever that means for an infinite dimensional object. In fact\, we will focus on the very special operator known as the Laplacian. There is a very concrete and straightforward way to understand the concept of diagonalization for this operator acting on functions on a compact domain\, but it will be much more subtle if we consider the Laplacian on all of R^n. My goal will be to highlight both the differences and similarities in the spectral properties of the Laplacian in these two cases.
URL:https://math.unc.edu/event/blake-keeler-unc-chapel-hill-gma-visions-seminar-2/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181015T160000
DTEND;TZID=America/New_York:20181015T170000
DTSTAMP:20221129T122821
CREATED:20181015T131304Z
LAST-MODIFIED:20181015T131304Z
UID:4782-1539619200-1539622800@math.unc.edu
SUMMARY:Samuel Jeralds\, UNC-Chapel Hill - GMA & Visions Seminar
DESCRIPTION:381 Phillips Hall\, 4:00 pm – 5:00 pm \nSpeaker: Samuel Jeralds\, UNC Chapel Hill \nTitle: A Gentle Introduction to Affine (and other) Lie Algebras \nAbstract: Affine Lie algebras are certain infinite-dimensional partners to the more familiar finite-dimensional semisimple Lie algebras. The goal of this talk is to give a gentle introduction to the construction and structure of the affine algebras\, and related results. We will begin with an overview of the necessary results and definitions in the finite case\, so those without any prior exposure to Lie algebras are also especially encouraged to attend.
URL:https://math.unc.edu/event/samuel-jeralds-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20181001T160000
DTEND;TZID=America/New_York:20181001T170000
DTSTAMP:20221129T122821
CREATED:20180926T130806Z
LAST-MODIFIED:20180926T130806Z
UID:4719-1538409600-1538413200@math.unc.edu
SUMMARY:Colin Guider\, UNC Chapel Hill - GMA & Visions Seminar
DESCRIPTION:Title: Data Assimilation with an Application to Sea Ice Modelling \nAbstract: The abundance of oceanic and atmospheric data presents the question of how to incorporate this data into scientific models. Data assimilation is the process by which observations are fused with these models. We consider both variational and statistical approaches to data assimilation\, which are equivalent under reasonable assumptions. We then derive the Kalman filter\, one of the most famous and useful algorithms in the field. A practical implementation of this process\, the Ensemble Kalman Filter (EnKF)\, can be modified for use in neXtSIM\, an arctic sea ice model.
URL:https://math.unc.edu/event/colin-guider-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180924T160000
DTEND;TZID=America/New_York:20180924T170000
DTSTAMP:20221129T122821
CREATED:20180906T190508Z
LAST-MODIFIED:20180906T190508Z
UID:4657-1537804800-1537808400@math.unc.edu
SUMMARY:Logan Tatham - GMA & Vision's Seminar
DESCRIPTION:Title: The Jones Polynomial and Representation Theory \nAbstract: In this talk\, I’ll briefly introduce knots and links. Then\, I’ll introduce the Jones Polynomial\, an invariant of knots and links. Finally\, I’ll show the connection between the Jones Polynomial and the representation theory of (quantum) sl2.
URL:https://math.unc.edu/event/colin-thompson-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180907T153000
DTEND;TZID=America/New_York:20180907T163000
DTSTAMP:20221129T122821
CREATED:20180831T200626Z
LAST-MODIFIED:20180831T200626Z
UID:4633-1536334200-1536337800@math.unc.edu
SUMMARY:NSA Representatives - GMA & Visions Seminar
DESCRIPTION:Joint GMA & Visions/STOR Seminar \n120 Hanes Hall\, 3:30 – 4:30 pm \nTitle: Summer Program for Operations Research Technology (SPORT) \nSpeaker: NSA Representatives \nAbstract: SPORT is a 12-week *PAID* summer internship offered by the National Security Agency (NSA) that provides 8 U.S. Citizen graduate students the opportunity to apply their technical skills to current\, real-world operations research problems at the NSA. SPORT looks for strong students in operations research\, applied math\, statistics\, data science\, and other related fields. \nProgram Highlights: \n\nPaid internship (12 weeks\, late May to mid-August 2019)\nApplications accepted September 1 – October 31\, 2018\nOpportunity to apply operations research\, mathematics\, statistics\, computer science\, and/or engineering skills\nReal NSA mission problems\nPaid annual and sick leave\, housing available\nFlexible work schedule\nOpportunity to network with other Intelligence Agencies\n\nNote: Anyone is welcome to attend the presentation\, but the SPORT program is only open to U.S. citizen graduate students who are graduating December 2019 or later.
URL:https://math.unc.edu/event/nsa-representatives-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180907T153000
DTEND;TZID=America/New_York:20180907T163000
DTSTAMP:20221129T122821
CREATED:20180831T200626Z
LAST-MODIFIED:20180831T200626Z
UID:8940-1536334200-1536337800@math.unc.edu
SUMMARY:NSA Representatives - GMA & Visions Seminar
DESCRIPTION:Joint GMA & Visions/STOR Seminar \n120 Hanes Hall\, 3:30 – 4:30 pm \nTitle: Summer Program for Operations Research Technology (SPORT) \nSpeaker: NSA Representatives \nAbstract: SPORT is a 12-week *PAID* summer internship offered by the National Security Agency (NSA) that provides 8 U.S. Citizen graduate students the opportunity to apply their technical skills to current\, real-world operations research problems at the NSA. SPORT looks for strong students in operations research\, applied math\, statistics\, data science\, and other related fields. \nProgram Highlights: \n\nPaid internship (12 weeks\, late May to mid-August 2019)\nApplications accepted September 1 – October 31\, 2018\nOpportunity to apply operations research\, mathematics\, statistics\, computer science\, and/or engineering skills\nReal NSA mission problems\nPaid annual and sick leave\, housing available\nFlexible work schedule\nOpportunity to network with other Intelligence Agencies\n\nNote: Anyone is welcome to attend the presentation\, but the SPORT program is only open to U.S. citizen graduate students who are graduating December 2019 or later.
URL:https://math.unc.edu/event/nsa-representatives-gma-visions-seminar-3/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20171002T160000
DTEND;TZID=America/New_York:20171002T170000
DTSTAMP:20221129T122821
CREATED:20170929T192046Z
LAST-MODIFIED:20170929T192046Z
UID:3645-1506960000-1506963600@math.unc.edu
SUMMARY:Yuan Gao (UNC Chapel Hill)\, GMA & Visions Seminar
DESCRIPTION:Title: Limiting dynamics of Metropolis-Hastings algorithm applied to n-vector spin model \nAbstract: The n-vector spin model is a simple system of interacting spins on a crystalline lattice with a Hamiltonian given by the interaction of nearest neighbors. The corresponding Gibbs distribution could be sampled by a Metropolis-Hastings (M-H) algorithm. It is also natural to think one could model the spin dynamics by a system of over-damped Langevin-type equations. When the number of spins goes to infinity\, the limiting Hamiltonian is in the form of the energy to give harmonic map heat flow. In the case n equals 3\, the model is used to describe ferromagnetism. It is also shown that the harmonic map heat flow equation on the unit sphere has the same form as Landau-Lifshitz equation of the ferromagnetic spin chain. \nWe are interested in understanding the relationship between these models and will show the result for the n=3 case from the 1D torus to the unit sphere. In the limit of decreasing proposal size\, we show that the M-H dynamics converge to a Langevin type stochastic differential equation. (Here\, a Stratonovich interpretation is used due to the geometric constraint of the sphere for each spin.) Then we will show that as the lattice size gets larger and a suitable scaling is chosen for the temperature in the Gibbs distribution and M-H proposal size\, the M-H dynamics converge to the deterministic Landau-Lifshitz equation\, a PDE describing the time evolution of magnetism.
URL:https://math.unc.edu/event/yuan-gao-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170925T160000
DTEND;TZID=America/New_York:20170925T160000
DTSTAMP:20221129T122821
CREATED:20170922T122746Z
LAST-MODIFIED:20170922T122746Z
UID:3615-1506355200-1506355200@math.unc.edu
SUMMARY:Blake Keeler (UNC Chapel Hill)\, GMA & Visions Seminar
DESCRIPTION:Title: Fluid-Construction of the Hadamard Parametrix for the Wave Operator on a Riemannian Manifold \nAbstract: A common object of interest in the study of PDEs is the fundamental solution of a differential operator. A fundamental solution allows one to invert the differential operator in question. In Euclidean space one can explicitly construct fundamental solutions for the wave operator\, but on a general Riemannian manifold the wave operator has variable coefficients\, and it is therefore much more difficult to construct a true fundamental solution. Thus\, we look for the next best thing\, called a parametrix\, which is an approximate inverse to the wave operator in the sense that if we apply the wave operator to the parametrix\, we obtain the identity map plus an operator which has smooth kernel. We will demonstrate a method for explicitly constructing this parametrix as a combination of increasingly smooth distributions associated with the flat wave operator which have useful recursion properties. \nLocation: Phillips Hall 381\, 4:00 pm – 5:00 pm
URL:https://math.unc.edu/event/blake-keeler-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170918T160000
DTEND;TZID=America/New_York:20170918T170000
DTSTAMP:20221129T122821
CREATED:20170915T130059Z
LAST-MODIFIED:20170915T130059Z
UID:3593-1505750400-1505754000@math.unc.edu
SUMMARY:Jae Ho Lee (UNC Chapel Hill)\, GMA & Visions Seminar
DESCRIPTION:Title: Fluid-structure interaction (FSI) model of in vitro left ventricle model \nAbstract: Cardiovascular diseases (CVD) such as stroke\, heart failure\, and sudden cardiac death are the leading cause of death in the U.S. In 2013\, CVD accounted for more than 17.3 million deaths globally\, and this number is expected to grow to over 23.6 million by 2030. Computational modeling and simulation became increasingly useful in medical device design and surgical planning. The ultimate goal is to develop experimentally validated IBAMR-based fluid-structure interaction (FSI) models for developing optimal design and regulation for cardiovascular devices and improvement ins surgical planning. However\, Experimentally validated computational models of cardiac FSI are lacking\, and before such models can be widely deployed\, substantial experimental and clinical validation is required. As an initial step\, we focus on experimental validation of computational models of left ventricle (LV) model whose experimental result for the intraventricular fluid dynamics is readily available to compare to. In this talk\, we will look at experimental and computational approaches\, modeling\, and some benchmark problems that will help answer questions that arise from this project.
URL:https://math.unc.edu/event/jae-ho-lee-unc-chapel-hill-gma-visions-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170424T160000
DTEND;TZID=America/New_York:20170424T170000
DTSTAMP:20221129T122821
CREATED:20170424T155548Z
LAST-MODIFIED:20170424T155548Z
UID:3307-1493049600-1493053200@math.unc.edu
SUMMARY:Paul Kruse (UNC-CH)\, GMA Seminar
DESCRIPTION:Title: An introduction to Cobordism. \n \nAbstract: The classification of manifolds has long been an active area of research. One of the many techniques developed was cobordism\, first introduced by Poincare. Pontrjagin and Thom then connected this to the stable homotopy problem. In the first half of this talk\, I will introduce the idea of a cobordism category. In the second half\, I will describe the link between the cobordism problem and the stable homotopy problem.
URL:https://math.unc.edu/event/paul-kruse-unc-ch-gma-seminar/
CATEGORIES:GMA Seminar
END:VEVENT
END:VCALENDAR