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CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA
A MERICAN M ATHEMATICAL S OCIETY CURRENT EVENTS BULLETIN Friday, January 8, 2016, 1:00 PM to 5:00 PM Room 4C-3 Washington State Convention Center Joint Mathematics Meetings, Seattle, WA 1:00 PM Carina Curto, Pennsylvania State University What can topology tell us about the neural code? Surprising new applications of what used to be thought of as “pure” mathematics. 2:00 PM Yuval Peres, Microsoft Research and University of California, Berkeley, and Lionel Levine, Cornell University Laplacian growth, sandpiles and scaling limits Striking large-scale structure arising from simple cellular automata. 3:00 PM Timothy Gowers, Cambridge University Probabilistic combinatorics and the recent work of Peter Keevash The major existence conjecture for combinatorial designs has been proven! 4:00 PM Amie Wilkinson, University of Chicago What are Lyapunov exponents, and why are they interesting? A basic tool in understanding the predictability of physical systems, explained. Organized by David Eisenbud, Mathematical Sciences Research Institute Introduction to the Current Events Bulletin Will the Riemann Hypothesis be proved this week? What is the Geometric Langlands Conjecture about? How could you best exploit a stream of data flowing by too fast to capture? I think we mathematicians are provoked to ask such questions by our sense that underneath the vastness of mathematics is a fundamental unity allowing us to look into many different corners -- though we couldn't possibly work in all of them. I love the idea of having an expert explain such things to me in a brief, accessible way. And I, like most of us, love common-room gossip. -
I. Overview of Activities, April, 2005-March, 2006 …
MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights -
What Are Lyapunov Exponents, and Why Are They Interesting?
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54, Number 1, January 2017, Pages 79–105 http://dx.doi.org/10.1090/bull/1552 Article electronically published on September 6, 2016 WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING? AMIE WILKINSON Introduction At the 2014 International Congress of Mathematicians in Seoul, South Korea, Franco-Brazilian mathematician Artur Avila was awarded the Fields Medal for “his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.”1 Although it is not explicitly mentioned in this citation, there is a second unify- ing concept in Avila’s work that is closely tied with renormalization: Lyapunov (or characteristic) exponents. Lyapunov exponents play a key role in three areas of Avila’s research: smooth ergodic theory, billiards and translation surfaces, and the spectral theory of 1-dimensional Schr¨odinger operators. Here we take the op- portunity to explore these areas and reveal some underlying themes connecting exponents, chaotic dynamics and renormalization. But first, what are Lyapunov exponents? Let’s begin by viewing them in one of their natural habitats: the iterated barycentric subdivision of a triangle. When the midpoint of each side of a triangle is connected to its opposite vertex by a line segment, the three resulting segments meet in a point in the interior of the triangle. The barycentric subdivision of a triangle is the collection of 6 smaller triangles determined by these segments and the edges of the original triangle: Figure 1. Barycentric subdivision. Received by the editors August 2, 2016. -
Boshernitzan's Condition, Factor Complexity, and an Application
BOSHERNITZAN’S CONDITION, FACTOR COMPLEXITY, AND AN APPLICATION VAN CYR AND BRYNA KRA Abstract. Boshernitzan found a decay condition on the measure of cylin- der sets that implies unique ergodicity for minimal subshifts. Interest in the properties of subshifts satisfying this condition has grown recently, due to a connection with the study of discrete Schr¨odinger operators. Of particular interest is the question of how restrictive Boshernitzan’s condition is. While it implies zero topological entropy, our main theorem shows how to construct minimal subshifts satisfying the condition whose factor complexity grows faster than any pre-assigned subexponential rate. As an application, via a theorem of Damanik and Lenz, we show that there is no subexponentially growing se- quence for which the spectra of all discrete Schr¨odinger operators associated with subshifts whose complexity grows faster than the given sequence, have only finitely many gaps. 1. Boshernitzan’s complexity conditions For a symbolic dynamical system (X, σ), many of the isomorphism invariants we have are statements about the growth rate of the word complexity function PX (n), which counts the number of distinct cylinder sets determined by words of length n having nonempty intersection with X. For example, the exponential growth of PX (n) is the topological entropy of (X, σ), while the linear growth rate of PX (n) gives an invariant to begin distinguishing between zero entropy systems. Of course there are different senses in which the growth of PX (n) could be said to be linear and different invariants arise from them. For example, one can consider systems with linear limit inferior growth, meaning lim infn→∞ PX (n)/n < ∞, or the stronger condition of linear limit superior growth, meaning lim supn→∞ PX (n)/n < ∞. -
2007 FISCAL YEAR ANNUAL REPORT 1 Join Us in Celebrating Our
2007 FISCAL YEAR ANNUAL REPORT 1 Join us in celebrating our ANNIVERSARY In 1987, under the direction of Chancellor Dr. Bill Stewart and the leadership of Executive Director Dr. Jim Meinert, the State Center Community College Foundation was established. The mission has not changed in two decades: to encourage philanthropic gifts that directly enhance the access to and quality of community college education for the students and faculty of the district. Over the years the Foundation has provided a stepping stone out of poverty for many people who might never had sought a higher education. Providing consistent oversight is the Foundation Board of Directors, a notable group of some of the most outstanding community leaders present in the Central Valley. Today, the Foundation has $12.8 million in assets, strong leadership, and a track record of hundreds of successful students. 2 STATE CENTER COMMUNITY COLLEGE FOUNDATION Table of Chancellor’sContents Message _________________________ 4 President’s Message ___________________________ 5 Financial Statement __________________________ 6 Board of Directors ___________________________ 7 Student Success Story _________________________ 8 Renaissance Feast for Scholars __________________ 9 Powerful Facts and Figures _____________________ 9 OAB: A Legacy Renewed _____________________ 10 Friends of the Foundation ____________________11 Thank You to our Donors ____________________ 12 2007 FISCAL YEAR ANNUAL REPORT 3 Chancellor’s Message The Foundation has been making history…one student at a time…for over twenty years. Since its inception in 1987, the Foundation has grown to more than $12.8 million in assets. These funds are a direct result of the generosity our donors have shown over the years. As a supporter of the Foundation, you have demonstrated your commitment to providing educational opportu- nities for students that may not otherwise have the ability to attend. -
Harmonic Analysis and Partial Differential Equations
AMERICAN MATHEMATICAL SOCIETY 107 Harmonic Analysis and Partial Differential Equations Proceedings of a Conference held April 4-5, 1988 http://dx.doi.org/10.1090/conm/107 Titles in This Series Volume 1 Markov random fields and their 19 Proceedings of the Northwestern applications, Ross Kindermann and homotopy theory conference, Haynes J. Laurie Snell R. Miller and Stewart B. Priddy, Editors 2 Proceedings of the conference on 20 Low dimensional topology, Samuel J. integration, topology, and geometry in Lomonaco, Jr., Editor linear spaces, William H. Graves, Editor 21 Topological methods in nonlinear 3 The closed graph and P-closed functional analysis, S. P. Singh, graph properties in general topology, S. Thomaier, and B. Watson, Editors T. R. Hamlett and L. L. Herrington 22 Factorizations of b" ± 1, b = 2, 4 Problems of elastic stability and 3, 5, 6, 7, 10, 11, 12 up to high vibrations, Vadim Komkov, Editor powers, John Brillhart, D. H. Lehmer, 5 Rational constructions of modules J. L. Selfridge, Bryant Tuckerman, and for simple Lie algebras, George B. S. S. Wagstaff, Jr. Seligman 23 Chapter 9 of Ramanujan's second 6 Umbral calculus and Hopf algebras, notebook-Infinite series identities, Robert Morris, Editor transformations, and evaluations, Bruce C. Berndt and Padmini T. Joshi 7 Complex contour integral representation of cardinal spline 24 Central extensions, Galois groups, and functions, Walter Schempp ideal class groups of number fields, A. Frohlich 8 Ordered fields and real algebraic geometry, D. W. Dubois and T. Recio, 25 Value distribution theory and its Editors applications, Chung-Chun Yang, Editor 9 Papers in algebra, analysis and 26 Conference in modern analysis statistics, R. -
Apollonian Circle Packings: Dynamics and Number Theory
APOLLONIAN CIRCLE PACKINGS: DYNAMICS AND NUMBER THEORY HEE OH Abstract. We give an overview of various counting problems for Apol- lonian circle packings, which turn out to be related to problems in dy- namics and number theory for thin groups. This survey article is an expanded version of my lecture notes prepared for the 13th Takagi lec- tures given at RIMS, Kyoto in the fall of 2013. Contents 1. Counting problems for Apollonian circle packings 1 2. Hidden symmetries and Orbital counting problem 7 3. Counting, Mixing, and the Bowen-Margulis-Sullivan measure 9 4. Integral Apollonian circle packings 15 5. Expanders and Sieve 19 References 25 1. Counting problems for Apollonian circle packings An Apollonian circle packing is one of the most of beautiful circle packings whose construction can be described in a very simple manner based on an old theorem of Apollonius of Perga: Theorem 1.1 (Apollonius of Perga, 262-190 BC). Given 3 mutually tangent circles in the plane, there exist exactly two circles tangent to all three. Figure 1. Pictorial proof of the Apollonius theorem 1 2 HEE OH Figure 2. Possible configurations of four mutually tangent circles Proof. We give a modern proof, using the linear fractional transformations ^ of PSL2(C) on the extended complex plane C = C [ f1g, known as M¨obius transformations: a b az + b (z) = ; c d cz + d where a; b; c; d 2 C with ad − bc = 1 and z 2 C [ f1g. As is well known, a M¨obiustransformation maps circles in C^ to circles in C^, preserving angles between them. -
Wmc Investigation: 10-Year Analysis of Gender & Oscar
WMC INVESTIGATION: 10-YEAR ANALYSIS OF GENDER & OSCAR NOMINATIONS womensmediacenter.com @womensmediacntr WOMEN’S MEDIA CENTER ABOUT THE WOMEN’S MEDIA CENTER In 2005, Jane Fonda, Robin Morgan, and Gloria Steinem founded the Women’s Media Center (WMC), a progressive, nonpartisan, nonproft organization endeav- oring to raise the visibility, viability, and decision-making power of women and girls in media and thereby ensuring that their stories get told and their voices are heard. To reach those necessary goals, we strategically use an array of interconnected channels and platforms to transform not only the media landscape but also a cul- ture in which women’s and girls’ voices, stories, experiences, and images are nei- ther suffciently amplifed nor placed on par with the voices, stories, experiences, and images of men and boys. Our strategic tools include monitoring the media; commissioning and conducting research; and undertaking other special initiatives to spotlight gender and racial bias in news coverage, entertainment flm and television, social media, and other key sectors. Our publications include the book “Unspinning the Spin: The Women’s Media Center Guide to Fair and Accurate Language”; “The Women’s Media Center’s Media Guide to Gender Neutral Coverage of Women Candidates + Politicians”; “The Women’s Media Center Media Guide to Covering Reproductive Issues”; “WMC Media Watch: The Gender Gap in Coverage of Reproductive Issues”; “Writing Rape: How U.S. Media Cover Campus Rape and Sexual Assault”; “WMC Investigation: 10-Year Review of Gender & Emmy Nominations”; and the Women’s Media Center’s annual WMC Status of Women in the U.S. -
Resistant Vulnerability in the Marvel Cinematic Universe's Captain America
Western University Scholarship@Western Electronic Thesis and Dissertation Repository 2-15-2019 1:00 PM Resistant Vulnerability in The Marvel Cinematic Universe's Captain America Kristen Allison The University of Western Ontario Supervisor Dr. Susan Knabe The University of Western Ontario Graduate Program in Media Studies A thesis submitted in partial fulfillment of the equirr ements for the degree in Master of Arts © Kristen Allison 2019 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Other Feminist, Gender, and Sexuality Studies Commons, Other Film and Media Studies Commons, and the Women's Studies Commons Recommended Citation Allison, Kristen, "Resistant Vulnerability in The Marvel Cinematic Universe's Captain America" (2019). Electronic Thesis and Dissertation Repository. 6086. https://ir.lib.uwo.ca/etd/6086 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. Abstract Established in 2008 with the release of Iron Man, the Marvel Cinematic Universe has become a ubiquitous transmedia sensation. Its uniquely interwoven narrative provides auspicious grounds for scholarly consideration. The franchise conscientiously presents larger-than-life superheroes as complex and incredibly emotional individuals who form profound interpersonal relationships with one another. This thesis explores Sarah Hagelin’s concept of resistant vulnerability, which she defines as a “shared human experience,” as it manifests in the substantial relationships that Steve Rogers (Captain America) cultivates throughout the Captain America narrative (11). This project focuses on Steve’s relationships with the following characters: Agent Peggy Carter, Natasha Romanoff (Black Widow), and Bucky Barnes (The Winter Soldier). -
SPATIAL STATISTICS of APOLLONIAN GASKETS 1. Introduction Apollonian Gaskets, Named After the Ancient Greek Mathematician, Apollo
SPATIAL STATISTICS OF APOLLONIAN GASKETS WEIRU CHEN, MO JIAO, CALVIN KESSLER, AMITA MALIK, AND XIN ZHANG Abstract. Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the nearest neighbor spacing, pair correlation, and electrostatic energy of centers of circles from Apol- lonian gaskets. Even though the centers of these circles are not uniformly distributed in any `ambient' space, after proper normalization, all these statistics seem to exhibit some interesting limiting behaviors. 1. introduction Apollonian gaskets, named after the ancient Greek mathematician, Apollonius of Perga (200 BC), are fractal sets obtained by starting from three mutually tangent circles and iter- atively inscribing new circles in the curvilinear triangular gaps. Over the last decade, there has been a resurgent interest in the study of Apollonian gaskets. Due to its rich mathematical structure, this topic has attracted attention of experts from various fields including number theory, homogeneous dynamics, group theory, and as a consequent, significant results have been obtained. Figure 1. Construction of an Apollonian gasket For example, it has been known since Soddy [23] that there exist Apollonian gaskets with all circles having integer curvatures (reciprocal of radii). This is due to the fact that the curvatures from any four mutually tangent circles satisfy a quadratic equation (see Figure 2). Inspired by [12], [10], and [7], Bourgain and Kontorovich used the circle method to prove a fascinating result that for any primitive integral (integer curvatures with gcd 1) Apollonian gasket, almost every integer in certain congruence classes modulo 24 is a curvature of some circle in the gasket. -
Probabilistic Models on Fibre Bundles by Shan Shan
Probabilistic Models on Fibre Bundles by Shan Shan Department of Mathematics Duke University Date: Approved: Ingrid Daubechies, Supervisor Sayan Mukherjee, Chair Doug Boyer Colleen Robles Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics in the Graduate School of Duke University 2019 ABSTRACT Probabilistic Models on Fibre Bundles by Shan Shan Department of Mathematics Duke University Date: Approved: Ingrid Daubechies, Supervisor Sayan Mukherjee, Chair Doug Boyer Colleen Robles An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics in the Graduate School of Duke University 2019 Copyright c 2019 by Shan Shan All rights reserved Abstract In this thesis, we propose probabilistic models on fibre bundles for learning the gen- erative process of data. The main tool we use is the diffusion kernel and we use it in two ways. First, we build from the diffusion kernel on a fibre bundle a projected kernel that generates robust representations of the data, and we test that it outperforms regular diffusion maps under noise. Second, this diffusion kernel gives rise to a nat- ural covariance function when defining Gaussian processes (GP) on the fibre bundle. To demonstrate the uses of GP on a fibre bundle, we apply it to simulated data on a M¨obiusstrip for the problem of prediction and regression. Parameter tuning can also be guided by a novel semi-group test arising from the geometric properties of dif- fusion kernel. For an example of real-world application, we use probabilistic models on fibre bundles to study evolutionary process on anatomical surfaces. -
2. Superoscillations.Pdf
When the Whole Vibrates Faster than Any of its Parts Computational Superoscillation Theory Nicholas Wheeler December 2017 Introduction. The phenomenon/theory of “superoscillations”—brought to my attention by my friend Ahmed Sebbar1—originated in the time-symmetric formulation of quantum mechanics2 that gave rise to the theory of “weak measurements.” Recognition of the role that superoscillations play in that work was brought into explicit focus by Aharonov et al in 1990, and since that date the concept has found application to a remarkable variety of physical subject areas. Yakir Aharonov took his PhD in 1960 from the University of Bristol, where he worked with David Bohm.3 In 1992 a conference was convened at Bristol to celebrate Aharonov’s 60th birthday. It was on that occasion that the superoscillation phenomenon came first to the attention of Michael Berry (of the Bristol faculty), who in an essay “Faster than Fourier” contributed to the proceedings of that conference4 wrote that “He [Aharonov] told me that it is possible for functions to oscillate faster than any of their Fourier components. This seemed unbelievable, even paradoxical; I had heard nothing like it before. ” Berry was inspired to write a series of papers relating to the theory of superoscillation and its potential applications, as also by now have a great many other authors. 1 Private communication, 17 November 2017. 2 Y. Aharonov, P. G. Bergmann & J. L. Libowitz, “Time symmetry in the quantum meassurement process,” Phys. Rev. B 134, 1410–1416 (1964). 3 It was, I suspect, at the invitation of E. P Gross—who had collaborated with Bohm when both were at Princeton—that Aharonov spent 1960–1961 at Brandeis University, from which I had taken the first PhD and departed to Utrecht/CERN in February of 1960, so we never met.