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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. -
2020-Commencement-Program.Pdf
One Hundred and Sixty-Second Annual Commencement JUNE 19, 2020 One Hundred and Sixty-Second Annual Commencement 11 A.M. CDT, FRIDAY, JUNE 19, 2020 2982_STUDAFF_CommencementProgram_2020_FRONT.indd 1 6/12/20 12:14 PM UNIVERSITY SEAL AND MOTTO Soon after Northwestern University was founded, its Board of Trustees adopted an official corporate seal. This seal, approved on June 26, 1856, consisted of an open book surrounded by rays of light and circled by the words North western University, Evanston, Illinois. Thirty years later Daniel Bonbright, professor of Latin and a member of Northwestern’s original faculty, redesigned the seal, Whatsoever things are true, retaining the book and light rays and adding two quotations. whatsoever things are honest, On the pages of the open book he placed a Greek quotation from the Gospel of John, chapter 1, verse 14, translating to The Word . whatsoever things are just, full of grace and truth. Circling the book are the first three whatsoever things are pure, words, in Latin, of the University motto: Quaecumque sunt vera whatsoever things are lovely, (What soever things are true). The outer border of the seal carries the name of the University and the date of its founding. This seal, whatsoever things are of good report; which remains Northwestern’s official signature, was approved by if there be any virtue, the Board of Trustees on December 5, 1890. and if there be any praise, The full text of the University motto, adopted on June 17, 1890, is think on these things. from the Epistle of Paul the Apostle to the Philippians, chapter 4, verse 8 (King James Version). -
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. -
2020-Commencement-Program.Pdf
THE JOHNS HOPKINS UNIVERSITY COMMENCEMENT 2020 Conferring of degrees at the close of the 144th academic year MAY 21, 2020 1 CONTENTS Degrees for Conferral .......................................................................... 3 University Motto and Ode ................................................................... 8 Awards ................................................................................................. 9 Honor Societies ................................................................................. 20 Student Honors ................................................................................. 25 Candidates for Degrees ..................................................................... 35 2 ConferringDegrees of Degrees for Conferral on Candidates CAREY BUSINESS SCHOOL Masters of Science Masters of Business Administration Graduate Certificates SCHOOL OF EDUCATION Doctors of Education Doctors of Philosophy Post-Master’s Certificates Masters of Science Masters of Education in the Health Professions Masters of Arts in Teaching Graduate Certificates Bachelors of Science PEABODY CONSERVATORY Doctors of Musical Arts Masters of Arts Masters of Audio Sciences Masters of Music Artist Diplomas Graduate Performance Diplomas Bachelors of Music SCHOOL OF NURSING Doctors of Nursing Practice Doctors of Philosophy Masters of Science in Nursing/Advanced Practice Masters of Science in Nursing/Entry into Nursing Practice SCHOOL OF NURSING AND BLOOMBERG SCHOOL OF PUBLIC HEALTH Masters of Science in Nursing/Masters of Public -
Read Press Release
The Work of Artur Avila Artur Avila has made outstanding contributions to dynamical systems, analysis, and other areas, in many cases proving decisive results that solved long-standing open problems. A native of Brazil who spends part of his time there and part in France, he combines the strong mathematical cultures and traditions of both countries. Nearly all his work has been done through collaborations with some 30 mathematicians around the world. To these collaborations Avila brings formidable technical power, the ingenuity and tenacity of a master problem-solver, and an unerring sense for deep and significant questions. Avila's achievements are many and span a broad range of topics; here we focus on only a few highlights. One of his early significant results closes a chapter on a long story that started in the 1970s. At that time, physicists, most notably Mitchell Feigenbaum, began trying to understand how chaos can arise out of very simple systems. Some of the systems they looked at were based on iterating a mathematical rule such as 3x(1−x). Starting with a given point, one can watch the trajectory of the point under repeated applications of the rule; one can think of the rule as moving the starting point around over time. For some maps, the trajectories eventually settle into stable orbits, while for other maps the trajectories become chaotic. Out of the drive to understand such phenomena grew the subject of discrete dynamical systems, to which scores of mathematicians contributed in the ensuing decades. Among the central aims was to develop ways to predict long-time behavior. -
Arithmetic Sums of Nearly Affine Cantor Sets
UNIVERSITY OF CALIFORNIA, IRVINE Arithmetic Sums of Nearly Affine Cantor Sets DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Mathematics by Scott Northrup Dissertation Committee: Associate Professor Anton Gorodetski, Chair Professor Svetlana Jitomirskaya Associate Professor Germ´anA. Enciso 2015 c 2015 Scott Northrup DEDICATION To Cynthia and Max. ii TABLE OF CONTENTS Page LIST OF FIGURES iv ACKNOWLEDGMENTS v CURRICULUM VITAE vi ABSTRACT OF THE DISSERTATION vii Introduction 1 1 Outline 7 1.1 Statement of the Results . 7 1.2 Organization of the Thesis . 9 2 Cantor Sets 11 2.1 Dynamically Defined Cantor Sets . 11 2.2 Dimension Theory . 15 2.3 The Palis Conjecture . 18 2.4 Middle-α Cantor Sets . 19 2.5 Homogeneous Self-Similar Cantor Sets . 21 2.6 A Positive Answer to the Palis Conjecture . 22 2.7 The dimH C1 + dimH C2 < 1 Case . 23 3 Results for Nearly Affine Cantor Sets 26 3.1 Absolute Continuity of Convolutions . 26 3.2 Theorem 1.1 . 27 3.3 Construction of Measures for K and Cλ ..................... 28 3.4 Verifying the Conditions of Proposition 3.1 . 32 3.5 Corollaries . 41 4 Open Questions 42 Bibliography 44 A Proof of Proposition 3.1 51 iii LIST OF FIGURES Page 1 The horseshoe map; ' contracts the square horizontally and expands it verti- cally, before folding it back onto itself. The set of points invariant under this map will form a hyperbolic set, called Smale's Horseshoe............ 4 2.1 The Horseshoe map, again . 12 2.2 A few iterations of the Stable Manifold . -
Provost List Fall Semester 2020 Chapman University
Provost List Gaia Adams Ashley Alexander Fall Semester 2020 Laura Adams Nayiri Alexander Zoe Adams Rahul Alexander Chapman University Sam Adler Zuhoor Alfardan Temma Adler Izzy Alfonso Salet Abadee Lauren Adolph Ida Ali Annabelle Abbott Kiran Aftab Kira Alkana Liam Abbott Yasmine Agahi Sara Allali Sarah Abdo Alyssa Agoado Tareq Allan Megan Abe Elias Aguiar Montani Josh Allee Alexandra Abi-Nader Demitri Aguilar Chloe Allen Hana Abiog Roxy Aguilera Emily Allen Gina Aboul-Hosn Chris Aguirre-Rossal Ella Allison Cecilia Marie Abrahamsson Brandon Ah Tye Bailey Allord Jack Abramson Courtney Ahdoot Natanael Alpay Yasmeen Abu Khalaf Alyssa Ahinger Ava Altmann Jill Acala Cooper Ahlers Megan Altsuler Emma Accacian Amara Ahmed Eric Alva Moses Acevedo Laila Ahmed Alondra Alvarez Jeevan Acharya Eissa Ahsan Ashley Alvarez Maddie Acheson Yu Akimoto Nallely Alvarez Diaz Mia Acker Olivia Akture Melissa Alves Annie Acosta Muhja Al-Wahaibi Jasmyn Alviter Cami Acosta Alessia Alamul Malak Aly Angelique Acuna Kelcie Albano Reese Amador Nathan Acupan Gabriel Alcantara Pearson Ames Renee Acupan Andrew Alcott Roxy Amirazizi Brendon Ada Amber Alexander Jacob Anabi Sara Adachi Anjelique Alexander Sakshi Anand Aiyana Adams Arye Anaya Peyton Anton Amy Asmussen Amelia Anbild Liza Antonova Larissa Atkins Ashley Anderson Karsyn Aoki Lauren Atkins Brian Anderson Ashley Arabian Sydni Au Hoy David Anderson Allie Arasi Mitchell AuBuchon Gabi Anderson Brooke Archer Makena Augenstein Gabriella Anderson Courtney Archerd Marit Aurin Gillian Anderson Emily Arendt Leah Auyoung -
Arxiv:1609.08664V2 [Math-Ph] 9 Dec 2017 Yhftde N[ in Hofstadter by Ae[ Case Atrpern Sntitne O Publication
UNIVERSAL HIERARCHICAL STRUCTURE OF QUASIPERIODIC EIGENFUNCTIONS SVETLANA JITOMIRSKAYA AND WENCAI LIU Abstract. We determine exact exponential asymptotics of eigenfunctions and of corre- sponding transfer matrices of the almost Mathieu operators for all frequencies in the lo- calization regime. This uncovers a universal structure in their behavior, governed by the continued fraction expansion of the frequency, explaining some predictions in physics liter- ature. In addition it proves the arithmetic version of the frequency transition conjecture. Finally, it leads to an explicit description of several non-regularity phenomena in the cor- responding non-uniformly hyperbolic cocycles, which is also of interest as both the first natural example of some of those phenomena and, more generally, the first non-artificial model where non-regularity can be explicitly studied. 1. Introduction A very captivating question and a longstanding theoretical challenge in solid state physics is to determine/understand the hierarchical structure of spectral features of operators describ- ing 2D Bloch electrons in perpendicular magnetic fields, as related to the continued fraction expansion of the magnetic flux. Such structure was first predicted in the work of Azbel in 1964 [11]. It was numerically confirmed through the famous butterfly plot and further argued for by Hofstadter in [29], for the spectrum of the almost Mathieu operator. This was even before this model was linked to the integer quantum Hall effect [48] and other important phenom- ena. Mathematically, it is known that the spectrum is a Cantor set for all irrational fluxes [5], and moreover, even all gaps predicted by the gap labeling are open in the non-critical case [6, 8]. -
Lecture Notes in Physics
Lecture Notes in Physics Editorial Board R. Beig, Wien, Austria W. Beiglböck, Heidelberg, Germany W. Domcke, Garching, Germany B.-G. Englert, Singapore U. Frisch, Nice, France P. Hänggi, Augsburg, Germany G. Hasinger, Garching, Germany K. Hepp, Zürich, Switzerland W. Hillebrandt, Garching, Germany D. Imboden, Zürich, Switzerland R. L. Jaffe, Cambridge, MA, USA R. Lipowsky, Golm, Germany H. v. Löhneysen, Karlsruhe, Germany I. Ojima, Kyoto, Japan D. Sornette, Nice, France, and Zürich, Switzerland S. Theisen, Golm, Germany W. Weise, Garching, Germany J. Wess, München, Germany J. Zittartz, Köln, Germany The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced grad- uate textbooks and the forefront of research to serve the following purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic; • to serve as an accessible introduction to the field to postgraduate students and nonspe- cialist researchers from related areas; • to be a source of advanced teaching material for specialized seminars, courses and schools. Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Pro- ceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive is available at springerlink.com. -
Provost List Spring Semester 2021 Chapman University
Provost List Brendon Saije Ada Jack Alexander Spring Semester Kaitlin Adachi Nayiri Alexander 2021 Gaia Adams Isabelle Alfonso Chapman University Laura Adams Ida Ali Kylie Abad Zoe Adams Kira Alkana Salet Abadee Samuel Adler Sara Allali McKenzie Abbott Temma Adler Chloe Allen William Abbott Lauren Adolph Zacharie Allen Kaitlyn Abdo Eliya Afshar Bailey Allord Sarah Abdo Yasmine Agahi Kayla Almeida Alexandra Abi-Nader Abigail Ageshen Jessica Almos Sophie Abiog Alyssa Agoado Naomi Alsop Kimia Abolhoda Elias Aguiar Montani Megan Altsuler Gina Aboul-Hosn Roxanne Aguilera Eric Alva Cecilia Marie Abrahamsson Christopher Aguirre-Rossal Alondra Alvarez Jack Abramson Brandon Ah Tye Ashley Alvarez Eitan Abu Alyssa Ahinger Nallely Alvarez Diaz Yasmeen Abu Khalaf Natalie Ahmadzadeh Melissa Alves Diana Abyad Amara Ahmed Arielle Amador Jillena Acala Shayan Akhtari Pearson Ames Emma Accacian Muhja Al-Wahaibi Roxanna Amirazizi Moses Acevedo Alessia Alamul Jacob Anabi Mia Acker Vanessa Alarcon Arye Anaya Annabella Acosta Kelcie Albano Amelia Anbild Camilla Acosta Maria Alcantar Ethan Joseph Andales Roman Acosta Alicia Alexander Ashley Anderson Angelique Acuna Amber Alexander Brian Anderson Nathan Acupan Anjelique Alexander Brian Anderson Renee Grace Acupan Ashley Alexander David Anderson Gabriella Anderson Courtney Archerd Luis Avila Gabrielle Anderson Mark Arditi Sophia Axiotis Hannah Anderson Pablo Arias Kadambari Ayithi Jillian Anderson Hannah Arico Vivienne Ayres John Louie Anderson Chasen Arima Erin Babbitt Kayla Anderson Grace Armbruster Anne Elise -
Yuki Takahashi
Yuki Takahashi Contact Saitama University [email protected] Information Department of Mathematics http://www.math.uci.edu/~takahasy/ Research Dynamical Systems, Spectral Theory and Fractal Geometry. Interests Employment Department of Mathematics, Saitama University • Assistant Professor, October 2020 - present Department of Mathematics, Michigan State University • Visiting Assistant Professor, January 2020 - August 2020 (research mentor: I. Kachkovskiy) AIMR Mathematical Science Group, Tohoku University • Assistant Professor (non tenure-track), April 2019 - December 2019 (Chiba research group) Department of Mathematics, Bar-Ilan University • Postdoc, June 2017 - March 2019 (supervisor: B. Solomyak) Education Department of Mathematics, University of California, Irvine • Ph.D. in Mathematics, May 2017 (advisor: A. Gorodetski) Ph.D. Thesis: Sums and products of Cantor sets and separable two-dimensional quasicrystal models The University of Tokyo • M.S. in Mathematics, March 2012 Master's Thesis: Irregular solutions of the periodic discrete Toda lattice equation (in Japanese) • B.A. in Mathematics, March 2009 Grants Spring 2020 Leibniz Fellowship Grant (Mathematisches Forschungsinstitut Oberwolfach) Fall 2019 FY2019 WPI-AIMR Fusion Research (Microfluidic, energy, and spin devices with fractal space-filling geometries, together with H. Izuchi, H. Kai and K. Kizu) Winter 2018 Leibniz Fellowship Grant (declined) (Mathematisches Forschungsinstitut Oberwolfach) Fall 2017 Postdoctoral Fellowship Grant (Institut Mittag-Leffler, postdoctoral fellowship) Honors and Spring 2017 Dissertation Fellowship (UC Irvine, department fellowship) Awards Winter 2017 Department Fellowship (UC Irvine, department fellowship) Spring 2014 Connelly Award (UC Irvine, department award) Spring 2013 Euler Outstanding Promise as a Graduate Student Award (UC Irvine, department award) Papers (in 1. Y. Takahashi, On the invariant measures for Iterated Function Systems with in- preparation) verses. -
Mathematics People
NEWS Mathematics People Assaf Naor was born in 1975 in Rehovot, Israel. He Naor Awarded received his PhD in mathematics from the Hebrew Univer- sity of Jerusalem in 2002 under the supervision of Joram Ostrowski Prize Lindenstrauss. He held positions at Microsoft Research, Assaf Naor of Princeton University the University of Washington, and the Courant Institute of has been awarded the 2019 Ostrowski Mathematical Sciences before joining the faculty of Prince- Prize “for his groundbreaking work in ton University in 2014. His honors include the European areas in the meeting point of the ge- Mathematical Society Prize (2008), the Salem Prize (2008), ometry of Banach spaces, the structure the Bôcher Memorial Prize (2011), and the Nemmers Prize of metric spaces, and algorithms.” The (2018). He is a Fellow of the AMS. He gave an invited ad- prize citation reads in part: “The na- dress at the 2010 International Congress of Mathematicians. ture of his contribution is threefold: The Ostrowski Prize is awarded in odd-numbered years Solutions of hard problems, setting for outstanding achievement in pure mathematics and the foundations of numerical mathematics. It carries a cash Assaf Naor a significant research direction for himself and others to follow, and award of 100,000 Swiss francs (approximately US$100,300). finding deep connections between pure mathematics and —Helmut Harbrecht, Universität Basel computer science. “Since the mid-nineties, geometric methods have played an influential role toward designing algorithms for com- Pham Awarded 2019 putational problems that a priori have little connection . to geometry. Assaf Naor is the world leader on this topic, ICTP-IMU Ramanujan Prize building a long-term, cohesive research program.