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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. -
Entuitive Credentials
CREDENTIALS SIMPLIFYING THE COMPLEX Entuitive | Credentials FIRM PROFILE TABLE OF CONTENTS Firm Profile i) The Practice 1 ii) Approach 3 iii) Better Design Through Technology 6 Services i) Structural Engineering 8 ii) Building Envelope 10 iii) Building Restoration 12 iv) Special Projects and Renovations 14 Sectors 16 i) Leadership Team 18 ii) Commercial 19 iii) Cultural 26 iv) Institutional 33 SERVICES v) Healthcare 40 vi) Residential 46 vii) Sports and Recreation 53 viii) Retail 59 ix) Hospitality 65 x) Mission Critical Facilities/Data Centres 70 xi) Transportation 76 SECTORS Image: The Bow*, Calgary, Canada FIRM PROFILE: THE PRACTICE ENTUITIVE IS A CONSULTING ENGINEERING PRACTICE WITH A VISION OF BRINGING TOGETHER ENGINEERING AND INTUITION TO ENHANCE BUILDING PERFORMANCE. We created Entuitive with an entrepreneurial spirit, a blank canvas and a new approach. Our mission was to build a consulting engineering firm that revolves around our clients’ needs. What do our clients need most? Innovative ideas. So we created a practice environment with a single overriding goal – realizing your vision through innovative performance solutions. 1 Firm Profile | Entuitive Image: Ripley’s Aquarium of Canada, Toronto, Canada BACKED BY DECADES OF EXPERIENCE AS CONSULTING ENGINEERS, WE’VE ACCOMPLISHED A GREAT DEAL TAKING DESIGN PERFORMANCE TO NEW HEIGHTS. FIRM PROFILE COMPANY FACTS The practice encompasses structural, building envelope, restoration, and special projects and renovations consulting, serving clients NUMBER OF YEARS IN BUSINESS throughout North America and internationally. 4 years. Backed by decades of experience as Consulting Engineers. We’re pushing the envelope on behalf of – and in collaboration with OFFICE LOCATIONS – our clients. They are architects, developers, building owners and CALGARY managers, and construction professionals. -
Karen Uhlenbeck Awarded the 2019 Abel Prize
RESEARCH NEWS Karen Uhlenbeck While she was in Urbana-Champagne (Uni- versity of Illinois), Karen Uhlenbeck worked Awarded the 2019 Abel with a postdoctoral fellow, Jonathan Sacks, Prize∗ on singularities of harmonic maps on 2D sur- faces. This was the beginning of a long journey in geometric analysis. In gauge the- Rukmini Dey ory, Uhlenbeck, in her remarkable ‘removable singularity theorem’, proved the existence of smooth local solutions to Yang–Mills equa- tions. The Fields medallist Simon Donaldson was very much influenced by her work. Sem- inal results of Donaldson and Uhlenbeck–Yau (amongst others) helped in establishing gauge theory on a firm mathematical footing. Uhlen- beck’s work with Terng on integrable systems is also very influential in the field. Karen Uhlenbeck is a professor emeritus of mathematics at the University of Texas at Austin, where she holds Sid W. Richardson Foundation Chair (since 1988). She is cur- Karen Uhlenbeck (Source: Wikimedia) rently a visiting associate at the Institute for Advanced Study, Princeton and a visiting se- nior research scholar at Princeton University. The 2019 Abel prize for lifetime achievements She has enthused many young women to take in mathematics was awarded for the first time up mathematics and runs a mentorship pro- to a woman mathematician, Professor Karen gram for women in mathematics at Princeton. Uhlenbeck. She is famous for her work in ge- Karen loves gardening and nature hikes. Hav- ometry, analysis and gauge theory. She has ing known her personally, I found she is one of proved very important (and hard) theorems in the most kind-hearted mathematicians I have analysis and applied them to geometry and ever known. -
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. -
Twenty Female Mathematicians Hollis Williams
Twenty Female Mathematicians Hollis Williams Acknowledgements The author would like to thank Alba Carballo González for support and encouragement. 1 Table of Contents Sofia Kovalevskaya ................................................................................................................................. 4 Emmy Noether ..................................................................................................................................... 16 Mary Cartwright ................................................................................................................................... 26 Julia Robinson ....................................................................................................................................... 36 Olga Ladyzhenskaya ............................................................................................................................. 46 Yvonne Choquet-Bruhat ....................................................................................................................... 56 Olga Oleinik .......................................................................................................................................... 67 Charlotte Fischer .................................................................................................................................. 77 Karen Uhlenbeck .................................................................................................................................. 87 Krystyna Kuperberg ............................................................................................................................. -
Copyright by Magdalena Czubak 2008 the Dissertation Committee for Magdalena Czubak Certifies That This Is the Approved Version of the Following Dissertation
Copyright by Magdalena Czubak 2008 The Dissertation Committee for Magdalena Czubak certifies that this is the approved version of the following dissertation: Well-posedness for the space-time Monopole Equation and Ward Wave Map. Committee: Karen Uhlenbeck, Supervisor William Beckner Daniel Knopf Andrea Nahmod Mikhail M. Vishik Well-posedness for the space-time Monopole Equation and Ward Wave Map. by Magdalena Czubak, B.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2008 Dla mojej Mamy. Well-posedness for the space-time Monopole Equation and Ward Wave Map. Publication No. Magdalena Czubak, Ph.D. The University of Texas at Austin, 2008 Supervisor: Karen Uhlenbeck We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods. v Table of Contents Abstract v Chapter 1. Introduction 1 1.1 Space-time Monopole and Ward Wave Map equations . 1 1.2 Chapter Summaries . 7 Chapter 2. Preliminaries 9 2.1 Notation . 9 2.2 Function Spaces & Inversion of the Wave Operator . 10 2.3 Estimates Used . 12 2.4 Classical Results . 16 2.5 Null Forms . 18 2.5.1 Symbols . -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological interwoven with the study of geometrical and reasons. The papers of Uhlenbeck, co-authored with topological problems. Specifically, one studies Sacks, on the energy functional for maps of surfaces objects such as curves, surfaces, connections and into a Riemannian manifold, have been extremely fields which are critical points of functionals influential and describe in detail what happens when representing geometric quantities such as energy the Palais-Smale condition is violated. A minimising and volume. For example, minimal surfaces are sequence of mappings converges outside a finite set critical points of the area and harmonic maps are of singular points and by using rescaling arguments, critical points of the Dirichlet energy. Uhlenbeck’s they describe the behaviour near the singularities major contributions include foundational results on as bubbles or instantons, which are the standard minimal surfaces and harmonic maps, Yang-Mills solutions of the minimising map from the 2-sphere to theory, and integrable systems. -
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. -
Research Notices
AMERICAN MATHEMATICAL SOCIETY Research in Collegiate Mathematics Education. V Annie Selden, Tennessee Technological University, Cookeville, Ed Dubinsky, Kent State University, OH, Guershon Hare I, University of California San Diego, La jolla, and Fernando Hitt, C/NVESTAV, Mexico, Editors This volume presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles are peer-reviewed for two major features: (I) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding how students think about and learn mathematics. This series is published in cooperation with the Mathematical Association of America. CBMS Issues in Mathematics Education, Volume 12; 2003; 206 pages; Softcover; ISBN 0-8218-3302-2; List $49;AII individuals $39; Order code CBMATH/12N044 MATHEMATICS EDUCATION Also of interest .. RESEARCH: AGul<lelbrthe Mathematics Education Research: Hothomatldan- A Guide for the Research Mathematician --lllll'tj.M...,.a.,-- Curtis McKnight, Andy Magid, and -- Teri J. Murphy, University of Oklahoma, Norman, and Michelynn McKnight, Norman, OK 2000; I 06 pages; Softcover; ISBN 0-8218-20 16-8; List $20;AII AMS members $16; Order code MERN044 Teaching Mathematics in Colleges and Universities: Case Studies for Today's Classroom Graduate Student Edition Faculty -
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 . -
3D Map1103.Pdf
CODE Building Name GRID CODE Building Name GRID 1 2 3 4 5 AB Astronomy and Astrophysics (E5) LM Lash Miller Chemical Labs (D2) AD WR AD Enrolment Services (A2) LW Faculty of Law (B4) Institute of AH Alumni Hall, Muzzo Family (D5) M2 MARS 2 (F4) Child Study JH ST. GEORGE OI SK UNIVERSITY OF TORONTO 45 Walmer ROAD BEDFORD AN Annesley Hall (B4) MA Massey College (C2) Road BAY SPADINA ST. GEORGE N St. George Campus 2017-18 AP Anthropology Building (E2) MB Lassonde Mining Building (F3) ROAD SPADINA Tartu A A BA Bahen Ctr. for Info. Technology (E2) MC Mechanical Engineering Bldg (E3) BLOOR STREET WEST BC Birge-Carnegie Library (B4) ME 39 Queen's Park Cres. East (D4) BLOOR STREET WEST FE WO BF Bancroft Building (D1) MG Margaret Addison Hall (A4) CO MK BI Banting Institute (F4) MK Munk School of Global Affairs - Royal BL Claude T. Bissell Building (B2) at the Observatory (A2) VA Conservatory LI BN Clara Benson Building (C1) ML McLuhan Program (D5) WA of Music CS GO MG BR Brennan Hall (C5) MM Macdonald-Mowat House (D2) SULTAN STREET IR Royal Ontario BS St. Basil’s Church (C5) MO Morrison Hall (C2) SA Museum BT Isabel Bader Theatre (B4 MP McLennan Physical Labs (E2) VA K AN STREET S BW Burwash Hall (B4) MR McMurrich Building (E3) PAR FA IA MA K WW HO WASHINGTON AVENUE GE CA Campus Co-op Day Care (B1) MS Medical Sciences Building (E3) L . T . A T S CB Best Institute (F4) MU Munk School of Global Affairs - W EEN'S EEN'S GC CE Centre of Engineering Innovation at Trinity (C3) CHARLES STREET WEST QU & Entrepreneurship (E2) NB North Borden Building (E1) MUSEUM VP BC BT BW CG Canadiana Gallery (E3) NC New College (D1) S HURON STREET IS ’ B R B CH Convocation Hall (E3) NF Northrop Frye Hall (B4) IN E FH RJ H EJ SU P UB CM Student Commons (F2) NL C. -
2017 Fields Medal Symposium
FIELDS VOLUME 17:3 - Fall 2017 NOTESTHE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES 2017 FIELDS MEDAL SYMPOSIUM WITH MARTIN HAIRER + The 2017 Fields Undergraduate Summer Research Program + Ada Lovelace Day + Spotlight on: MESH Consultants FIELDS NOTES VOLUME 17:3 - Fall 2017 16 FIELDS UNDERGRADUATE SUMMER PROGRAM 18 ADA LOVELACE DAY AT FIELDS And the Mathematics of Genomes 14 2017 FIELDS MEDAL SYMPOSIUM Featuring Martin Hairer DIRECTOR 24 SPOTLIGHT ON Ian Hambleton MESH Consultants DEPUTY DIRECTOR Huaxiong Huang MANAGING EDITOR Malgosia Ip DISTRIBUTION COORDINATOR In every issue Tanya Nebesna The Fields Institute for Research in Mathematical Sciences 03 Message from the Director publishes FIELDSNOTES three times a year. 04 News CONNECT WITH US Questions? Comments? 07 Calendar E-mail [email protected] 08 Life at Fields @fieldsinstitute 25 @FieldsInstitute 26 Back Pages COVER IMAGE Diogenes Baena 2 Message from the Director That’s one of the great things about the Fields Institute – one day you’re talking to the winner of one of the most prestigious prizes in mathematics, the next you’re chatting with an aspiring young undergraduate. This issue of Fields Notes features two major events That’s one of the great things about the Fields Institute from somewhat opposite sides of the spectrum. First – one day you’re talking to the winner of one of the there is the 2017 Fields Medal Symposium – an exciting most prestigious prizes in mathematics, the next you’re 4-day event featuring the work of Martin Hairer (Fields chatting with an aspiring young undergraduate. Medal 2014). The Symposium opened with a packed public lecture by Martin, hosted at MaRS Discovery Additionally, Fields hosted its first Ada Lovelace Day District, and continued with a top-notch scientific celebration in collaboration with Ryerson University.