2014 Newsletter
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Department of Mathematics — Fall/Winter 2014
Department of Mathematics Spring/Summer 2014 Math Times Department of Mathematics — Fall/Winter 2014 Internships provide new opportunities for graduate students Students arrive at graduate school passionate about Summer internships provide work experience, confidence, mathematics—but unsure of where it might lead them later in and sometimes even a job offer after graduation. The growth life. Perhaps to a university professorship doing research and of interest from our graduate students in these research and teaching, or to a government agency working on cryptography, development positions is striking: seventeen students went this or a national lab modeling disaster response, or to industry summer to internships in industry, government and scientific labs. doing data analytics or a position in consulting or finance. Some internships from summer 2014 include: Students receive both a “push” and a “pull” from the job market in determining their career direction. • Stephen Berning, Han Wang and Sishen Zhou—vehicle routing algorithms and inverse problems for crop yield The “push” is that the number of PhDs granted in the maps, at John Deere’s Technology and Innovation Center mathematical sciences nationwide has increased almost 90% in (UI Research Park). the past twelve years, while tenure-track job openings remain essentially flat. Our graduates still fare well when seeking • Jed Chou and Anna Weigandt—image-segmentation for academic positions, but the intense competition pushes many video conferences, at Personify (a UI startup). students to reconsider their nonacademic options. • Erin Compaan and Lisa Hickok—network behavioral analytics and uncovering latent factors through machine learning and linear algebra, in organizations within the Department of Defense. -
LINEAR ALGEBRA METHODS in COMBINATORICS László Babai
LINEAR ALGEBRA METHODS IN COMBINATORICS L´aszl´oBabai and P´eterFrankl Version 2.1∗ March 2020 ||||| ∗ Slight update of Version 2, 1992. ||||||||||||||||||||||| 1 c L´aszl´oBabai and P´eterFrankl. 1988, 1992, 2020. Preface Due perhaps to a recognition of the wide applicability of their elementary concepts and techniques, both combinatorics and linear algebra have gained increased representation in college mathematics curricula in recent decades. The combinatorial nature of the determinant expansion (and the related difficulty in teaching it) may hint at the plausibility of some link between the two areas. A more profound connection, the use of determinants in combinatorial enumeration goes back at least to the work of Kirchhoff in the middle of the 19th century on counting spanning trees in an electrical network. It is much less known, however, that quite apart from the theory of determinants, the elements of the theory of linear spaces has found striking applications to the theory of families of finite sets. With a mere knowledge of the concept of linear independence, unexpected connections can be made between algebra and combinatorics, thus greatly enhancing the impact of each subject on the student's perception of beauty and sense of coherence in mathematics. If these adjectives seem inflated, the reader is kindly invited to open the first chapter of the book, read the first page to the point where the first result is stated (\No more than 32 clubs can be formed in Oddtown"), and try to prove it before reading on. (The effect would, of course, be magnified if the title of this volume did not give away where to look for clues.) What we have said so far may suggest that the best place to present this material is a mathematics enhancement program for motivated high school students. -
Exploring Continuous Tensegrities
Exploring Continuous Tensegrities by Edward Bruce “Ted” Ashton (Under the direction of Dr. Jason Cantarella) Abstract A discrete tensegrity framework can be thought of as a graph in Euclidean n-space where each edge is of one of three types: an edge with a fixed length (bar) or an edge with an upper (cable) or lower (strut) bound on its length. Roth and Whiteley, in their 1981 paper “Tensegrity Frameworks”, showed that in certain cases, the struts and cables can be replaced with bars when analyzing the framework for infinitesimal rigidity. In that case we call the tensegrity bar equivalent. In specific, they showed that if there exists a set of positive weights, called a positive stress, on the edges such that the weighted sum of the edge vectors is zero at every vertex, then the tensegrity is bar equivalent. In this paper we consider an extended version of the tensegrity framework in arXiv:0704.2784v2 [math.MG] 14 May 2007 which the vertex set is a (possibly infinite) set of points in Euclidean n-space and the edgeset is a compact set of unordered pairs of vertices. These are called continuous tensegrities. We show that if a continuous tensegrity has a strictly positive stress, it is bar equivalent and that it has a semipositive stress if and only if it is partially bar equivalent. We also show that if a tensegrity is minimally bar equivalent (it is bar equivalent but removing any open set of edges makes it no longer so), then it has a strictly positive stress. In particular, we examine the case where the vertices form a rectifiable curve and the possible motions of the curve are limited to local isometries of it. -
Linear Algebra Over a Division Ring Cédric Milliet
Linear Algebra over a division ring Cédric Milliet To cite this version: Cédric Milliet. Linear Algebra over a division ring. 2016. hal-01283071v4 HAL Id: hal-01283071 https://hal.archives-ouvertes.fr/hal-01283071v4 Preprint submitted on 14 Aug 2016 (v4), last revised 2 Jun 2020 (v7) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. GÉOMÉTRIE ALGÉBRIQUE ÉLÉMENTAIRE AU-DESSUS D’UN CORPS NON COMMUTATIF CÉDRIC MILLIET Résumé. On considère un analogue de la topologie de Zariski sur un corps non commuta- tif K. Un fermé de base est donné par les zéros d’un polynôme en la conjugaison par un élément de K fixé à coefficients à droite dans K. Cela nous permet de développer des notions de géométrie algébrique élémentaire : variété algébrique affine, morphisme, comorphisme, une dimension de Zariski, un théorème de Chevalley pour les ensembles constructibles et un Null- stellensatz. On applique ces résultats à la théorie des modèles des corps non commutatifs, en considérant un corps non commutatif K dont la théorie dans le langage (+, ×, 0, 1) n’a pas la propriété d’indépendance de Shelah. Si K est de caractéristique p, on montre qu’il est de dimension finie sur son centre. -
Single Digits
...................................single digits ...................................single digits In Praise of Small Numbers MARC CHAMBERLAND Princeton University Press Princeton & Oxford Copyright c 2015 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu All Rights Reserved The second epigraph by Paul McCartney on page 111 is taken from The Beatles and is reproduced with permission of Curtis Brown Group Ltd., London on behalf of The Beneficiaries of the Estate of Hunter Davies. Copyright c Hunter Davies 2009. The epigraph on page 170 is taken from Harry Potter and the Half Blood Prince:Copyrightc J.K. Rowling 2005 The epigraphs on page 205 are reprinted wiht the permission of the Free Press, a Division of Simon & Schuster, Inc., from Born on a Blue Day: Inside the Extraordinary Mind of an Austistic Savant by Daniel Tammet. Copyright c 2006 by Daniel Tammet. Originally published in Great Britain in 2006 by Hodder & Stoughton. All rights reserved. Library of Congress Cataloging-in-Publication Data Chamberland, Marc, 1964– Single digits : in praise of small numbers / Marc Chamberland. pages cm Includes bibliographical references and index. ISBN 978-0-691-16114-3 (hardcover : alk. paper) 1. Mathematical analysis. 2. Sequences (Mathematics) 3. Combinatorial analysis. 4. Mathematics–Miscellanea. I. Title. QA300.C4412 2015 510—dc23 2014047680 British Library -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Complexity Results for Fourier-Motzkin Elimination
Western University Scholarship@Western Electronic Thesis and Dissertation Repository 12-11-2018 2:30 PM Complexity Results for Fourier-Motzkin Elimination Delaram Talaashrafi The University of Western Ontario Supervisor Moreno Maza, Marc The University of Western Ontario Graduate Program in Computer Science A thesis submitted in partial fulfillment of the equirr ements for the degree in Master of Science © Delaram Talaashrafi 2018 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Theory and Algorithms Commons Recommended Citation Talaashrafi, Delaram, "Complexity Results for Fourier-Motzkin Elimination" (2018). Electronic Thesis and Dissertation Repository. 5981. https://ir.lib.uwo.ca/etd/5981 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 In this thesis, we propose a new method for removing all the redundant inequalities gener- ated by Fourier-Motzkin elimination. This method is based on Kohler’s work and an improved version of Balas’ work. Moreover, this method only uses arithmetic operations on matrices. Algebraic complexity estimates and experimental results show that our method outperforms alternative approaches based on linear programming. Keywords: polyhedron, projection, Fourier-Motzkin elimination, linear algebra, polyhe- dral cone, parametric linear programming i Acknowledgments First and foremost, I would like to offer my sincerest gratitude to my supervisor Professor Marc Moreno Maza, I am very thankful for his great advice and support. It is my honor to have Professor Graham Denham, Professor Roberto Solis-Oba, and Professor Kaizhong Zhang as the examiners. -
2016-2017 Annual Report
Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2016 – April 30, 2017 Brendan Hassett, Director Mathew Borton, IT Director Jeff Brock, Associate Director Ruth Crane, Assistant Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Associate Director Jill Pipher, Consulting Associate Director Sinai Robins, Deputy Director Bjorn Sandstede, Associate Director Homer Walker, Deputy Director Ulrica Wilson, Associate Director for Diversity and Outreach 1 Table of Contents Mission ......................................................................................................................................................... 5 Core Programs and Events ............................................................................................................................. 5 Participant Summaries by Program Type ....................................................................................................... 8 ICERM Funded Participants .................................................................................................................................................................................. 8 All Participants (ICERM funded and Non-ICERM funded) ....................................................................................................................... 9 ICERM Funded Speakers .................................................................................................................................................................................... -
Dov Jarden Born 17 January 1911 (17 Tevet, Taf Resh Ain Aleph) Deceased 29 September 1986 (25 Elul, Taf Shin Mem Vav) by Moshe Jarden12
Dov Jarden Born 17 January 1911 (17 Tevet, Taf Resh Ain Aleph) Deceased 29 September 1986 (25 Elul, Taf Shin Mem Vav) by Moshe Jarden12 http://www.dov.jarden.co.il/ 1Draft of July 9, 2018 2The author is indebted to Gregory Cherlin for translating the original biography from Hebrew and for his help to bring the biography to its present form. 1 Milestones 1911 Birth, Motele, Russian Empire (now Motal, Belarus) 1928{1933 Tachkemoni Teachers' College, Warsaw 1935 Immigration to Israel; enrolls in Hebrew University, Jerusalem: major Mathematics, minors in Bible studies and in Hebrew 1939 Marriage to Haya Urnstein, whom he called Rachel 1943 Master's degree from Hebrew University 1943{1945 Teacher, Bnei Brak 1945{1955 Completion of Ben Yehuda's dictionary under the direction of Professor Tur-Sinai 1946{1959 Editor and publisher, Riveon LeMatematika (13 volumes) 1947{1952 Assisting Abraham Even-Shoshan on Milon Hadash, a new He- brew Dictionary 1953 Publication of two Hebrew Dictionaries, the Popular Dictionary and the Pocket Dictionary, with Even-Shoshan 1956 Doctoral degree in Hebrew linguistics from Hebrew Unversity, under the direction of Professor Tur-Sinai; thesis published in 1957 1960{1962 Curator of manuscripts collection, Hebrew Union College, Cincinnati 1965 Publication of the Dictionary of Hebrew Acronyms with Shmuel Ashkenazi 1966 Publication of the Complete Hebrew-Spanish Dictionary with Arye Comay 1966 Critical edition of Samuel HaNagid's Son of Psalms under the Hebrew Union College Press imprint 1969{1973 Critical edition of -
Curriculum Vitae KAROLA MÉSZ ´AROS
Curriculum Vitae KAROLA MESZ´ AROS´ Work Address: Department of Mathematics Home Address: 115 Midway Rd Cornell University Ithaca, NY 14850 Ithaca, NY 14853 Homepage: http://www.math.cornell.edu/~karola Email Address: karola@math:cornell:edu Employment 2020 { Associate Professor of Mathematics, Cornell University. 2014 { 2020 Assistant Professor of Mathematics, Cornell University. 2012 { 2014 H.C.Wang Assistant Professor, Department of Mathematics, Cornell University. 2011 { 2012 NSF Fellow, Department of Mathematics, University of Michigan, Ann Arbor. 2010 { 2011 Lecturer, Department of Mathematics, MIT. Short-term Positions Summer 2019 Visiting Assistant Professor, Department of Mathematics, MIT. 2018 { 2019 von Neumann Fellow, Institute for Advanced Study. Winter 2016 Invit´eeParis 7, Invited Scholar at Universit´eParis 7 Diderot. Education 2005 { 2010 Ph. D. in Mathematics, Massachusetts Institute of Technology. Thesis: Root polytopes, triangulations, and subdivision algebras, advised by Richard P. Stanley 2001 { 2005 B.S. in Mathematics, Massachusetts Institute of Technology. Scientific/Academic Honors 2019 { 2024 CAREER National Science Foundation Grant, DMS-1847284 2018 { 2019 von Neumann Fellowship at the Institute for Advanced Study 2015 { 2019 National Science Foundation Grant DMS-1501059 2011 { 2014 National Science Foundation Postdoctoral Research Fellowship 2009 { 2010 MIT Department of Mathematics Graduate Student Appreciation Fellowship 2005 { 2006 AKAMAI Fellowship 2005 AMITA (Association of MIT Alumnae) Senior Academic Award 2005 MIT Jon A. Bucsela Prize in Mathematics Research Interests Algebraic combinatorics, discrete geometry. Publications and Preprints preprints 1. Karola M´esz´aros,Avery St. Dizier and Arthur Tanjaya, Principal specialization of dual charac- ters of flagged Weyl modules, arXiv:2105.06531 2. Karola M´esz´arosand Arthur Tanjaya, Inclusion-exclusion on Schubert polynomials, arXiv:2102.11179 3. -
Stillwell J. Elements of Mathematics. from Euclid to Godel (PUP
Elements of Mathematics Elements of Mathematics FROM EUCLID TO GÖDEL John Stillwell PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright c 2016 by John Stillwell Requests for permission to reproduce material from this work should be sent to Permissions, Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket art: The Ideal City by Fra Carnevale (c. 1420–1484). Donated by the Walters Art Museum, Baltimore, MD Excerpt from “Mr. Harrington’s Washing” (taken from Ashenden) by W. Somerset Maugham reproduced by permission of United Agents LLP on behalf of The Royal Literary Fund Excerpt from The Adventures of Don Quixote by Miguel de Cervantes Saavedra, translated by J. M. Cohen (Penguin Classics, 1950). Translation copyright c 1950 by J. M. Cohen. Reproduced by permission of Penguin Books Ltd. All Rights Reserved Library of Congress Cataloging-in-Publication Data Names: Stillwell, John. Title: Elements of mathematics : from Euclid to Gödel / John Stillwell. Description: Princeton : Princeton University Press, [2016] | Includes bibliographical references and index. Identifiers: LCCN 2015045022 | ISBN 9780691171685 (hardcover : alk. paper) Subjects: LCSH: Mathematics—Study and teaching (Higher) Classification: LCC QA11.2 .S8485 2016 | DDC 510.71/1—dc23 LC record available at http://lccn.loc.gov/2015045022 British Library Cataloging-in-Publication Data is available This book has been composed in Minion Pro Printed on acid-free paper. ∞ Typeset by Nova Techset Pvt Ltd, Bangalore, India Printed in the United States of America 13579108642 To Hartley Rogers Jr. -
Curriculum Vitae KAROLA MESZ´ AROS´
Curriculum Vitae KAROLA MESZ´ AROS´ Work Address: Department of Mathematics Home Address: 115 Midway Rd Cornell University Ithaca, NY 14850 Ithaca, NY 14853 Homepage: http://www.math.cornell.edu/~karola Email Address: karola@math:cornell:edu Employment 2014 { Assistant Professor of Mathematics, Cornell University. 2012 { 2014 H.C.Wang Assistant Professor, Department of Mathematics, Cornell University. 2011 { 2012 NSF Fellow, Department of Mathematics, University of Michigan, Ann Arbor. 2010 { 2011 Lecturer, Department of Mathematics, MIT. Education 2005 { 2010 Ph. D. in Mathematics, Massachusetts Institute of Technology. Thesis: Root polytopes, triangulations, and subdivision algebras, advised by Richard P. Stanley 2001 { 2005 B.S. in Mathematics, Massachusetts Institute of Technology. Grants and Fellowships 2015 { 2018 National Science Foundation Grant DMS-1501059 2011 { 2014 National Science Foundation Postdoctoral Research Fellowship 2009 { 2010 MIT Department of Mathematics Graduate Student Appreciation Fellowship Honors 2016 Jan. Invit´eeParis 7, Invited Scholar at Universit´eParis 7 Diderot. Research Interests Algebraic combinatorics, discrete geometry. Publications and Preprints preprints 1. Karola M´esz´arosand Avery St. Dizier, From generalized permutahedra to Grothendieck polyno- mials via flow polytopes. http://www.math.cornell.edu/∼karola/papers/ArxivVersion.pdf 2. Sylvie Corteel, Jang Soo Kim and Karola M´esz´aros, Volumes of generalized Chan-Robbins-Yuen polytopes. arXiv:1704.02701 3. Ricky I. Liu, Karola M´esz´arosand Alejandro H. Morales, Flow polytopes and the space of diagonal harmonics. arXiv:1610.08370 4. Karola M´esz´aros,Alejandro H. Morales and Jessica Striker, On flow polytopes, order polytopes, and a certain face of the alternating sign matrix polytope. arXiv:1510.03357 5.