DOCSLIB.ORG

Program of the Sessions Baltimore, Maryland, January 16–19, 2019

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Program of the Sessions Baltimore, Maryland, January 16–19, 2019 Program of the Sessions Baltimore, Maryland, January 16–19, 2019 Monday, January 14 Tuesday, January 15 AMS Short Course on Sum of Squares: AMS Department Chairs Workshop Theory and Applications, Part I 8:00 AM –6:30PM Grand Ballroom ABC, 8:15 AM –5:30PM Holiday Ballroom 1-3, 1st Floor, Marriott Inner Harbor 2nd Floor, Hilton Organizers: Malcolm Adams,University Organizers: Pablo A Parrilo, of Georgia Massachusetts Institute of Gloria Mari-Beffa,University Technology of Wisconsin-Madison Rekha R Thomas,University of Washington Douglas Mupasiri, University of Northern Iowa 8:15AM Introduction Jennifer Zhao,Universityof 8:30AM Overview of SOS polynomials. Michigan-Dearborn (1) Grigoriy Blekherman, Georgia Institute of Technology AMS Short Course on Sum of Squares: 10:10AM Break Theory and Applications, Part II 10:40AM The geometry of spectrahedra. (2) Cynthia Vinzant, North Carolina State 8:30 AM –5:30PM Holiday Ballroom 1-3, University 2nd Floor, Hilton 12:20PM Lunch Organizers: Pablo A Parrilo, 2:00PM Engineering applications of SOS Massachusetts Institute of (3) polynomials. Technology Georgina Hall,INSEAD Rekha R Thomas,University 3:40PM Break of Washington 4:10PM Problem session 8:30AM Algebraic geometry through the lens of AMS Short Course Reception (4) sums of squares. Mauricio Velasco, Universidad de los 5:00 PM –6:00PM Holiday Ballroom 1-3, Andes 2nd Floor, Hilton 10:10AM Break The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 40, Issue 1 of Abstracts is ten minutes. The time limit for each MAA contributed of papers presented to the American Mathematical Society, paper varies. In the Special Sessions the time limit varies ordered according to the numbers in parentheses following from session to session and within sessions. To maintain the the listings. The middle two digits, e.g., 897-20-1136, refer to schedule, time limits will be strictly enforced. the Mathematical Reviews subject classification assigned by Forpaperswithmorethanoneauthor,an asterisk follows the individual author. Groups of papers for each subject are the name of the author who plans to present the paper at the listed chronologically in the Abstracts. The last one to four meeting. digits, e.g., 897-20-1136, refer to the receipt number of the Papers flagged with a solid triangle () have been desig- abstract; abstracts are further sorted by the receipt number nated by the author as being of possible interest to under- within each classification. MAA abstracts are listed toward graduate students. the back of the issue sorted by session name. Abstracts of papers presented in the sessions at this 57 Program of the Sessions – Tuesday, January 15 (cont’d.) 10:40AM Connections to theoretical computer 9:00AM Optimal bounds for single-source (5) science. (9) Kolmogorov extractors. Ankur Moitra,MIT Laurent Bienvenu,Universityof 12:20PM Lunch Montpellier, Barbara F Csima*, University of Waterloo, and Matthew 2:00PM Lifts of convex sets. Harrison-Trainor, Victoria University of (6) Hamza Fawzi, University of Cambridge Wellington (1145-03-1676) (1145-90-2300) 9:30AM Short Paths in the Sierpinski´ Carpet and 3:40PM Break (10) Menger Sponge. 4:10PM Problem session Derek Smith*andEthan Berkove, Lafayette College (1145-51-1997) AMS Council 10:00AM Normal numbers with digit dependencies. (11) Veronica´ Becher,Universidadde 1:30 PM – 10:00 PM Holiday Ballroom 4-6, Buenos Aires & CONICET, Argentina 2nd Floor, Hilton (1145-41-1693) 10:30AM Weak Computabilities of Real Numbers Joint Meetings Registration (12) and Relative Randomness. Xizhong Zheng, Department of 3:00 PM –7:00PM Pratt Street Lobby, Computer Science and Mathematics, 300 Level, BCC Arcadia University (1145-03-1700) Advanced registration will remain open until 7:30 pm. AMS Special Session on 25 years of Conferences for African-American Email Center Researchers in the Mathematical Sciences (CAARMS times 25), I 3:00 PM –7:30PM Pratt Street Lobby, 300 Level, BCC 8:00 AM –10:50AM Room 314, BCC Organizer: William A. Massey, Princeton University 9:00AM The Falconer Distance Set Problem. (13) Xiumin Du, Institute for Advanced Study, Larry Guth, Massachusetts Institute Wednesday, January 16 of Technology, Yumeng Ou,The City University of New York, Baruch Joint Meetings Registration College, Hong Wang, Massachusetts Institute of Technology, Bobby Wilson*, 7:00 AM –6:00PM Pratt Street Lobby, University of Washington, and Ruixiang 300 Level, BCC Zhang, Institute for Advanced Study (1145-42-2034) Email Center 9:30AM Queueing Theory in the Age of (14) Technology. 7:00 AM – 11:00 PM Pratt Street Jamol Pender, Cornell University Lobby, 300 Level, BCC (Operations Research and Information Engineering) (1145-90-2235) MAA Minority Chairs Meeting 10:00AM Algorithms for Computing Tau (15) Signatures. 7:00 AM –8:45AM Peale, 1st Floor, Hilton Alfred G Noel*, Steven Glenn Jackson, Todor Milev and Thomas AMS-ASL Special Session on Algorithmic Folz-Donahue,Universityof Dimensions and Fractal Geometry, I Massachusetts Boston (1145-22-675) 10:30AM Numerical and Analytic Study of 8:00 AM –10:50AM Room 343, BCC (16) Dynamic Materials. Organizers: Jack H. Lutz, Iowa State Suzanne L. Weekes, Worcester University Polytechnic Institute (1145-65-2348) Elvira Mayordomo, AMS Special Session on A Showcase of University of Zaragoza, Number Theory at Undergraduate Spain Institutions, I 8:00AM The effective dimension of points on lines. (7) Don Stull, Inria Nancy Grand Est 8:00 AM –10:50AM Room 325, BCC (1145-68-1878) 8:30AM Algorithmic Dimensions of Projected Organizers: Adriana Salerno,Bates (8) Points. College Neil Lutz, University of Pennsylvania Lola Thompson, Oberlin (1145-03-2599) College 58 Wednesday, January 16 – Program of the Sessions 8:00AM Rank and Bias in Families of Curves via 9:30AM Defect formation probability in stochastic (17) Nagao’s Conjecture. Preliminary report. (26) models of Ising type. Steven J Miller, Williams College Nathan Hayford*andRazvan (1145-11-1207) Teodorescu, University of South Florida (1145-60-2451) 8:30AM On a Frobenius problem for integral (18) domains. Preliminary report. 10:00AM Boundary value problems for a fractional Ricardo Conceic¸˜ao*, Gettysburg College, (27) differential inclusion with a Hadamard and Rodrigo Gondim,UFPE-Brazil type derivative. (1145-11-2892) John R Graef, University of Tennessee at Chattanooga (1145-34-1064) 9:00AM Factoring m2 +1. Preliminary report. (19) Marc Chamberland*andEugene 10:30AM On Two Fractional q-Derivative Herman, Grinnell College (1145-11-797) (28) Inclusions. Preliminary report. S. Melike Aydogan, Istanbul Technical 9:30AM Almost Prime Components in Apollonian University (1145-49-80) (20) Circle Packings. Preliminary report. Holley Friedlander*, Dickinson College, AMS Special Session on Commutative Ring Elena Fuchs, University of California, Theory: Research for Undergraduate and Davis, Piper H, University of Hawaii at Early Graduate Students, I Manoa, Catherine Hsu,Universityof Bristol, Katherine Sanden,Universityof 8:00 AM –10:50AM Room 320, BCC California, Davis, Damaris Schindler, Utretch University, and Katherine Organizers: Nicholas Baeth, Franklin Stange, University of Colorado, Boulder and Marshall College (1145-11-2633) Branden Stone, Hamilton 10:00AM Non-abelian generalizations of the College (21) Cohen-Lenstra heuristics. 8:00AM Depths of Powers of Ideals and the Power Michael R. Bush*, Washington and Lee (29) of Depth of Understanding Algebra. University, Nigel Boston,Universityof Susan Morey, Texas State University Wisconsin, Madison, and Farshid Hajir, (1145-13-1004) University of Massachusetts, Amherst (1145-11-2189) 8:30AM Algebraic Invariants and Symbolic (30) Powers of Edge Ideals. 10:30AM Quadratic relations between Feynman Joseph W Skelton, Tulane University (22) integrals. (1145-13-1759) David P. Roberts,Universityof 9:00AM The index of stability: a project for Minnesota Morris (1145-11-633) (31) undergraduate students. Janet Striuli*, National Science AMS Special Session on Analysis of Foundation, Corey Brooke,Universityof Fractional, Stochastic, and Hybrid Dynamic Oregon, Molly Hoch, Wellesley College, Systems with Applications, I Sabrina Lato, University of Waterloo, and Bryan Wang, University of California 8:00 AM –10:50AM Room 328, BCC Berkeley (1145-13-1670) 9:30AM Associated Primes of h-Wheels and Other Organizers: John R. Graef,Universityof (32) Graphs. Tennessee at Chattanooga Corey Brooke, University of Oregon G. S. Ladde,Universityof (1145-13-1622) South Florida 10:00AM Trace Ideals and the Gorenstein Property. (33) *and , Williams College A. S. Vatsala,Universityof H. Lindo NPande Louisiana at Lafayette (1145-13-1849) 10:30AM Graphs and Commutative Rings. 8:00AM Existence of local solutions for a (34) Joe A. Stickles, Jr., Millikin University, (23) fractional difference equation with Decatur, IL (1145-13-1060) Dirichlet boundary conditions. Johnny Henderson, Baylor University AMS Special Session on Financial (1145-39-65) Mathematics, I 8:30AM Coercive Nonlocal Elements in Fractional (24) Differential Equations. 8:00 AM –10:50AM Room 338, BCC Christopher S. Goodrich,Creighton Preparatory School (1145-34-2141) Organizers: Maxim Bichuch, Johns Hopkins University 9:00AM Nonlinear Caputo Impulsive Fractional (25) Differential Equations and Generalized Anja Richter,Baruch Monotone Method. Preliminary report. College, City University of Yunxiang Bai*andAghalaya S Vatsala, New York University of Louisiana at Lafayette Stephan Sturm, Worcester (1145-34-743) Polytechnic Institute 59 Program
Load more

Recommended publications
  • 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.
    [Show full text]
  • Annual Report 2005-2006
    CORNELL UNIVERSITY DEPARTMENT OF MATHEMATICS ANNUAL REPORT 2005–2006 The Department of Mathematics at Cornell University is known throughout the world for its distinguished faculty and stimulating mathematical atmosphere. Close to 40 tenured and tenure-track faculty represent a broad spectrum of current mathematical research, with a lively group of postdoctoral fellows and frequent research and teaching visitors. The graduate program includes over 70 graduate students from many different countries. The undergraduate program includes several math major programs, and the department offers a wide selection of courses for all types of users of mathematics. A private endowed university and the federal land-grant institution of New York State, Cornell is a member of the Ivy League and a partner of the State University of New York. There are approximately 19,500 students at Cornell’s Ithaca campus enrolled in seven undergraduate units and four graduate and professional units. Nearly 14,000 of those students are undergraduates, and most of those take at least one math course during their time at Cornell. The Mathematics Department is part of the College of Arts and Sciences, a community of 6,000 students and faculty in 50 departments and programs, encompassing the humanities, sciences, mathematics, fine arts, and social sciences. We are located in Malott Hall, in the center of the Cornell campus, atop a hill between two spectacular gorges that run down to Cayuga Lake in the beautiful Finger Lakes region of New York State. Department Chair: Prof. Kenneth Brown Director of Undergraduate Studies (DUS): Prof. Allen Hatcher Director of Graduate Studies (DGS): Prof.
    [Show full text]
  • Jeffrey Hoffstein Jill Pipher Joseph H. Silverman
    Undergraduate Texts in Mathematics Je rey Ho stein Jill Pipher Joseph H. Silverman An Introduction to Mathematical Cryptography Second Edition Undergraduate Texts in Mathematics Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University, San Francisco, CA, USA Kenneth Ribet University of California, Berkeley, CA, USA Advisory Board: Colin Adams, Williams College, Williamstown, MA, USA Alejandro Adem, University of British Columbia, Vancouver, BC, Canada Ruth Charney, Brandeis University, Waltham, MA, USA Irene M. Gamba, The University of Texas at Austin, Austin, TX, USA Roger E. Howe, Yale University, New Haven, CT, USA David Jerison, Massachusetts Institute of Technology, Cambridge, MA, USA Jeffrey C. Lagarias, University of Michigan, Ann Arbor, MI, USA Jill Pipher, Brown University, Providence, RI, USA Fadil Santosa, University of Minnesota, Minneapolis, MN, USA Amie Wilkinson, University of Chicago, Chicago, IL, USA Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interre- lations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. More information about this series at http://www.springer.com/series/666 Jeffrey Hoffstein • Jill Pipher Joseph
    [Show full text]
  • 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
    [Show full text]
  • President's Report
    Newsletter Volume 42, No. 5 • SePTemBeR–oCT oBeR 2012 PRESIDENT’S REPORT AWM Prize Winners. I am pleased to announce the winners of two of the three major prizes given by AWM at the Joint Mathematics Meetings (JMM). The Louise Hay Award is given to Amy Cohen, Rutgers University, in recognition of The purpose of the Association her “contributions to mathematics education through her writings, her talks, and for Women in Mathematics is her outstanding service to professional organizations.” The Gweneth Humphreys • to encourage women and girls to Award is given to James Morrow, University of Washington, in recognition of study and to have active careers in his “outstanding achievements in inspiring undergraduate women to discover and the mathematical sciences, and • to promote equal opportunity and pursue their passion for mathematics.” I quote from the citations written by the the equal treatment of women and selection committees and extend warm congratulations to the honorees. These girls in the mathematical sciences. awards will be presented at the Prize Session at JMM 2013 in San Diego. Congratulations to Raman Parimala, Emory University, who will present the AWM Noether Lecture at JMM 2013, entitled “A Hasse Principle for Quadratic Forms over Function Fields.” She is honored for her groundbreaking research in theory of quadratic forms, hermitian forms, linear algebraic groups, and Galois cohomology. The Noether Lecture is the oldest of the three named AWM Lectures. (The Falconer Lecture is presented at MathFest, and the Sonia Kovalevsky at the SIAM Annual Meeting.) The first Noether Lecture was given by F. Jessie MacWilliams in 1980 in recognition of her fundamental contributions to the theory of error correcting codes.
    [Show full text]
  • 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.
    [Show full text]
  • Strength in Numbers: the Rising of Academic Statistics Departments In
    Agresti · Meng Agresti Eds. Alan Agresti · Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics DepartmentsStatistics in the U.S. Rising of Academic The in Numbers: Strength Statistics Departments in the U.S. Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. Alan Agresti • Xiao-Li Meng Editors Strength in Numbers: The Rising of Academic Statistics Departments in the U.S. 123 Editors Alan Agresti Xiao-Li Meng Department of Statistics Department of Statistics University of Florida Harvard University Gainesville, FL Cambridge, MA USA USA ISBN 978-1-4614-3648-5 ISBN 978-1-4614-3649-2 (eBook) DOI 10.1007/978-1-4614-3649-2 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942702 Ó Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer.
    [Show full text]
  • Downloads Over 8,000)
    Volume 47 • Issue 1 IMS Bulletin January/February 2018 National Academy new member The US National Academy of Medicine (NAM) has announced the election of 70 reg- CONTENTS ular members and 10 international members. Among them is Nicholas Patrick Jewell, 1 National Academy of University of California, Berkeley. Medicine elects Jewell Election to the Academy is considered one of the highest honors in the fields of 2 Members’ news: Nick Horton, health and medicine, recognizing individuals who have made major contributions to Eric Kolaczyk, Hongzhe Li, the advancement of the medical sciences, health care, and public health. A diversity Runze Li, Douglas Simpson, of talent among NAM’s membership is Greg Lawler, Mike Jordan, Mir assured by its Articles of Organization, Masoom Ali which stipulate that at least one-quarter 3 Journal news: EJP, ECP, Prob of the membership is selected from fields Surveys; OECD guidelines outside the health professions, for exam- 4 Takis Konstantopoulos: new ple, from law, engineering, social sciences, column and the humanities—and statistics. The newly elected members bring 6 Recent papers: Electronic Journal of Probability; Electronic NAM’s total membership to 2,127 and Communications in Probability the number of international members to 172. 11 Special Invited Lecturers; IMS Fellow Nicholas P. Jewell is New Textbook Professor of Biostatistics and Statistics 12 Obituary: Ron Getoor at the University of California, Berkeley. 13 IMS Awards Since arriving at Berkeley in 1981, he has held various academic and administrative 15 Student Puzzle Corner 19; New Researcher Award positions, most notably serving as Vice Provost from 1994 to 2000.
    [Show full text]
  • On the Iwasawa Invariants of Kato's Zeta Elements for Modular Forms
    ON THE IWASAWA INVARIANTS OF KATO’S ZETA ELEMENTS FOR MODULAR FORMS CHAN-HO KIM, JAEHOON LEE, AND GAUTIER PONSINET Abstract. We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato’s main conjecture without p-adic L-functions under congruences. It general- izes the work of Greenberg–Vatsal, Emerton–Pollack–Weston, B.D. Kim, Greenberg–Iovita– Pollack, and one of us simultaneously. As a consequence, we establish the propagation of Kato’s main conjecture for modular forms of higher weight at arbitrary good prime under the assumption on the mod p non-vanishing of Kato’s zeta elements. The application to the ± and ♯/♭-Iwasawa theory for modular forms is also discussed. Contents 1. Introduction 1 2. Main results and applications 6 3. “Prime-to-p local” Iwasawa theory 8 4. The zeta element side 11 5. The H2-side 16 6. The invariance of λ-invariants 18 7. Beyond the Fontaine–Laffaille range: the semi-stable ordinary case 19 Acknowledgement 21 References 21 1. Introduction 1.1. Overview. In Iwasawa theory for elliptic curves and modular forms, the techniques of congruences of modular forms has played important roles. Especially, in their ground-breaking work [GV00], Greenberg and Vatsal observed that both algebraic and analytic Iwasawa in- variants of elliptic curves with good ordinary reduction over the cyclotomic Zp-extension Q∞ of Q can be described in terms of the information of the residual representations and the local arXiv:1909.01764v2 [math.NT] 29 Nov 2019 behavior at bad reduction primes under the µ = 0 assumption.
    [Show full text]
  • L-Invariants of Low Symmetric Powers of Modular Forms and Hida Deformations
    L-invariants of low symmetric powers of modular forms and Hida deformations Robert William Harron A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Mathematics Adviser: Andrew Wiles September 2009 c Copyright by Robert William Harron, 2009. All Rights Reserved Abstract We obtain formulae for Greenberg's L-invariant of symmetric square and symmetric sixth power motives attached to p-ordinary modular forms in the vein of theorem 3.18 of [GS93]. For the symmetric square of f, the formula obtained relates the L- invariant to the derivative of the p-adic analytic function interpolating the pth Fourier coefficient (equivalently, the unit root of Frobenius) in the Hida family attached to f. We present a different proof than Hida's, [Hi04], with slightly different assumptions. The symmetric sixth power of f requires a bigger p-adic family. We take advantage of a result of Ramakrishnan{Shahidi ([RS07]) on the symmetric cube lifting to GSp(4)=Q, Hida families on the latter ([TU99] and [Hi02]), as well as results of several authors on the Galois representations attached to automorphic representations of GSp(4)=Q, to compute the L-invariant of the symmetric sixth power of f in terms of the derivatives of the p-adic analytic functions interpolating the eigenvalues of Frobenius in a Hida family on GSp(4)=Q. We must however impose stricter conditions on f in this case. Here, Hida's work (e.g. [Hi07]) does not provide answers as specific as ours.
    [Show full text]
  • Benedict Gross Harvard University, Professor
    THE ALBERT LEON WHITEMAN MEMORIAL MATHEMATICS LECTURES February 22 and 23, 2016 Benedict Gross Harvard University, Professor Benedict Gross is the George Vasmer Leverett Professor of Mathematics at Harvard University and the former Dean of Harvard College. He is very well known for his research in number theory. His many honors and awards include his election as a Fellow of the American Academy of Arts and Sciences, Membership of the National Academy of Sciences and a Fellow of the American Mathematical Society. He received a MacArthur Fellowship and the Cole Prize in number theory from the AMS. How large is n! = n(n-1)(n-2)…3.2.1 ? Monday, February 22, 2016 Andrus Gerontology Center Time: 4:00-4:30 pm: Reception in Gerontology Courtyard Time: 4:30 pm: LECTURE - Gerontology: Leonard Davis Auditorium located in 124 Short abstract: The number n! (pronounced "n factorial") occurs in many counting problems. For example, that 52! is the number of ways to shuffle a deck of cards. This number grows very rapidly with n, and mathematicians of the 17th century used the new methods of calculus to estimate it. After reviewing some of this work, I'll discuss Euler's Gamma function, which interpolates the function F(n) = (n-1)! to the real numbers, as well as a more recent analog. The rank of elliptic curves Tuesday, February 23, 2016 3:00-3:30 pm: Reception in Kaprielian Hall 410 3:30-4:30 pm: LECTURE in Kaprielian Hall 414 Abstract: Elliptic curves, which are given by cubic equations in two variables, have been a central object of study in number theory since the time of Fermat.
    [Show full text]
  • Henri Darmon
    Henri Darmon Address: Dept of Math, McGill University, Burnside Hall, Montreal, PQ. E-mail: [email protected] Web Page: http://www.math.mcgill.ca/darmon Telephone: Work (514) 398-2263 Home: (514) 481-0174 Born: Oct. 22, 1965, in Paris, France. Citizenship: Canadian, French, and Swiss. Education: 1987. B.Sc. Mathematics and Computer Science, McGill University. 1991. Ph.D. Mathematics, Harvard University. Thesis: Refined class number formulas for derivatives of L-series. University Positions: 1991-1994. Princeton University, Instructor. 1994-1996. Princeton University, Assistant Professor. 1994-1997. McGill University, Assistant Professor. 1997-2000. McGill University, Associate Professor. 2000- . McGill University, Professor. 2005-2019. James McGill Professor, McGill University. Other positions: 1991-1994. Cercheur hors Qu´ebec, CICMA. 1994- . Chercheur Universitaire, CICMA. 1998- . Director, CICMA (Centre Interuniversitaire en Calcul Math´ematique Alg´ebrique). 1999- . Member, CRM (Centre de Recherches Math´ematiques). 2005-2014. External member, European network in Arithmetic Geometry. Visiting Positions: 1991. IHES, Paris. 1995. Universit´a di Pavia. 1996. Visiting member, MSRI, Berkeley. 1996. Visiting professor and guest lecturer, University of Barcelona. 1997. Visiting Professor, Universit´e Paris VI (Jussieu). 1997. Visitor, Institut Henri Poincar´e. 1998. Visiting Professor and NachDiplom lecturer, ETH, Zuric¨ h. 1999. Visiting professor, Universit`a di Pavia. 2001. Visiting professor, Universit`a di Padova. 2001. Korea Institute for Advanced Study. 2002. Visiting professor, RIMS and Saga University (Japan). 1 2003. Visiting Professor, Universit´e Paris VI, Paris. 2003. Visiting professor, Princeton University. 2004. Visiting Professor, Universit´e Paris VI, Paris. 2006. Visiting Professor, CRM, Barcelona, Spain. 2008. Visiting Professor, Universit´e Paris-Sud (Orsay).
    [Show full text]