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Of the American Mathematical Society August 2017 Volume 64, Number 7
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society August 2017 Volume 64, Number 7 The Mathematics of Gravitational Waves: A Two-Part Feature page 684 The Travel Ban: Affected Mathematicians Tell Their Stories page 678 The Global Math Project: Uplifting Mathematics for All page 712 2015–2016 Doctoral Degrees Conferred page 727 Gravitational waves are produced by black holes spiraling inward (see page 674). American Mathematical Society LEARNING ® MEDIA MATHSCINET ONLINE RESOURCES MATHEMATICS WASHINGTON, DC CONFERENCES MATHEMATICAL INCLUSION REVIEWS STUDENTS MENTORING PROFESSION GRAD PUBLISHING STUDENTS OUTREACH TOOLS EMPLOYMENT MATH VISUALIZATIONS EXCLUSION TEACHING CAREERS MATH STEM ART REVIEWS MEETINGS FUNDING WORKSHOPS BOOKS EDUCATION MATH ADVOCACY NETWORKING DIVERSITY blogs.ams.org Notices of the American Mathematical Society August 2017 FEATURED 684684 718 26 678 Gravitational Waves The Graduate Student The Travel Ban: Affected Introduction Section Mathematicians Tell Their by Christina Sormani Karen E. Smith Interview Stories How the Green Light was Given for by Laure Flapan Gravitational Wave Research by Alexander Diaz-Lopez, Allyn by C. Denson Hill and Paweł Nurowski WHAT IS...a CR Submanifold? Jackson, and Stephen Kennedy by Phillip S. Harrington and Andrew Gravitational Waves and Their Raich Mathematics by Lydia Bieri, David Garfinkle, and Nicolás Yunes This season of the Perseid meteor shower August 12 and the third sighting in June make our cover feature on the discovery of gravitational waves -
Tommaso De Fernex
Tommaso de Fernex Department of Mathematics Phone: +1 (801) 581-7121 University of Utah Fax: +1 (801) 581-6851 155 South 1400 East [email protected] Salt Lake City, UT 84112 www.math.utah.edu/∼defernex education July 2002 Ph.D. in Mathematics, University of Illinois at Chicago February 2001 Dottorato di Ricerca in Matematica, Universit`adi Genova February 1996 Laurea in Matematica (summa cum laude), Universit`adi Milano appointments 07/17{06/19 Associate Department Chair, University of Utah 07/14{present Professor, University of Utah 07/09{06/14 Associate Professor, University of Utah 07/05{06/09 Assistant Professor, University of Utah 08/02{07/05 T. H. Hildebrandt Research Assistant Professor, University of Michigan visiting positions 01/19{05/19 Research Professor, MSRI, Birational Geometry and Moduli Spaces 05/11{06/11 Visiting Professor, Ecole´ Normale Sup´erieure,Paris 05/09{07/09 Visiting Scholar, Institut de Math´ematiquesde Jussieu 01/09{04/09 Research Member, MSRI, Jumbo Program in Algebraic Geometry May 2006 Visiting Scholar, Universit`adi Genova 09/05{04/06 Member, Institute for Advanced Study 09/99{12/99 Visiting Research Assistant, University of Hong Kong research grants 2020-2023 NSF Grant DMS-2001254, PI fellowships class 2019 Fellow of the American Mathematical Society & honors 2017{2020 NSF Grant DMS-1700769, PI 2014{2017 NSF Grant DMS-1402907, PI 2013{2016 NSF FRG Grant DMS-1265285, PI 2012{2013 Simons Fellow in Mathematics 2009{2014 NSF CAREER Grant DMS-0847059, PI 2009 Fellowship, Fondation Sciences Math´ematiques de Paris 2005{2011 John E. -
Mathematics People, Volume 52, Number 6
Mathematics People Fourier-Mukai transform. He is also working on under- 2005–2006 AMS Centennial standing the structure of cones of divisors on smooth Fellowships Awarded projective varieties by analyzing asymptotic invariants as- sociated to base loci of linear series. He plans to use his The AMS has awarded two Centennial Fellowships for Centennial Fellowship at the University of Michigan and 2005–2006. The recipients are YUAN-PIN LEE of the Univer- the University of Rome, as well as at the University of sity of Utah and MIHNEA POPA of Harvard University. The Chicago. amount of each fellowship is $62,000. The Centennial Please note: Information about the competition for the 2006–2007 AMS Centennial Fellowships will be published in the “Mathematics Opportunities” section of an upcom- ing issue of the Notices. —Allyn Jackson Cerf and Kahn Receive Turing Award The Association for Computing Machinery (ACM) has named VINTON G. CERF and ROBERT E. KAHN the winners of the 2004 A. M. Turing Award, considered the “Nobel Prize of Computing”, for pioneering work on the design and Yuan-Pin Lee Mihnea Popa implementation of the Internet’s basic communications protocols. Cerf is the senior vice president for technology Fellows also receive an expense allowance of $3,000 and strategy at MCI. Kahn is chairman, chief executive officer, a complimentary Society membership for one year. and president of the Corporation for National Research Initiatives (CNRI), a not-for-profit organization for research Yuan-Pin Lee in the public interest on strategic development of Yuan-Pin Lee received his Ph.D. in 1999 from the University network-based information technologies. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Algebraic Geometry Is One of the Most Diverse Fields of Research In
Excerpt Index Cambridge University Press 978-1-107-45946-5- Current Developments in Algebraic Geometry Edited by Lucia Caporaso, James McKernan, Mircea Mustață and Mihnea Popa Frontmatter More information Algebraic geometry is one of the most diverse fields of research in mathematics. It has had an incredible evolution over the past century, with new subfields constantly branching off and spectacular progress in certain directions and, at the same time, with many fundamental unsolved problems still to be tackled. In the spring of 2009 the first main workshop of the MSRI algebraic ge- ometry program served as an introductory panorama of current progress in the field, addressed to both beginners and experts. This volume reflects that spirit, offering expository overviews of the state of the art in many areas of algebraic geometry. Prerequisites are kept to a minimum, making the book accessible to a broad range of mathematicians. Many chapters present approaches to long-standing open problems by means of modern techniques currently under development and contain questions and conjectures to help spur future research. © in this web service Cambridge University Press www.cambridge.org Excerpt Index Cambridge University Press 978-1-107-45946-5- Current Developments in Algebraic Geometry Edited by Lucia Caporaso, James McKernan, Mircea Mustață and Mihnea Popa Frontmatter More information © in this web service Cambridge University Press www.cambridge.org Excerpt Index Cambridge University Press 978-1-107-45946-5- Current Developments in Algebraic Geometry -
![Arxiv:1807.02375V2 [Math.AG]](https://docslib.b-cdn.net/cover/6062/arxiv-1807-02375v2-math-ag-916062.webp)
Arxiv:1807.02375V2 [Math.AG]
D-MODULES IN BIRATIONAL GEOMETRY MIHNEA POPA Abstract. It is well known that numerical quantities arising from the theory of D-modules are related to invariants of singularities in birational geometry. This paper surveys a deeper relationship between the two areas, where the numerical connections are enhanced to sheaf theoretic constructions facilitated by the theory of mixed Hodge modules. The emphasis is placed on the recent theory of Hodge ideals. 1. Introduction. Ad hoc arguments based on differentiating rational functions or sections of line bundles abound in complex and birational geometry. To pick just a couple of examples, topics where such arguments have made a deep impact are the study of adjoint linear series on smooth projective varieties, see for instance Demailly’s work on effective very ampleness [Dem93] and its more algebraic incarnation in [ELN96], and the study of hyperbolicity, see for instance Siu’s survey [Siu04] and the references therein. A systematic approach, as well as an enlargement of the class of objects to which differ- entiation techniques apply, is provided by the theory of D-modules, which has however only recently begun to have a stronger impact in birational geometry. The new developments are mainly due to a better understanding of Morihiko Saito’s theory of mixed Hodge modules [Sai88], [Sai90], and hence to deeper connections with Hodge theory and coherent sheaf theory. Placing problems in this context automatically brings in important tools such as vanishing theorems, perverse sheaves, or the V -filtration, in a unified way. Connections between invariants arising from log resolutions of singularities and invariants arising from the theory of D-modules go back a while however. -
Meetings & Conferences of The
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting. Mihnea Popa, University of Illinois at Chicago, Vanish- Alba Iulia, Romania ing theorems and holomorphic one-forms. Dan Timotin, Institute of Mathematics of the Romanian University of Alba Iulia Academy, Horn inequalities: Finite and infinite dimensions. June 27–30, 2013 Special Sessions Thursday – Sunday Algebraic Geometry, Marian Aprodu, Institute of Meeting #1091 Mathematics of the Romanian Academy, Mircea Mustata, University of Michigan, Ann Arbor, and Mihnea Popa, First Joint International Meeting of the AMS and the Ro- University of Illinois, Chicago. manian Mathematical Society, in partnership with the “Simion Stoilow” Institute of Mathematics of the Romanian Articulated Systems: Combinatorics, Geometry and Academy. Kinematics, Ciprian S. Borcea, Rider University, and Ileana Associate secretary: Steven H. Weintraub Streinu, Smith College. Announcement issue of Notices: January 2013 Calculus of Variations and Partial Differential Equations, Program first available on AMS website: Not applicable Marian Bocea, Loyola University, Chicago, Liviu Ignat, Program issue of electronic Notices: Not applicable Institute of Mathematics of the Romanian Academy, Mihai Issue of Abstracts: Not applicable Mihailescu, University of Craiova, and Daniel Onofrei, University of Houston. -
DERIVATIVE COMPLEX, BGG CORRESPONDENCE, and NUMERICAL INEQUALITIES 3 Are Surjective, I.E
DERIVATIVE COMPLEX, BGG CORRESPONDENCE, AND NUMERICAL INEQUALITIES FOR COMPACT KAHLER¨ MANIFOLDS ROBERT LAZARSFELD AND MIHNEA POPA Introduction Given an irregular compact K¨ahler manifold X, one can form the derivative complex of X, which governs the deformation theory of the groups Hi(X, α) as α varies over Pic0(X). Together with its variants, it plays a central role in a body of work involving generic vanishing theorems. The purpose of this paper is to present two new applications of this complex. First, we show that it fits neatly into the setting of the so-called Bernstein-Gel’fand-Gel’fand (BGG) correspondence between modules over an exterior algebra and linear complexes over a symmetric algebra (cf. [BGG], [EFS], [Eis], [Co]). What comes out here is that some natural cohomology modules associated to X have a surprisingly simple algebraic structure, and that conversely one can read off from these modules some basic geometric invariants associated to the Albanese mapping of X. Secondly, under an additional hypothesis, the derivative complex determines a vector bundle on the projectivized tangent space to Pic0(X) at the origin. We show that this bundle, which encodes the infinitesimal behavior of the Hilbert scheme of paracanonical divisors along the canonical linear series, can be used to generate inequalities among numerical invariants of X. Turning to details, we start by introducing the main homological players in our story. 1 Let X be a compact K¨ahler manifold of dimension d, with H (X, X ) = 0, and let P = 1 O 6 1 Psub H (X, X ) be the projective space of one-dimensional subspaces of H (X, X ). -
Report No. 26/2008
Mathematisches Forschungsinstitut Oberwolfach Report No. 26/2008 Classical Algebraic Geometry Organised by David Eisenbud, Berkeley Joe Harris, Harvard Frank-Olaf Schreyer, Saarbr¨ucken Ravi Vakil, Stanford June 8th – June 14th, 2008 Abstract. Algebraic geometry studies properties of specific algebraic vari- eties, on the one hand, and moduli spaces of all varieties of fixed topological type on the other hand. Of special importance is the moduli space of curves, whose properties are subject of ongoing research. The rationality versus general type question of these spaces is of classical and also very modern interest with recent progress presented in the conference. Certain different birational models of the moduli space of curves have an interpretation as moduli spaces of singular curves. The moduli spaces in a more general set- ting are algebraic stacks. In the conference we learned about a surprisingly simple characterization under which circumstances a stack can be regarded as a scheme. For specific varieties a wide range of questions was addressed, such as normal generation and regularity of ideal sheaves, generalized inequalities of Castelnuovo-de Franchis type, tropical mirror symmetry constructions for Calabi-Yau manifolds, Riemann-Roch theorems for Gromov-Witten theory in the virtual setting, cone of effective cycles and the Hodge conjecture, Frobe- nius splitting, ampleness criteria on holomorphic symplectic manifolds, and more. Mathematics Subject Classification (2000): 14xx. Introduction by the Organisers The Workshop on Classical Algebraic Geometry, organized by David Eisenbud (Berkeley), Joe Harris (Harvard), Frank-Olaf Schreyer (Saarbr¨ucken) and Ravi Vakil (Stanford), was held June 8th to June 14th. It was attended by about 45 participants from USA, Canada, Japan, Norway, Sweden, UK, Italy, France and Germany, among of them a large number of strong young mathematicians. -
Local Positivity, Multiplier Ideals, and Syzygies of Abelian Varieties 3
LOCAL POSITIVITY, MULTIPLIER IDEALS, AND SYZYGIES OF ABELIAN VARIETIES ROBERT LAZARSFELD, GIUSEPPE PARESCHI, AND MIHNEA POPA Introduction In a recent paper [10], Hwang and To observed that there is a relation between local positivity on an abelian variety A and the projective normality of suitable embeddings of A. The purpose of this note is to extend their result to higher syzygies, and to show that the language of multiplier ideals renders the computations extremely quick and transparent. Turning to details, let A be an abelian variety of dimension g, and let L be an ample line bundle on A. Recall that the Seshadri constant ε(A, L) is a positive real number that measures the local positivity of L at any given point x ∈ A: for example, it can be defined by counting asymptotically the number of jets that the linear series |kL| separates at x as k →∞. We refer to [14, Chapter 5] for a general survey of the theory, and in particular to Section 5.3 of that book for a discussion of local positivity on abelian varieties. Our main result is Theorem A. Assume that ε(A, L) > (p + 2)g. Then L satisfies property (Np). The reader may consult for instance [14, Chapter 1.8.D], [9] or [6] for the definition of property (Np) and further references. Suffice it to say here that (N0) holds when L defines a projectively normal embedding of A, while (N1) means that the homogeneous ideal of A in arXiv:1003.4470v1 [math.AG] 23 Mar 2010 this embedding is generated by quadrics. -
Some Effective Problems in Algebraic Geometry and Their Applications
NORTHWESTERN UNIVERSITY Some Effective Problems in Algebraic Geometry and Their Applications A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY Field of Mathematics By Yajnaseni Dutta EVANSTON, ILLINOIS September 2019 2 c Copyright by Yajnaseni Dutta 2019 All Rights Reserved 3 ABSTRACT Some Effective Problems in Algebraic Geometry and Their Applications Yajnaseni Dutta In this thesis, we study pushforwards of canonical and log-pluricanonical bundles on projective log canonical pairs over the complex numbers. We partially answer a Fujita- type conjecture proposed by Popa and Schnell in the log canonical setting. Built on Kawamata's result for morphisms that are smooth outside a simple normal crossing divi- sor, we show a global generation result for morphisms that are log-smooth with respect to a reduced snc pair outside such divisors. Furthermore, we partially generalize this result to arbitrary log canonical pairs and obtain generic effective global generation. In the pluricanonical setting, we show two different effective statements. First, when the morphism surjects onto a projective variety, we show a quadratic bound for generic generation for twists by big and nef line bundles. Second, when the morphism is fibred over a smooth projective variety, we give a linear bound for twists by ample line bundles. In each context we give descriptions of the loci over which these global generations hold. These results in particular give effective nonvanishing statements. As an application, we prove an effective weak positivity statement for log-pluricanonical bundles in this 4 setting, with a description of the loci where this positivity is valid. -
![[Math.AG] 3 May 2005 Fdvsr.Dnt by Denote Divisors](https://docslib.b-cdn.net/cover/4618/math-ag-3-may-2005-fdvsr-dnt-by-denote-divisors-2884618.webp)
[Math.AG] 3 May 2005 Fdvsr.Dnt by Denote Divisors
ASYMPTOTIC INVARIANTS OF LINE BUNDLES LAWRENCE EIN, ROBERT LAZARSFELD, MIRCEA MUSTAT¸ A,ˇ MICHAEL NAKAMAYE, AND MIHNEA POPA Introduction Let X be a smooth complex projective variety of dimension d. It is classical that ample divisors on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By contrast, examples due to Cutkosky and others ([8], [10], [27, Chapter 2.3]) have led to the common impression that the linear series associated to non-ample effective divisors are in general mired in pathology. However, starting with fundamental work of Fujita [18], Nakayama [32], and Tsuji [35], it has recently become apparent that arbitrary effective (or “big”) divisors in fact display a surprising number of properties analogous to those of ample line bundles.1 The key is to study the properties in question from an asymptotic perspective. At the same time, many interesting questions and open problems remain. The purpose of the present expository note is to give an invitation to this circle of ideas. Our hope is that this informal overview might serve as a jumping off point for the more technical literature in the area. Accordingly, we sketch many examples but include no proofs. In an attempt to make the story as appealing as possible to non-specialists, we focus on one particular invariant — the “volume” — that measures the rate of growth of sections of powers of a line bundle. Unfortunately, we must then content ourselves with giving references for a considerable amount of related work. The papers [3], [4] of Boucksom from the analytic viewpoint, and the exciting results of Boucksom–Demailly– Paun–Peternell [5] deserve particular mention: the reader can consult [12] for a survey.