Rapport Annuel 2014-2015
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Raport De Activitate Pe Anul 2009
Raport de Activitate - 2009 Colectivul IMAR January 26, 2010 1 Lucrari publicate la finele lui 2008 si necontinute in Raportul pe 2008 1.1 In reviste cotate ISI 1. Belinschi, Serban; Nica, Alexandru: On a remarkable semigroup of homomorphisms with respect to free multiplicative convolution, Indiana University Mathematics Journal, volum 57, No.4 (2008), pag. 1679 – 1713 2. D. Beltit¸˘a,K.-H. Neeb: A non-smooth continuous unitary representation of a Banach-Lie group, Journal of Lie Theory 18 (2008), no. 4, pag. 933–936. 3. C. Calinescu, J. Lepowsky, A. Milas Vertex-algebraic structure of the principal subspaces (1) of certain A1 -modules, II: higher level case , Journal of Pure and Applied Algebra, 212 (2008), pag. 1928– 1950 4. Dorin Cheptea, Kazuo Habiro, Gwenael Massuyeau: A functorial LMO invariant for Lagrangian cobordisms, Geometry & Topology 12:2 (2008), pag. 1091 – 1170 (MR 2403806) 5. Alexandru Constantinescu Hilbert Function and Betti Numbers of Algebras with Lefschetz Property of Order m, Communications in Algebra, 36 (2008), pag. 4704 – 4720 6. Bruno Benedetti, Alexandru Constantinescu, Matteo Varbaro Dimension, Depth and Zero-Divisors of the Algebra of Basic k-Covers of a Graph, Le Matematiche, Volume LXIII, Issue II, (2008) , pag. 117–156. 7. Alexandru Constantinescu, Le Dinh Nam The Standard Graded Property for Vertex Cover Algebras of Quasi-Trees, Le Matematiche, Volume LXIII, Issue II, (2008), pag. 173–183. 8. I.Aberbach, F. Enescu: Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension, Mich. Math. Journal vol. 57 (2008) special volume in honor of M. Hochster, pag. 1-16 9. -
Mathematisches Forschungsinstitut Oberwolfach Arithmetic Geometry
Mathematisches Forschungsinstitut Oberwolfach Report No. 38/2016 DOI: 10.4171/OWR/2016/38 Arithmetic Geometry Organised by Gerd Faltings, Bonn Johan de Jong, New York Peter Scholze, Bonn 7 August – 13 August 2016 Abstract. Arithmetic geometry is at the interface between algebraic geom- etry and number theory, and studies schemes over the ring of integers of number fields, or their p-adic completions. An emphasis of the workshop was on p-adic techniques, but various other aspects including Hodge theory, Arakelov theory and global questions were discussed. Mathematics Subject Classification (2010): 11G99. Introduction by the Organisers The workshop Arithmetic Geometry was well attended by over 50 participants from various backgrounds. It covered a wide range of topics in algebraic geometry and number theory, with some focus on p-adic questions. Using the theory of perfectoid spaces and related techniques, a number of results have been proved in recent years. At the conference, Caraiani, Gabber, Hansen and Liu reported on such results. In particular, Liu explained general p-adic versions of the Riemann–Hilbert and Simpson correspondences, and Caraiani reported on results on the torsion in the cohomology of Shimura varieties. This involved the geometry of the Hodge–Tate period map, which Hansen extended to a general Shimura variety, using the results reported by Liu. Moreover, Gabber proved degeneration of the Hodge spectral sequence for all proper smooth rigid spaces over nonarchimedean fields of characteristic 0, or even in families, by proving a spreading out result for proper rigid spaces to reduce to a recent result in p-adic Hodge theory. -
Department of Mathematics
Department of Mathematics The Department of Mathematics seeks to maintain its top ranking in mathematics research and education in the United States. The department is a key part of MIT’s educational mission at both the undergraduate and graduate levels and produces the most sought-after young researchers. Key to the department’s success is recruitment of the best faculty members, postdoctoral associates, and graduate students in an ever more competitive environment. The department strives to be diverse at all levels in terms of race, gender, and ethnicity. It continues to serve the varied needs of its graduate students, undergraduate students majoring in mathematics, and the broader MIT community. Awards and Honors The faculty received numerous distinctions this year. Professor Victor Kac received the Leroy P. Steele Prize for Lifetime Achievement, for “groundbreaking contributions to Lie Theory and its applications to Mathematics and Mathematical Physics.” Larry Guth (together with Netz Katz of the California Institute of Technology) won the Clay Mathematics Institute Research Award. Tomasz Mrowka was elected as a member of the National Academy of Sciences and William Minicozzi was elected as a fellow of the American Academy of Arts and Sciences. Alexei Borodin received the 2015 Loève Prize in Probability, given by the University of California, Berkeley, in recognition of outstanding research in mathematical probability by a young researcher. Alan Edelman received the 2015 Babbage Award, given at the IEEE International Parallel and Distributed Processing Symposium, for exceptional contributions to the field of parallel processing. Bonnie Berger was elected vice president of the International Society for Computational Biology. -
Department of Mathematics, Report to the President 2015-2016
Department of Mathematics The Department of Mathematics continues to be the top-ranked mathematics department in the United States. The department is a key part of MIT’s educational mission at both the undergraduate and graduate levels and produces top sought- after young researchers. Key to the department’s success is recruitment of the very best faculty, postdoctoral fellows, and graduate students in an ever-more competitive environment. The department aims to be diverse at all levels in terms of race, gender, and ethnicity. It continues to serve the varied needs of the department’s graduate students, mathematics majors, and the broader MIT community. Awards and Honors The faculty received numerous distinctions this year. Professor Emeritus Michael Artin was awarded the National Medal of Science. In 2016, President Barack Obama presented this honor to Artin for his outstanding contributions to mathematics. Two other emeritus professors also received distinctions: Professor Bertram Kostant was selected to receive the 2016 Wigner Medal, in recognition of “outstanding contributions to the understanding of physics through Group Theory.” Professor Alar Toomre was elected member of the American Philosophical Society. Among active faculty, Professor Larry Guth was awarded the New Horizons in Mathematics Prize for “ingenious and surprising solutions to long standing open problems in symplectic geometry, Riemannian geometry, harmonic analysis, and combinatorial geometry.” He also received a 2015 Teaching Prize for Graduate Education from the School of Science. Professor Alexei Borodin received the 2015 Henri Poincaré Prize, awarded every three years at the International Mathematical Physics Congress to recognize outstanding contributions in mathematical physics. He also received a 2016 Simons Fellowship in Mathematics. -
Analysis & PDE Vol. 5 (2012)
ANALYSIS & PDE Volume 5 No. 1 2012 mathematical sciences publishers Analysis & PDE msp.berkeley.edu/apde EDITORS EDITOR-IN-CHIEF Maciej Zworski University of California Berkeley, USA BOARD OF EDITORS Michael Aizenman Princeton University, USA Nicolas Burq Université Paris-Sud 11, France [email protected] [email protected] Luis A. Caffarelli University of Texas, USA Sun-Yung Alice Chang Princeton University, USA [email protected] [email protected] Michael Christ University of California, Berkeley, USA Charles Fefferman Princeton University, USA [email protected] [email protected] Ursula Hamenstaedt Universität Bonn, Germany Nigel Higson Pennsylvania State Univesity, USA [email protected] [email protected] Vaughan Jones University of California, Berkeley, USA Herbert Koch Universität Bonn, Germany [email protected] [email protected] Izabella Laba University of British Columbia, Canada Gilles Lebeau Université de Nice Sophia Antipolis, France [email protected] [email protected] László Lempert Purdue University, USA Richard B. Melrose Massachussets Institute of Technology, USA [email protected] [email protected] Frank Merle Université de Cergy-Pontoise, France William Minicozzi II Johns Hopkins University, USA [email protected] [email protected] Werner Müller Universität Bonn, Germany Yuval Peres University of California, Berkeley, USA [email protected] [email protected] Gilles Pisier Texas A&M University, and Paris 6 Tristan Rivière ETH, Switzerland [email protected] [email protected] Igor Rodnianski Princeton University, USA Wilhelm Schlag University of Chicago, USA [email protected] [email protected] Sylvia Serfaty New York University, USA Yum-Tong Siu Harvard University, USA [email protected] [email protected] Terence Tao University of California, Los Angeles, USA Michael E. -
Mathematician Unleashes 'A Wave of New Results' in Geometric Analysis 4 June 2014, by Helen Knight
Mathematician unleashes 'a wave of new results' in geometric analysis 4 June 2014, by Helen Knight would form with that shape as its boundary. Although intuition would tell you that it should do this, there is no way to physically test the infinite number of possible variations that could be made to the shape of the wire in order to provide mathematical proof, Minicozzi says. A top geometric analyst Answering Plateau's question—and addressing subsequent conjectures on the properties of complex minimal surfaces—has kept mathematicians busy ever since. The most notable of these researchers in recent years have been Minicozzi and his colleague Tobias Colding, the MIT mathematics professor William Minicozzi in his Cecil and Ida Green Distinguished Professor of office at Building E17. Minicozzi studies the theory of Mathematics at MIT. Together, Minicozzi and surface tension in solutions. Credit: Dominick Reuter Colding are widely considered to be the world's leading geometric analysts of their generation. In 2004 the duo jointly published a series of papers It's something children do every day when blowing in the Annals of Mathematics that resolved a bubbles: Stick a circular wire in a pot of soapy number of longstanding conjectures in the field; this water, pull it out, and behold the film forming earned them the prestigious Oswald Veblen Prize across it. in Geometry. But it's not only children who are amused by this Of particular interest to Minicozzi and Colding was phenomenon—which has also kept mathematicians whether it is possible to describe what all minimal occupied since the 18th century, says William surfaces look like. -
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). -
Arxiv:2012.02249V3 [Math.DG] 24 May 2021
BUILDING MANIFOLDS FROM QUANTUM CODES MICHAEL FREEDMAN AND MATTHEW HASTINGS ABSTRACT. We give a procedurefor “reverseengineering”a closed, simply connected, Riemannian manifold with boundedlocal geometry from a sparse chain complex over Z. Applying this procedure to chain complexes obtained by “lifting” recently developed quantum codes, which correspond to chain complexes over Z2, we construct the first examples of power law Z2 systolic freedom. As a result that may be of independent interest in graph theory, we give an efficient randomized algorithm to construct a weakly fundamental cycle basis for a graph, such that each edge appears only polylogarithmically times in the basis. We use this result to trivialize the fundamental group of the manifold we construct. 1. BUILDING MANIFOLDS FROM QUANTUM CODES 1.1. Introduction. The last fifty years has seen a glorious exploration of the possible “shapes” of Riemannian manifolds. Often the new ideas contained a combinatorial element reminiscent of geometric topology and rather far from the study of homogenous spaces in which Riemann- ian geometry had incubated during the previous fifty years. This paper is in the modern spirit of building and studying Riemannian manifolds from a combinatorial perspective. In this case we use recently discovered quantum codes to build closed Riemannian manifolds with a surprising prop- erty: power law Z2-systolic freedom. This discovery in effect reverses the historical flow of infor- mation. Twenty years ago one of us helped to create quantum codes exhibiting a weaker poly(log) Z2-systolic freedom [FML02,Fre99], starting with a certain family of Riemannian 3-manifolds. In retrospect it is not surprising that the most efficient constructions will necessarily have a combina- torial complexity beyond a geometer’s intuition, perhaps even requiring computer search, and are better discovered within coding theory and then translated into geometry. -
Mathematics Calendar
Mathematics Calendar The most comprehensive and up-to-date Mathematics Calendar information is available on e-MATH at http://www.ams.org/mathcal/. August 2005 Brown, Antonio Campillo, Max Karoubi, Jean-Louis Loday, Susan Montgomery, Adrian Ocneanu, Jose Antonio de la Pena,˜ Vladimir Mathematical Modeling of Infectious Diseases: Dynamics and Popov, Hans-Jurgen Schneider, Aron Simis, Frank Sottile, Richard Control, Institute for Mathematical Sciences, National University Stanley, Boris Tsygan, Mariusz Wodzicki. of Singapore, Singapore 118402. (May 2005, p. 568) Organizing and Scientific Committee: Walter Ferrer Santos (Co- Information: KP Chua, Administrative Officer, Institute for Mathe- ord.), Gerardo Gonzalez-Sprinberg, Alfredo Jones, Alvaro Rittatore, matical Sciences, National University of Singapore, 3 Prince George’s Andrea Solotar. Park, Singapore 118402; tel: (+65) 6874 1893; Facsimile: (+65) 6873 8292; http://www.ims.nus.edu.sg. Deadline: May 1st, 2005. Information:http://www.cmat.edu.uy/cmat/eventos/16cla/en; 1–5 14th USENIX Security Symposium, Baltimore, Maryland. (May Walter Ferrer: email: [email protected] 2005, p. 568) Description: The USENIX Security Symposium brings together 1–December 23 Pattern Formation in Large Domains, Isaac researchers, practitioners, system administrators, system pro- Newton Institute for Mathematical Sciences, Cambridge, England. grammers, and others interested in the latest advances in security (Aug. 2004, p. 834) of computer systems. Organizers: J.H.P. Dawes (Cambridge), M. Golubitsky (Houston), Information: Contact: Conference Department, email: conference@ P.C. Matthews (Nottingham), A.M. Rucklidge (Leeds). usenix.org; tel: 510-528-8649; http://www.usenix.org/sec05/. Information: http://www.newton.cam.ac.uk/programmes/PFD/; Isaac Newton Institute for Mathematical Sciences, 20 Clarkson 1–9 XVI Coloquio Latinoamericano de Algebra, Colonia, Uruguay. -
Joint Journals Catalogue EMS / MSP 2020
Joint Journals Cataloguemsp EMS / MSP 1 2020 Super package deal inside! msp 1 EEuropean Mathematical Society Mathematical Science Publishers msp 1 The EMS Publishing House is a not-for-profit Mathematical Sciences Publishers is a California organization dedicated to the publication of high- nonprofit corporation based in Berkeley. MSP quality peer-reviewed journals and high-quality honors the best traditions of quality publishing books, on all academic levels and in all fields of while moving with the cutting edge of information pure and applied mathematics. The proceeds from technology. We publish more than 16,000 pages the sale of our publications will be used to keep per year, produce and distribute scientific and the Publishing House on a sound financial footing; research literature of the highest caliber at the any excess funds will be spent in compliance lowest sustainable prices, and provide the top with the purposes of the European Mathematical quality of mathematically literate copyediting and Society. The prices of our products will be set as typesetting in the industry. low as is practicable in the light of our mission and We believe scientific publishing should be an market conditions. industry that helps rather than hinders scholarly activity. High-quality research demands high- Contact addresses quality communication – widely, rapidly and easily European Mathematical Society Publishing House accessible to all – and MSP works to facilitate it. Technische Universität Berlin, Mathematikgebäude Straße des 17. Juni 136, 10623 Berlin, Germany Contact addresses Email: [email protected] Mathematical Sciences Publishers Web: www.ems-ph.org 798 Evans Hall #3840 c/o University of California Managing Director: Berkeley, CA 94720-3840, USA Dr. -
THE UNIVERSITY of CALIFORNIA, IRVINE on Singularities and Weak
THE UNIVERSITY OF CALIFORNIA, IRVINE On Singularities and Weak Solutions of Mean Curvature Flow DISSERTATION Submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in mathematics by Alexander Everest Mramor Dissertation Committee: Professor Richard Schoen, Chair Associate Professor Li-Sheng Tseng Assistant Professor Xiangwen Zhang 2019 • Portions of chapter 4 of this thesis were originally published in Entropy and the generic mean curvature flow in curved ambient spaces, Proc. Amer. Math. Soc. 146, 2663-2677, American Mathematical Society, Providence, RI, 2018. • Portions of chapter 6 of this thesis were originally published in A finiteness the- orem via the mean curvature flow with surgery, Journal of geometric analysis, December 2018, Volume 28, Issue 4, pp 3348{3372, Springer Nature Switzer- land AG. • Portions of chapter 7 of this thesis are to appear in Regularity and stability results for the level set flow via the mean curvature flow with surgery in Com- munications in Analysis and Geometry, International Press of Boston, Boston, Mass • Portions of chapter 8 of this thesis are to appear in On the topological rigidity of self shrinkers in R3 in Int. Math. Res. Not., Oxford univerisity press, Oxford, UK, 2019. All other materials c 2019 Alexander Mramor ii Table of contents List of Figures . vi Acknowledgements . vii Curriculum Vitae . ix Abstract of the dissertation . .x Preface 1 1 Introduction to the mean curvature flow 4 1.1 Classical formulation of the mean curvature flow . .5 1.2 Mean curvature flow with surgery for compact 2-convex hypersurfaces 11 1.2.1 Mean curvature flow with surgery according to Huisken and Sinestrari . -
Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves Over a Totally Real Field
Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field Shan Gao AThesis In the Department of Mathematics and Statistics Presented in Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy (Mathematics) at Concordia University Montreal, Quebec, Canada September 2016 c Shan Gao, 2016 CONCORDIA UNIVERSITY SCHOOL OF GRADUATE STUDIES This is to verify that the thesis prepared By: Shan Gao Entitled: Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field and submitted in partial fulfilment of requirements for the degree of Docotor of Philosophy (Mathematics) complies with the regulations of the University and meets the accepted standards with respect to originality and quality. Signed by the final examining committee: Dr. Marcie Frank Chair Dr. Henri Darmon External Examiner Dr. Pablo Bianucci External to Program Dr. Hershy Kisilevsky Examiner Dr. Christopher Cummins Examiner Dr. Adrian Iovita Thesis Supervisor Approved by Dr. Arusharka Sen Chair of Department or Graduate Program Director September 8, 2016 Dr. Andr´eRoy Dean of Faculty ABSTRACT Overconvergent Eichler-Shimura Isomorphisms on Shimura Curves over a Totally Real Field Shan Gao, Ph.D. Concordia University, 2016 In this work we construct overconvergent Eichler-Shimura isomorphisms on Shimura curves over a totally real field F . More precisely, for a prime p>2 and a wide open disk U in the weight space, we construct a Hecke-Galois-equivariant morphism from the space of families of overconvergent modular symbols over U to the space of families of overconvergent modular forms over U. In addition, for all but finitely many weights λ ∈ U, this morphism provides a description of the finite slope part of the space of overconvergent modular symbols of weight λ in terms of the finite slope part of the space of overconvergent modular forms of weight λ + 2.