Focm 2017 Foundations of Computational Mathematics Barcelona, July 10Th-19Th, 2017 Organized in Partnership With
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Anna C. Gilbert
Anna C. Gilbert Dept. of Mathematics University of Michigan 530 Church Street Ann Arbor, MI 48109-1109 [email protected] 734-763-5728 (phone) http://www.math.lsa.umich.edu/~annacg 734-763-0937 (fax) Revision date: 30 October, 2017. Research • General interests: analysis, probability, signal processing, and algorithms. • Specialization: randomized algorithms with applications to massive datasets and signal processing. Education • Ph.D., Mathematics, Princeton University, June 1997, Multiresolution homogenization schemes for differential equations and applications, Professor Ingrid Daubechies, advisor. • S.B., Mathematics (with honors), University of Chicago, June 1993. Positions Held • Herman H. Goldstine Collegiate Professor. Department of Mathematics, University of Michigan, 2014{ present. • Full Professor (Courtesy appointment). Division of Electrical and Computer Engineering, University of Michigan, 2010{present. • Full Professor. Department of Mathematics, University of Michigan, 2010{present. • Associate Professor (Courtesy appointment). Division of Electrical and Computer Engineering, Uni- versity of Michigan, 2008{2010. • Associate Professor. Department of Mathematics, University of Michigan, 2007{2010. • Assistant Professor. Department of Mathematics, University of Michigan, 2004{2007. • Principal technical staff member. Internet and Network Systems Research Center, AT&T Labs-Research, 2002{2004. • Senior technical staff member. Information Sciences Research Center, AT&T Labs-Research, 1998{ 2002. • Visiting instructor. Department of Mathematics, Stanford University, Winter quarter 2000. • Postdoctoral research associate. Yale University and AT&T Labs-Research, 1997{1998. • Intern. Lucent Technologies Bell Laboratories, summer 1996. • Research assistant. Princeton University, 1994{1995. • Intern. AT&T Bell Laboratories, summers 1993{1995. Publications Refereed Journal Publications • F. J. Chung, A. C. Gilbert, J. G. Hoskins, and J. C. Schotland, \Optical tomography on graphs", Inverse Problems, Volume 33, Number 5, 2017. -
Martin J. Strauss April 22, 2015
Martin J. Strauss April 22, 2015 Work Address: Dept. of Mathematics University of Michigan Ann Arbor, MI 48109-1043 [email protected] http://www.eecs.umich.edu/~martinjs/ +1-734-717-9874 (cell) Research Interests • Sustainable Energy. • Fundamental algorithms, especially randomized and approximation algorithms. • Algorithms for massive data sets. • Signal processing and and computational harmonic analysis. • Computer security and cryptography. • Complexity theory. Pedagogical Interests • Manipulative Mathematics (teaching via pipe cleaners, paper folding and other mutilation, etc.) • Kinesthetic Mathematics (teaching through movement, including acting out algorithms, per- mutations, and other transformations). Education • Ph.D., Mathematics, Rutgers University, October 1995. Thesis title: Measure in Feasible Complexity Classes. Advisor: Prof. E. Allender, Dept. of Computer Science. • A.B. summa cum laude, Mathematics, Columbia University, May 1989. Minor in Computer Science. Employment History • Professor, Dept. of Mathematics and Dept. of Electrical Engineering and Computer Science (jointly appointed), University of Michigan, 2011{present. • Associate Professor, Dept. of Mathematics and Dept. of Electrical Engineering and Computer Science (jointly appointed), University of Michigan, 2008{2011. • Assistant Professor, Dept. of Mathematics and Dept. of Electrical Engineering and Computer Science (jointly appointed), University of Michigan, 2004{2008. • Visiting Associate Research Scholar, Program in Applied and Computational Mathematics, Princeton University, Sept. 2006{Feb. 2007. Page 1 of 17 • Principal investigator, AT&T Laboratories|Research, 1997{2004. Most recent position: Principal Technical Staff Member, Internet and Network Systems Research Center. • Consultant, Network Services Research Center, AT&T Laboratories, 1996. • Post-Doctoral Research Associate, Department of Computer Science, Iowa State University, September 1995{May 1996. • Intern. Speech recognition group, IBM Watson Research Center, summers, 1989{1990. -
Condition Length and Complexity for the Solution of Polynomial Systems
Condition length and complexity for the solution of polynomial systems Diego Armentano∗ Carlos Beltr´an† Universidad de La Rep´ublica Universidad de Cantabria URUGUAY SPAIN [email protected] [email protected] Peter B¨urgisser‡ Felipe Cucker§ Technische Universit¨at Berlin City University of Hong Kong GERMANY HONG KONG [email protected] [email protected] Michael Shub City University of New York U.S.A. [email protected] October 2, 2018 Abstract Smale’s 17th problem asks for an algorithm which finds an approximate arXiv:1507.03896v1 [math.NA] 14 Jul 2015 zero of polynomial systems in average polynomial time (see Smale [17]). The main progress on Smale’s problem is Beltr´an-Pardo [6] and B¨urgisser- Cucker [9]. In this paper we will improve on both approaches and we prove an important intermediate result. Our main results are Theorem 1 on the complexity of a randomized algorithm which improves the result of [6], Theorem 2 on the average of the condition number of polynomial systems ∗Partially supported by Agencia Nacional de Investigaci´on e Innovaci´on (ANII), Uruguay, and by CSIC group 618 †partially suported by the research projects MTM2010-16051 and MTM2014-57590 from Spanish Ministry of Science MICINN ‡Partially funded by DFG research grant BU 1371/2-2 §Partially funded by a GRF grant from the Research Grants Council of the Hong Kong SAR (project number CityU 100813). 1 which improves the estimate found in [9], and Theorem 3 on the complexity of finding a single zero of polynomial systems. This last Theorem is the main result of [9]. -
Dagrep-V005-I006-Complete.Pdf
Volume 5, Issue 6, June 2015 Computational Social Choice: Theory and Applications (Dagstuhl Seminar 15241) Britta Dorn, Nicolas Maudet, and Vincent Merlin ................................ 1 Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242) Peter Bürgisser, Felipe Cucker, Marek Karpinski, and Nicolai Vorobjov . 28 Sparse Modelling and Multi-exponential Analysis (Dagstuhl Seminar 15251) Annie Cuyt, George Labahn, Avraham Sidi, and Wen-shin Lee ................... 48 Logics for Dependence and Independence (Dagstuhl Seminar 15261) Erich Grädel, Juha Kontinen, Jouko Väänänen, and Heribert Vollmer . 70 DagstuhlReports,Vol.5,Issue6 ISSN2192-5283 ISSN 2192-5283 Published online and open access by Aims and Scope Schloss Dagstuhl – Leibniz-Zentrum für Informatik The periodical Dagstuhl Reports documents the GmbH, Dagstuhl Publishing, Saarbrücken/Wadern, program and the results of Dagstuhl Seminars and Germany. Online available at Dagstuhl Perspectives Workshops. http://www.dagstuhl.de/dagpub/2192-5283 In principal, for each Dagstuhl Seminar or Dagstuhl Perspectives Workshop a report is published that Publication date contains the following: February, 2016 an executive summary of the seminar program and the fundamental results, Bibliographic information published by the Deutsche an overview of the talks given during the seminar Nationalbibliothek (summarized as talk abstracts), and The Deutsche Nationalbibliothek lists this publica- summaries from working groups (if applicable). tion in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at This basic framework can be extended by suitable http://dnb.d-nb.de. contributions that are related to the program of the seminar, e. g. summaries from panel discussions or License open problem sessions. This work is licensed under a Creative Commons Attribution 3.0 DE license (CC BY 3.0 DE). -
Algebraic Settings for the Problem P6=NP?"
Lectures in Applied Mathematics Volume 00, 19xx Algebraic Settings for the Problem \P 6= NP?" Lenore Blum, Felip e Cucker, MikeShub, and Steve Smale Abstract. When complexity theory is studied over an arbitrary unordered eld K , the classical theory is recaptured with K = Z . The fundamental 2 result that the Hilb ert Nullstellensatz as a decision problem is NP-complete over K allows us to reformulate and investigate complexity questions within an algebraic framework and to develop transfer principles for complexity theory. Here we show that over algebraically closed elds K of characteristic 0 the fundamental problem \P 6= NP?" has a single answer that dep ends on the tractability of the Hilb ert Nullstellensatz over the complex numb ers C .Akey comp onent of the pro of is the Witness Theorem enabling the eliminationof transcendental constants in p olynomial time. 1. Statement of Main Theorems We consider the Hilb ert Nullstellensatz in the form HN=K : given a nite set of p olynomials in n variables over a eld K , decide if there is a common zero over K . At rst the eld is taken as the complex numb er eld C . Relationships with other elds and with problems in numb er theory will b e develop ed here. This article is essentially Chapter 6 of our b o ok Complexity and Real Compu- tation to b e published by Springer. Background material can b e found in [Blum, Shub, and Smale 1989]. Only machines and algorithms which branchon\hx = 0?" are considered here. The symbol is not used. -
On the Mathematical Foundations of Learning
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 39, Number 1, Pages 1{49 S 0273-0979(01)00923-5 Article electronically published on October 5, 2001 ON THE MATHEMATICAL FOUNDATIONS OF LEARNING FELIPE CUCKER AND STEVE SMALE The problem of learning is arguably at the very core of the problem of intelligence, both biological and artificial. T. Poggio and C.R. Shelton Introduction (1) A main theme of this report is the relationship of approximation to learning and the primary role of sampling (inductive inference). We try to emphasize relations of the theory of learning to the mainstream of mathematics. In particular, there are large roles for probability theory, for algorithms such as least squares,andfor tools and ideas from linear algebra and linear analysis. An advantage of doing this is that communication is facilitated and the power of core mathematics is more easily brought to bear. We illustrate what we mean by learning theory by giving some instances. (a) The understanding of language acquisition by children or the emergence of languages in early human cultures. (b) In Manufacturing Engineering, the design of a new wave of machines is an- ticipated which uses sensors to sample properties of objects before, during, and after treatment. The information gathered from these samples is to be analyzed by the machine to decide how to better deal with new input objects (see [43]). (c) Pattern recognition of objects ranging from handwritten letters of the alpha- bet to pictures of animals, to the human voice. Understanding the laws of learning plays a large role in disciplines such as (Cog- nitive) Psychology, Animal Behavior, Economic Decision Making, all branches of Engineering, Computer Science, and especially the study of human thought pro- cesses (how the brain works). -
Valued Constraint Satisfaction Problems Over Infinite Domains
Valued Constraint Satisfaction Problems over Infnite Domains DISSERTATION zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Bereich Mathematik und Naturwissenschaften der Technischen Universit¨atDresden von M.Sc. Caterina Viola Eingereicht am 18. Februar 2020 Verteidigt am 17. Juni 2020 Gutachter: Prof. Dr.rer.nat. Manuel Bodirsky Prof. Ph.D. Andrei Krokhin Die Dissertation wurde in der Zeit von M¨arz2016 bis Februar 2020 am Institut f¨urAlgebra angefertigt. This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License. To view a copy of this license, visit http:// creativecommons.org/licenses/by-sa/4.0/deed.en_GB. \Would you tell me, please, which way I ought to go from here?" \That depends a good deal on where you want to get to," said the Cat. \I don't much care where {" said Alice. \Then it doesn't matter which way you go," said the Cat. \{ so long as I get somewhere," Alice added as an explanation. \Oh, you're sure to do that," said the Cat, \if you only walk long enough." | Lewis Carroll, Alice in Wonderland Acknowledgements First and foremost, I want to express my deepest and most sincere gratitude to my supervisor, Manuel Bodirsky. He ofered me his knowledge, guided my research, and rescued in many ways the scientist I eventually became. I am glad and honoured to have been one of his doctoral students. I am very grateful to my collaborator and co-author Marcello Mamino, who was also a mentor during my frst years in Dresden. His enthusiasm and eclectic mathematical knowledge have been crucial to the success of my doctoral studies. -
2021 Students, Who Have Studied at Any of the Local Institutions, to Stay and Work in Hong Kong for a Further 12 Months After Graduation
2022 CITY UNIVERSITY OF HONG KONG HONG KONG A CITY OF OPPORTUNITIES Situated in the heart of Asia, Hong Kong is a humming metropolis of immense opportunities. Home to people from all manner of backgrounds and ethnicities, the city attracts people from around the globe with its unique cultural heritage, accessibility, open economy, and bold focus on the future. Coloured by its colonial past and strong ties to mainland China, Hong Kong continues to be influenced by its diverse population of more than 7 million, and has a longstanding reputation as being one of the safest cities in the world. Not only is Hong Kong famous for its endless skyscrapers, it is also a place of great natural beauty, where people can go hiking in the magnificent countryside, relax on pristine beaches, and visit any of the charming outlying islands. Thanks to its unique location in the region, it is also the perfect place from which to explore any of the neighbouring countries in this dynamic corner of the world. A city of perpetual motion, as well as excitement, Hong Kong truly is a place where East meets West and tradition meets innovation. 01 FUTURE CAREERS DYNAMIC AND FORWARD THINKING, Boasting one of the world’s most free and competitive economies, Hong Kong is a leading financial centre and economic hub. Its excellent infrastructure and strategic CITY UNIVERSITY OF HONG KONG #53 IN THE WORLD IS THE UNIVERSITY FOR YOUR FUTURE. IN THE QS WORLD location also make it a perfect gateway to the countless opportunities in mainland UNIVERSITY RANKINGS 2022 China and the rest of Asia. -
Jahresbericht Annual Report 2013
Mathematisches Forschungsinstitut Oberwolfach Jahresbericht 2013 Annual Report www.mfo.de Herausgeber/Published by Mathematisches Forschungsinstitut Oberwolfach Direktor Gerhard Huisken Gesellschafter Gesellschaft für Mathematische Forschung e.V. Adresse Mathematisches Forschungsinstitut Oberwolfach gGmbH Schwarzwaldstr. 9-11 77709 Oberwolfach Germany Kontakt http://www.mfo.de [email protected] Tel: +49 (0)7834 979 0 Fax: +49 (0)7834 979 38 Das Mathematische Forschungsinstitut Oberwolfach ist Mitglied der Leibniz-Gemeinschaft. © Mathematisches Forschungsinstitut Oberwolfach gGmbH (2015) Jahresbericht 2013 – Annual Report 2013 Inhaltsverzeichnis/Table of Contents Vorwort des Direktors/Director’s Foreword ........................................................................... 6 1. Besondere Beiträge/Special contributions 1.1. Amtsübergabe des Direktors/Change of Directorship ................................................ 10 1.2. Simons Visiting Professors ..................................................................................... 12 1.3. IMAGINARY 2013 und Mathematik des Planeten Erde/ IMAGINARY 2013 and Mathematics of Planet Earth .................................................... 14 1.4. swMATH .............................................................................................................. 22 1.5. MiMa - Museum für Mineralien und Mathematik Oberwolfach/ MiMa - Museum for Minerals and Mathematics Oberwolfach ........................................ 27 1.6. Oberwolfach Vorlesung 2013/Oberwolfach Lecture 2013 ........................................... -
Focm 2017 Foundations of Computational Mathematics Barcelona, July 10Th-19Th, 2017 Organized in Partnership With
FoCM 2017 Foundations of Computational Mathematics Barcelona, July 10th-19th, 2017 http://www.ub.edu/focm2017 Organized in partnership with Workshops Approximation Theory Computational Algebraic Geometry Computational Dynamics Computational Harmonic Analysis and Compressive Sensing Computational Mathematical Biology with emphasis on the Genome Computational Number Theory Computational Geometry and Topology Continuous Optimization Foundations of Numerical PDEs Geometric Integration and Computational Mechanics Graph Theory and Combinatorics Information-Based Complexity Learning Theory Plenary Speakers Mathematical Foundations of Data Assimilation and Inverse Problems Multiresolution and Adaptivity in Numerical PDEs Numerical Linear Algebra Karim Adiprasito Random Matrices Jean-David Benamou Real-Number Complexity Alexei Borodin Special Functions and Orthogonal Polynomials Mireille Bousquet-Mélou Stochastic Computation Symbolic Analysis Mark Braverman Claudio Canuto Martin Hairer Pierre Lairez Monique Laurent Melvin Leok Lek-Heng Lim Gábor Lugosi Bruno Salvy Sylvia Serfaty Steve Smale Andrew Stuart Joel Tropp Sponsors Shmuel Weinberger 2 FoCM 2017 Foundations of Computational Mathematics Barcelona, July 10th{19th, 2017 Books of abstracts 4 FoCM 2017 Contents Presentation . .7 Governance of FoCM . .9 Local Organizing Committee . .9 Administrative and logistic support . .9 Technical support . 10 Volunteers . 10 Workshops Committee . 10 Plenary Speakers Committee . 10 Smale Prize Committee . 11 Funding Committee . 11 Plenary talks . 13 Workshops . 21 A1 { Approximation Theory Organizers: Albert Cohen { Ron Devore { Peter Binev . 21 A2 { Computational Algebraic Geometry Organizers: Marta Casanellas { Agnes Szanto { Thorsten Theobald . 36 A3 { Computational Number Theory Organizers: Christophe Ritzenhaler { Enric Nart { Tanja Lange . 50 A4 { Computational Geometry and Topology Organizers: Joel Hass { Herbert Edelsbrunner { Gunnar Carlsson . 56 A5 { Geometric Integration and Computational Mechanics Organizers: Fernando Casas { Elena Celledoni { David Martin de Diego . -
Condition the Geometry of Numerical Algorithms
Grundlehren der mathematischen Wissenschaften 349 A Series of Comprehensive Studies in Mathematics Series editors M. Berger P. de la Harpe N.J. Hitchin A. Kupiainen G. Lebeau F.-H. Lin S. Mori B.C. Ngô M. Ratner D. Serre N.J.A. Sloane A.M. Vershik M. Waldschmidt Editor-in-Chief A. Chenciner J. Coates S.R.S. Varadhan For further volumes: www.springer.com/series/138 Peter Bürgisser r Felipe Cucker Condition The Geometry of Numerical Algorithms Peter Bürgisser Felipe Cucker Institut für Mathematik Department of Mathematics Technische Universität Berlin City University of Hong Kong Berlin, Germany Hong Kong, Hong Kong SAR ISSN 0072-7830 Grundlehren der mathematischen Wissenschaften ISBN 978-3-642-38895-8 ISBN 978-3-642-38896-5 (eBook) DOI 10.1007/978-3-642-38896-5 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013946090 Mathematics Subject Classification (2010): 15A12, 52A22, 60D05, 65-02, 65F22, 65F35, 65G50, 65H04, 65H10, 65H20, 90-02, 90C05, 90C31, 90C51, 90C60, 68Q25, 68W40, 68Q87 © Springer-Verlag Berlin Heidelberg 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. -
40 IS10 Abstracts
40 IS10 Abstracts IP1 age and video restoration. I will present the framework Approximate Inference in Graphical Models: The and provide numerous examples showing state-of-the-art Fenchel Duality Perspective results. I will then briefly show how to extend this to im- age classification, deriving energies and optimization pro- Quite a number of problems involving inference from data, cedures that lead to learning non-parametric dictionaries whether visual data or otherwise, can be set as a prob- for sparse representations optimized for classification. I lem of finding the most likely setting of variables of a will conclude by showing results on the extension of this to joint distribution over locally interacting variables. These sensing and the learning of incoherent dictionaries. Models include stereopsis, figure-ground segmentation, model-to- derived from universal coding are presented as well. The image matching, super-resolution, and so forth. Inference work I present in this talk is the result of great collabo- over locally interacting variables can be naturally repre- rations with J. Mairal, F. Rodriguez, J. Martin-Duarte, I. sented by a graphical model, however exact inference over Ramirez, F. Lecumberry, F. Bach, M. Elad, J. Ponce, and general graphs is computationally unwieldy. In the context A. Zisserman. of approximate inference, I will describe a general scheme for message passing update rules based on the framework Guillermo Sapiro of Fenchel duality. Using the framework we derive all University of Minnesota past inference algorithms like the Belief Propagation sum- Dept Electrical & Computer Engineering product and max-product, the Tree-Re-Weighted (TRW) [email protected] model as well as new convergent algorithms for maximum- a-posteriori (MAP) and marginal estimation using ”convex free energies”.