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Report for the Academic Year 1995
Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1994 - 95 PRINCETON NEW JERSEY Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1 994 - 95 OLDEN LANE PRINCETON • NEW JERSEY 08540-0631 609-734-8000 609-924-8399 (Fax) Extract from the letter addressed by the Founders to the Institute's Trustees, dated June 6, 1930. Newark, New jersey. It is fundamental in our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. TABLE OF CONTENTS 4 BACKGROUND AND PURPOSE 5 • FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 8 • ADMINISTRATION 11 REPORT OF THE CHAIRMAN 15 REPORT OF THE DIRECTOR 23 • ACKNOWLEDGMENTS 27 • REPORT OF THE SCHOOL OF HISTORICAL STUDIES ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 36 • REPORT OF THE SCHOOL OF MATHEMATICS ACADEMIC ACTIVITIES MEMBERS AND VISITORS 42 • REPORT OF THE SCHOOL OF NATURAL SCIENCES ACADEMIC ACTIVITIES MEMBERS AND VISITORS 50 • REPORT OF THE SCHOOL OF SOCIAL SCIENCE ACADEMIC ACTIVITIES MEMBERS, VISITORS AND RESEARCH STAFF 55 • REPORT OF THE INSTITUTE LIBRARIES 57 • RECORD OF INSTITUTE EVENTS IN THE ACADEMIC YEAR 1994-95 85 • INDEPENDENT AUDITORS' REPORT INSTITUTE FOR ADVANCED STUDY: BACKGROUND AND PURPOSE The Institute for Advanced Study is an independent, nonprofit institution devoted to the encouragement of learning and scholarship. -
Brief Curriculum Vitae
Brief Curriculum Vitae Name Vasilakopoulou Christina E-mail christie DOT vasi AT gmail EMPLOYMENT Jun 2019 – now University of Patras, Greece Researcher, Department of Mathematics PI of research grant “Duality and enrichment in operadic theory; interactions with Hopf structures and abstract machines modeling”, H.F.R.I. (ELIDEK) Oct 2017 – June 2019 University of Calfornia at Riverside (USA) Visiting Assistant Professor, Department of Mathematics Oct 2016 – Sep 2017 Université Libre de Bruxelles (Belgium) Postdoctoral Fellow, Department of Mathematics Oct 2015 – Jun 2016 Massachusetts Institute of Technology (USA) Postdoctoral Associate, Department of Mathematics May – Sep 2015 Athens University of Economics and Business (Greece) Postdoctoral Researcher, Department of Informatics Sep 2014 – Feb 2015 University of Hawaii at Manoa (USA) Postdoctoral Research Fellow, Department of Information and Computer Sciences EDUCATION 2010 – 2014 University of Cambridge (UK) – PhD in Category Theory Supervisors: Martin Hyland, Ignacio Lopez Franco Thesis title: “Generalization of algebraic operations via enrichment” 2009 – 2010 University of Cambridge (UK) – MASt in Mathematics 2005 – 2009 University of Patras (Greece) – Ptychion in Mathematics (B.Sc.) Direction: Pure Mathematics, Final mark: 9,26/10 “Excellent” PAPERS To appear Mitchell Buckley, Timmy Fieremans, Christina Vasilakopoulou and Joost Vercruysse, Oplax Hopf Algebras, Higher Structures 2021 Mitchell Buckley, Timmy Fieremans, Christina Vasilakopoulou and Joost Vercruysse, A Larson- Sweedler Theorem for Hopf V-categories, Advances in Mathematics 376 2021 Georgios Bakirtzis, Cody H. Fleming and Christina Vasilakopoulou, Categorical Semantics of Cyber-Physical Systems Theory, ACM Transactions on Cyber-Physical Systems (3) 5, 1–32 2020 Joe Moeller and Christina Vasilakopoulou, Monoidal Grothendieck Construction, Theory and Applications of Categories 35, no. -
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. Tamar Zeigler, Technion, Israel Institute of Technology, Tel Aviv, Israel Patterns in primes and dynamics on nilmanifolds. Bar-Ilan University, Ramat-Gan and Special Sessions Tel-Aviv University, Ramat-Aviv Additive Number Theory, Melvyn B. Nathanson, City University of New York, and Yonutz V. Stanchescu, Afeka June 16–19, 2014 Tel Aviv Academic College of Engineering. Monday – Thursday Algebraic Groups, Division Algebras and Galois Co- homology, Andrei Rapinchuk, University of Virginia, and Meeting #1101 Louis H. Rowen and Uzi Vishne, Bar Ilan University. The Second Joint International Meeting between the AMS Applications of Algebra to Cryptography, David Garber, and the Israel Mathematical Union. Holon Institute of Technology, and Delaram Kahrobaei, Associate secretary: Michel L. Lapidus City University of New York Graduate Center. Announcement issue of Notices: January 2014 Asymptotic Geometric Analysis, Shiri Artstein and Boaz Program first available on AMS website: To be announced Klar’tag, Tel Aviv University, and Sasha Sodin, Princeton Program issue of electronic Notices: To be announced University. Issue of Abstracts: Not applicable Combinatorial Games, Aviezri Fraenkel, Weizmann University, Richard Nowakowski, Dalhousie University, Deadlines Canada, Thane Plambeck, Counterwave Inc., and Aaron For organizers: To be announced Siegel, Twitter. -
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. abstract submission form found at http://www.ams.org/ Knoxville, Tennessee cgi-bin/abstracts/abstract.pl. University of Tennessee, Knoxville Algebraic Methods in Graph Theory and Combinator- ics (Code: SS 7A), Felix Lazebnik, University of Delaware, March 21–23, 2014 Andrew Woldar, Villanova University, and Bangteng Xu, Friday – Sunday Eastern Kentucky University. Arithmetic of Algebraic Curves (Code: SS 9A), Lubjana Meeting #1097 Beshaj, Oakland University, Caleb Shor, Western New Eng- Southeastern Section land University, and Andreas Malmendier, Colby College. Associate secretary: Brian D. Boe Commutative Ring Theory (in honor of the retirement Announcement issue of Notices: January 2014 of David E. Dobbs) (Code: SS 1A), David Anderson, Uni- Program first available on AMS website: February 6, 2014 versity of Tennessee, Knoxville, and Jay Shapiro, George Program issue of electronic Notices: March 2014 Mason University. Issue of Abstracts: Volume 35, Issue 2 Completely Integrable Systems and Dispersive Nonlinear Deadlines Equations (Code: SS 12A), Robert Buckingham, University of Cincinnati, and Peter Perry, University of Kentucky. For organizers: Expired Complex Analysis, Probability, and Metric Geometry For abstracts: January 28, 2014 (Code: SS 11A), Matthew Badger, Stony Brook University, Jim Gill, St. -
The Posse Foundation
THE POSSE scholar 2010 ANNUAL REPORT introduction Becoming a Posse Scholar is no small feat. The journey begins with the student being nominated by her high school followed by an intensive set of interviews with Posse staff to assess CONTENTS leadership and academic potential, communication skills, propensity for group work and level of motivation. Only the best 2. CONCEPT, MISSION, GOALS will receive four-year, full-tuition scholarships from one of Posse’s 38 top-tier partner colleges and universities. But before 4. LETTER FROM THE PRESIDENT + FOUNDER a Scholar matriculates on campus, she will also complete AND CHAIR Posse’s rigorous, eight-month Pre-Collegiate Training Program consisting of two-hour weekly workshop sessions designed to sharpen her growing leadership skills. 6. PROGRAM COMPONENTS The result of this involved process is a student uniquely prepared 8. COLLEGE + UNIVERSITY PARTNERS to make her mark on campus. And that’s exactly what Posse Scholars have been doing since the program’s inception in 9. CAREER PARTNERS 1989. In addition to graduating at a rate of 90 percent— nearly double the national average—more than 70 percent of Posse Scholars found or become presidents of campus 10 . HIGHLIGHTS organizations. Over the years they have earned a reputation as student leaders who enliven classroom discussions, build 12 . CITY REPORTS bridges between disparate sections of the campus community and foster an atmosphere of integrated diversity. 19 . MEET THE SCHOLARS There are currently more than 1,500 Posse Scholars on campuses across the country. They hail from some of our 36. CONTRIBUTORS country’s largest cities. -
Some Reasons for Generalizing Domain Theory
Under consideration for publication in Math. Struct. in Comp. Science Some Reasons for Generalizing Domain Theory Martin Hyland Received 9 October 2009 One natural way to generalize Domain Theory is to replace partially ordered sets by categories. This kind of generalization has recently found application in the study of concurrency. An outline is given of the elegant mathematical foundations which have been developed. This is specialized to give a construction of cartesian closed categories of domains, which throws light on standard presentations of Domain Theory. Introduction This paper is one of what I hope will be a series written in conscious homage to Kreisel’s paper (Kreisel 1971). That paper was prepared for the European Meeting of the ASL in Manchester 1969, was widely aired at the time and was finally published in the pro- ceedings in 1971. It is a survey of the state of Recursion Theory and its generalizations around 1970. At one level it is a remarkable attempt to influence the development of logic, providing concrete proposals and problems as well as more general reflections on future directions. At times, for example in connection with the theory of admissible sets, the discussion foreshadows developments whose significance was only later fully appreciated. At other points, for example in connection with axiomatics, an approach is promoted which has been explored extensively but has in my view been less successful. (It is of course a positive feature that suggestions can even now be regarded as contentious.) However one can read the paper on another level as providing a case study of the value of generalization in a specific area of mathematics. -
From Brouwer's Thesis to the Fan Functional
From Brouwer's Thesis to the Fan Functional Ulrich Berger Swansea University University of Birmingham Theoretical Computer Science Seminar February 21, 2020 1 / 36 Overview 1. Introduction 2. Brouwer's thesis 3. Abstract bar induction 4. Vacuous truth 5. Proving uniform continuity 6. Extracting the fan functional 2 / 36 Introduction What are the logical roots of intriguing algorithms/computing principles? I Primitive recursion comes from induction on N. I General recursion comes from wellfounded induction. I The extended Euklidean algorithm comes from a classical proof that Z is a principal ideal ring. I Normalization by evaluation (for the typed lambda-calculus) comes from the Tait/Girard proof of strong normalization, respectively a completeness proof for intuitionistic logic. I ... Where does Tait's fan functional come from? 3 / 36 The fan functional The fan functional computes for every continuous function on Cantor space with values in N its least modulus of uniform continuity: FAN :(f0; 1gN ! N) ! N FAN(F ) = µn 8α; β (α =n β ! F α = F β) Def where α =n β = 8k 2 N (k < n ! α k = β k). So, clearly, this must come from: Fan theorem: Every continuous function on Cantor space with values in N is uniformly continuous. The real question is what are the right logical and mathematical principles and what is the right formal system for a proof of this theorem in order to extract the fan functional, more precisely, a purely functional program that computes it? 4 / 36 Brief history of the fan functional Tait introduced the Fan functional in 1963 and showed that it is recursively continuous but not computable by Kleene's schemata S1-S9, thus shattering Kleene's hope that S1-S9 is a universal notion of computation in higher types. -
Wellfounded Trees and Dependent Polynomial Functors
Wellfounded Trees and Dependent Polynomial Functors Nicola Gambino? and Martin Hyland Department of Pure Mathematics and Mathematical Statistics University of Cambridge {N.Gambino,M.Hyland}@dpmms.cam.ac.uk Abstract. We set out to study the consequences of the assumption of types of wellfounded trees in dependent type theories. We do so by in- vestigating the categorical notion of wellfounded tree introduced in [16]. Our main result shows that wellfounded trees allow us to define initial algebras for a wide class of endofunctors on locally cartesian closed cat- egories. 1 Introduction Types of wellfounded trees, or W-types, are one of the most important com- ponents of Martin-L¨of’s dependent type theories. First, they allow us to define a wide class of inductive types [5, 15]. Secondly, they play an essential role in the interpretation of constructive set theories in dependent type theories [3]. Finally, from the proof-theoretic point of view, they represent the paradigmatic example of a generalised inductive definition and contribute considerably to the proof-theoretic strength of dependent type theories [8]. In [16] a categorical counterpart of the notion of W-type was introduced. In a locally cartesian closed category, W-types are defined as the initial algebras for endofunctors of a special kind, to which we shall refer here as polynomial functors. The purpose of this paper is to study polynomial endofunctors and W-types more closely. In particular, we set out to explore some of the consequences of the assumption that a locally cartesian closed category has W-types, i.e. that every polynomial endofunctor has an initial algebra. -
EMS Newsletter No 38
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF ROBIN WILSON Department of Pure Mathematics The Open University Milton Keynes MK7 6AA, UK e-mail: [email protected] ASSOCIATE EDITORS STEEN MARKVORSEN Department of Mathematics Technical University of Denmark Building 303 NEWSLETTER No. 38 DK-2800 Kgs. Lyngby, Denmark e-mail: [email protected] December 2000 KRZYSZTOF CIESIELSKI Mathematics Institute Jagiellonian University EMS News: Reymonta 4 Agenda, Editorial, Edinburgh Summer School, London meeting .................. 3 30-059 Kraków, Poland e-mail: [email protected] KATHLEEN QUINN Joint AMS-Scandinavia Meeting ................................................................. 11 The Open University [address as above] e-mail: [email protected] The World Mathematical Year in Europe ................................................... 12 SPECIALIST EDITORS INTERVIEWS The Pre-history of the EMS ......................................................................... 14 Steen Markvorsen [address as above] SOCIETIES Krzysztof Ciesielski [address as above] Interview with Sir Roger Penrose ............................................................... 17 EDUCATION Vinicio Villani Interview with Vadim G. Vizing .................................................................. 22 Dipartimento di Matematica Via Bounarotti, 2 56127 Pisa, Italy 2000 Anniversaries: John Napier (1550-1617) ........................................... 24 e-mail: [email protected] MATHEMATICAL PROBLEMS Societies: L’Unione Matematica -
The Continuum Hypothesis in Algebraic Set Theory
The Continuum Hypothesis in Algebraic Set Theory T. P. Kusalik Department of Mathematics and Statistics McGill University Montreal,Quebec December 31, 2008 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Science ©T. Kusalik. 2008 Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington OttawaONK1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-53761-9 Our file Notre reference ISBN: 978-0-494-53761-9 NOTICE: AVIS: The author has granted a non L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. -
Curriculum Vitae
10221 Phar Lap Dr Cupertino 95014 H 408 219 6912 T 408 725 0460 B [email protected] Í http://vcvpaiva.github.io/ Valeria de Paiva http://www.cs.bham.ac.uk/~vdp Profile: Mathematician with strong industrial and academic background, and over 100 publications. Project leader with a rare ability to get people from different technical backgrounds communicating and working together. Education 1990 PhD, Pure Mathematics, University of Cambridge, Cambridge, UK. Thesis: The Dialectica Categories, supervisor: Prof M. J. E. Hyland 1985 Part III Mathematical Tripos (MSc), University of Cambridge, Cambridge, UK. Lucy Cavendish College 1984 MSc, Algebra, Pontifical Catholic University (PUC), Rio de Janeiro, Brazil. Thesis: The Hurwitz-Radon Transformations, supervisor: Dr D. Randall 1982 BSc, Pure Mathematics, Pontifical Catholic University (PUC), Rio de Janeiro, Brazil. Work Experience Mar Principal Research Scientist, Samsung Research America, Mountain View, CA. 2019–Jan Research, design and deployment of conversational systems, related to smart devices in the 2020 connected home. I also serve a a connection to the academic community. Sep Senior Research Scientist, Nuance Communications, Sunnyvale, CA. 2012–Dec Research, design and deployment of conversational systems. My first project was on a "living 2018 room" assistant such as Amazon’s Alexa. The most recent project was on a car concierge. In the NAIL lab I am the bridge between the Natural Language processing (NLP) experts and the knowledge representation (KR) experts. April Senior Research Scientist, Rearden Commerce, Foster City, CA. 2011–2012 Design and deployment of sentiment analysis tools. { Sentiment analysis mechanisms, especially geared towards to reviews of hotels, using logical knowledge representation and ontologies, as well as statistical natural language processing modules. -
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads Martin Hyland2 Dept of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge, ENGLAND John Power1 ,3 Laboratory for the Foundations of Computer Science University of Edinburgh Edinburgh, SCOTLAND Abstract Lawvere theories and monads have been the two main category theoretic formulations of universal algebra, Lawvere theories arising in 1963 and the connection with monads being established a few years later. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. A generation later, the definition of monad began to appear extensively in theoretical computer science in order to model computational effects, without reference to universal algebra. But since then, the relevance of universal algebra to computational effects has been recognised, leading to renewed prominence of the notion of Lawvere theory, now in a computational setting. This development has formed a major part of Gordon Plotkin’s mature work, and we study its history here, in particular asking why Lawvere theories were eclipsed by monads in the 1960’s, and how the renewed interest in them in a computer science setting might develop in future. Keywords: Universal algebra, Lawvere theory, monad, computational effect. 1 Introduction There have been two main category theoretic formulations of universal algebra. The earlier was by Bill Lawvere in his doctoral thesis in 1963 [23]. Nowadays, his central construct is usually called a Lawvere theory, more prosaically a single-sorted finite product theory [2,3]. It is a more flexible version of the universal algebraist’s notion 1 This work is supported by EPSRC grant GR/586372/01: A Theory of Effects for Programming Languages.