Part B 2015-16 for Examination in 2016
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Santiago Schnell, Dphil (Oxon), FRSC Education Postdoctoral Training
CURRICULUM VITAE 1st July 2021 Santiago Schnell, DPhil (Oxon), FRSC John A. Jacquez Collegiate Professor of Physiology Professor, Molecular and Integrative Physiology Professor, Computational Medicine and Bioinformatics William K. Brehm Investigator, Brehm Center for Diabetes Research Chair, Department of Molecular & Integrative Physiology The University of Michigan Medical School Enquires: +1-734-763-5727 Department of Molecular & Integrative Physiology Assistant: +1-734-764-4376 7744C Medical Science II Direct: +1-734-615-8733 1137 E. Catherine St. Fax: +1-734-936-8813 Ann Arbor, MI 48109-5622 E-mail: [email protected] USA Web: www.med.umich.edu/schnell-lab/ Effectively, 1st September 2021 William K. Warren Foundation Dean of the College of Science The University of Notre Dame Education 10/1991-12/1996 License in Biology, Universidad Simón Bolívar, Venezuela (Awarded: 24 Jan 1997). Dissertation: Descripción Teórica de la Reacción en Cadena de la Polimerasa. Advisor: Prof. Claudio Mendoza 10/1998-07/2002 Doctor of Philosophy (Mathematics), University of Oxford, UK (Awarded: 8 Nov 2003). Dissertation: On the Quasi-Steady-State Approximation: Enzyme- substrate reactions as a case study. Advisor: Prof. Philip K. Maini, FRS Postdoctoral Training 10/2001-07/2004 Junior Research Fellow, Christ Church, University of Oxford, UK. Mentor: Prof. Philip K. Maini, FRS 12/2002-07/2004 Ordinary Research Fellow of the Wellcome Trust, Centre for Mathematical Biology, Mathematical Institute, University of Oxford, UK, Mentors: Prof. Philip K. Maini, FRS -
Pila, O-Minimality and Diophantine Geometry
O-minimality and Diophantine geometry Jonathan Pila Abstract. This lecture is concerned with some recent applications of mathematical logic to Diophantine geometry. More precisely it concerns applications of o-minimality, a branch of model theory which treats tame structures in real geometry, to certain finiteness problems descending from the classical conjecture of Mordell. Mathematics Subject Classification (2010). Primary 03C64, 11G18. Keywords. O-minimal structure, Andr´e-Oortconjecture, Zilber-Pink conjecture. 1. Introduction This is a somewhat expanded version of my lecture at ICM 2014 in Seoul. It surveys some recent interactions between model theory and Diophantine geometry. The Diophantine problems to be considered are of a type descending from the classical Mordell conjecture (theorem of Faltings). I will describe the passage from Mordell's conjecture to the far-reaching Zilber-Pink conjecture, which is very much open and the subject of lively study by a variety of methods on several fronts. The model theory is \o-minimality", which studies tame structures in real geometry, and offers powerful tools applicable to certain “definable” sets. In combination with an elementary analytic method for \counting rational points" it leads to a general result about the height distribution of rational points on definable sets. This result can be successfully applied to Zilber-Pink problems in the presence of certain functional transcendence and arithmetic ingredients which are known in many cases but seemingly quite difficult in general. Both the methods and problems have connections with transcendental number theory. My further objective is to explain these connections and to bring out the pervasive presence of Schanuel's conjecture. -
Algebra & Number Theory Vol. 7 (2013)
Algebra & Number Theory Volume 7 2013 No. 3 msp Algebra & Number Theory msp.org/ant EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Raman Parimala Emory University, USA John H. Coates University of Cambridge, UK Jonathan Pila University of Oxford, UK J-L. Colliot-Thélène CNRS, Université Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hélène Esnault Freie Universität Berlin, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universität, Germany Joseph H. Silverman Brown University, USA Edward Frenkel University of California, Berkeley, USA Michael Singer North Carolina State University, USA Andrew Granville Université de Montréal, Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Virginia, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale University, USA Ravi Vakil Stanford University, -
Ax-Schanuel and Strong Minimality for the $ J $-Function
AX-SCHANUEL AND STRONG MINIMALITY FOR THE j-FUNCTION VAHAGN ASLANYAN Abstract. Let K := (K;+, ·, D, 0, 1) be a differentially closed field of character- istic 0 with field of constants C. In the first part of the paper we explore the connection between Ax-Schanuel type theorems (predimension inequalities) for a differential equation E(x, y) and the geometry of the fibres Us := {y : E(s,y) ∧ y∈ / C} where s is a non-constant element. We show that certain types of predimension inequalities imply strong minimality and geometric triviality of Us. Moreover, the induced structure on the Cartesian powers of Us is given by special subvarieties. In particular, since the j-function satisfies an Ax-Schanuel inequality of the required form (due to Pila and Tsimerman), applying our results to the j-function we recover a theorem of Freitag and Scanlon stating that the differential equation of j defines a strongly minimal set with trivial geometry. In the second part of the paper we study strongly minimal sets in the j-reducts of differentially closed fields. Let Ej (x, y) be the (two-variable) differential equation of the j-function. We prove a Zilber style classification result for strongly minimal sets in the reduct K := (K;+, ·, Ej ). More precisely, we show that in K all strongly minimal sets are geometrically trivial or non-orthogonal to C. Our proof is based on the Ax-Schanuel theorem and a matching Existential Closedness statement which asserts that systems of equations in terms of Ej have solutions in K unless having a solution contradicts Ax-Schanuel. -
Newsletter37.Pdf
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 DK-2800 Kgs. Lyngby, Denmark NEWSLETTER No. 37 e-mail: [email protected] KRZYSZTOF CIESIELSKI September 2000 Mathematics Institute Jagiellonian University Reymonta 4 30-059 Kraków, Poland EMS News : Agenda, Editorial, 3ecm report, Summer Schools ...................... 2 e-mail: [email protected] KATHLEEN QUINN The Open University [address as above] Mathematical Modelling in the Biosciences (Philip Maini) .......................... 16 e-mail: [email protected] SPECIALIST EDITORS EMS Poster Competition ............................................................................... 19 INTERVIEWS Steen Markvorsen [address as above] SOCIETIES Interview with Martin Grötschel ................................................................... 20 Krzysztof Ciesielski [address as above] EDUCATION Vinicio Villani Interview with Bernt Wegner ........................................................................ 24 Dipartimento di Matematica Via Bounarotti, 2 56127 Pisa, Italy A stamp for World Mathematical Year ..........................................................27 e-mail: [email protected] MATHEMATICAL PROBLEMS Paul Jainta Societies: The London Mathematical Society ................................................ 28 Werkvolkstr. -
O-Minimality and the André-Oort Conjecture for Cn
Annals of Mathematics 173 (2011), 1779{1840 doi: 10.4007/annals.2011.173.3.11 O-minimality and the Andr´e-Oortconjecture for Cn By Jonathan Pila Abstract We give an unconditional proof of the Andr´e-Oortconjecture for arbi- trary products of modular curves. We establish two generalizations. The first includes the Manin-Mumford conjecture for arbitrary products of el- liptic curves defined over Q as well as Lang's conjecture for torsion points in powers of the multiplicative group. The second includes the Manin- Mumford conjecture for abelian varieties defined over Q. Our approach uses the theory of o-minimal structures, a part of Model Theory, and follows a strategy proposed by Zannier and implemented in three recent papers: a new proof of the Manin-Mumford conjecture by Pila-Zannier; a proof of a special (but new) case of Pink's relative Manin-Mumford conjecture by Masser-Zannier; and new proofs of certain known results of Andr´e-Oort- Manin-Mumford type by Pila. 1. Introduction In this paper we give an unconditional proof of the Andr´e-Oortconjecture for arbitrary products of modular curves. Under the Generalized Riemann Hypothesis for imaginary quadratic fields this result is due to Edixhoven [32], [34]; for n = 2 it is an unconditional result of Andr´e[3]. Our approach uses the theory of o-minimal structures, a part of Model Theory. It leads naturally to a more general result that is an \Andr´e-Oort-Manin-Mumford-Lang"statement for varieties of the form ` X = Y1 × · · · × Yn × E1 × · · · × Em × G ; where n; m; ` are nonnegative integers, Y1 = Γ1nH;:::;Yn = ΓnnH are modular curves corresponding to the quotient of the upper half-plane H by congruence subgroups Γi of SL2(Z), E1;:::;Em are elliptic curves defined over Q, and G = Gm(C) is the multiplicative group of nonzero complex numbers. -
Andrew L. Krause – CURRICULUM VITAE
Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Andrew L. Krause Stockton Rd, Durham, DH1 3LE, United Kingdom B [email protected] CURRICULUM VITAE Í www.andrewkrause.org Education 2019–20 PGCert in Teaching and Learning in Higher Education, University of Oxford, UK, Distinction. 2014–18 DPhil in Mathematics, University of Oxford, UK. 2012–14 M.S. in Mathematics, Specialization in Analysis, New Mexico Tech, USA. 2008–12 B.S. in Mathematics and joint B.S. in Computer Science, New Mexico Tech, USA, Highest Honors. Positions Held 2021- Assistant Professor in Applied Mathematics, Department of Mathematical Sciences, University of Durham. 2019-21 Departmental Lecturer in Applied Mathematics, Mathematical Institute, University of Oxford. 2017-19 Postdoctoral Research Assistant, Mathematical Institute, University of Oxford. 2017-19 Stipendiary Lecturer, Pembroke College, University of Oxford. 2015-16 Stipendiary Lecturer, St Anne’s College, University of Oxford. 2014-16 Teaching Assistant/Tutor, Mathematical Institute, University of Oxford. 2014 Technical Writing Tutor, Graduate Writing Center, English Department, New Mexico Tech. 2012–14 Teaching Assistant, Mathematics Department, New Mexico Tech. Publications See www.andrewkrause.org/research-publications for journal and open access links. Journal Articles [32] A. L. Krause, E. A. Gaffney, P. K. Maini, and V. Klika. Modern perspectives on near-equilibrium analysis of Turing systems. Philosophical Transactions of the Royal Society A. In Press. [31] A. L. Krause, Václav Klika, Philip K Maini, Denis Headon, and Eamonn A Gaffney. Isolating patterns in open reaction–diffusion systems. Bulletin of Mathematical Biology, 83(7):1–35, 2021. [30] R. A. Van Gorder, A. Kamilova, and A. -
Jonathan Adam Sherratt July 29, 2019 Department of Mathematics, Heriot-Watt University Edinburgh EH14 4AS, UK
Curriculum Vitae Jonathan Adam Sherratt July 29, 2019 Department of Mathematics, Heriot-Watt University Edinburgh EH14 4AS, UK. Tel: +44 131 451 3740 Fax: +44 131 451 3249 Email: [email protected] Date of Birth: 2 February 1967 Citizenship: British Education Sept 1978{Oct 1984 Tiffin School, Kingston-upon-Thames Oct 1985{June 1988 University of Cambridge (Queens' College) Sept 1988{Aug 1989 Department of Applied Mathematics, University of Washington Oct 1989{July 1991 University of Oxford (Lincoln College) Academic Career Oct 1991{ Dec 1993 Merton College, Oxford Junior Research Fellow Jan 1994{Sept 1997 Department of Mathematics, University of Warwick Lecturer in Mathematics Oct 1997{Dec 1997 Department of Mathematics, University of Warwick Senior Lecturer in Mathematics Jan 1998{ Department of Mathematics, Heriot-Watt University Professor of Mathematics Degrees B.A. (hons) in mathematics, University of Cambridge, triple first class (June 1988) D.Phil. in mathematics, University of Oxford (June 1991) Thesis: \Mathematical models of wound healing" Supervisors: by J.D. Murray frs and P.K. Maini frs Curriculum Vitae Jonathan Adam Sherratt July 29, 2019 Page 2 of 23 Fellowships and Prizes I received various undergraduate and postgraduate prizes which are not listed. • Sixth Bellman Prize, for the best paper published in Mathematical Biosciences during 1994 and 1995. Awarded to co-authors Paul Dale, Philip Maini and myself in October 1997. • EPSRC Advanced Research Fellowship, October 2000{September 2005. • Elected to a Fellowship of the Royal Society of Edinburgh, March 2001. • Sir Edward Whittaker Memorial Prize, awarded in October 2001 by the Edinburgh Math- ematical Society. -
Arabic at St John's Life in a Changing Arctic Ocean Jane Austen and St
TW 2017 St John’s College, Oxford John’s St The magazine of St John’s College, Oxford Arabic at St John’s Life in a Changing Arctic Ocean Jane Austen and St John’s Winter is Coming 2017 An Unusual Collaboration Contents 2 From the President 4 News 8 Lecture Notes 10 Arrivals and leavers 13 Arabic at St John’s A long association 19 Life in a Changing Arctic Ocean Climate change in the far north 13 Arabic at St John’s 24 The Reading List 29 Jane Austen at St John’s An intimate insight 34 Artists in Residence 36 Winter is Coming The Medieval World of Game of Thrones 39 Achievements 42 Celebrating Mathematics at St John’s 44 From the Junior and Middle Common Rooms 46 Sport 53 An Unusual Collaboration Unexpected meetings at alumni events 19 Life in a Changing Arctic Ocean 57 In Memoriam 75 College Record 90 News Of Alumni 93 Calendar St John’s College, Oxford From the Editor s I write, a furious debate is going on about Britain’s universities. True enough, that sentence could have been written at any time in the last two hundred years (trust me – I’ve written a very long book Aabout the subject). But the intensity of the argument is still remarkable. Questions about university funding, student fees, the quality of teaching, the volume of research, even – from one former minister who really ought to know better – the length of the Long Vacation: all these have filled newspapers, social media, and the election campaign in 2017. -
Thesis Rests with Its Author
University of Bath PHD Mathematical models for the coexistence of sexual and asexual conspecifics Carrillo Medrano, Claudia del Carmen Award date: 2002 Awarding institution: University of Bath Link to publication Alternative formats If you require this document in an alternative format, please contact: [email protected] General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 09. Oct. 2021 Mathematical Models for the Coexistence of Sexual and Asexual Conspecifics Submitted by Claudia del Carmen Carrillo Medrano for the degree of Doctor of Philosophy of the University of Bath COPYRIGHT Attention is drawn to the fact that copyright of this thesis rests with its author. This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and no information derived from it may be published without the prior written consent of the author. -
Encaenia 2015
WEDNESDay 1 july 2015 • SuPPlEMENT (1) TO NO 5102 • VOl 145 Gazette Supplement Encaenia 2015 Congregation 24 June inimicis pro virili parte contendit: ita cum greatest power and eminence; instead, his David quidam perversus non monstrum books dealt with cholera, poverty and capital 1 Conferment of Honorary Degrees necare sed eos qui monstruosa illius punishment, and they were written with so The Public Orator made the following tyrannidis scelera ostenderant supprimere sharp a pen that even the experts admitted speeches in presenting the recipients of conaretur, errores eius manifestos reddidit, that they were now seeing the German past Honorary Degrees at the Encaenia held in in foro quinque dies luctatus est, victoriam with new eyes. But while educating the the Sheldonian Theatre on Wednesday, haud dubiam reportavit. libellum quoque learned, he did not neglect a wider public: 24 june: ad historiam defendendam edidit, sane turning his attention from the nineteenth to eloquentem et sapientia refertum; quam the twentieth century, he wrote an account Degree of Doctor of Letters tamen exemplum omnibus eius scriptis of the Third Reich, in which, as Catullus’ PROFESSOR SIR RICHARD EVANS praebitum forsitan vel melius approbet. friend Cornelius Nepos did in his study of Italy, he dared to write Historian Praesento rerum Germanicarum Qui dicunt doctos turres eburneas habitare, investigatorem indefessum, Ricardum Three volumes’ worth of history: credere solent eos de laboribus atque Iohannem Evans, equitem auratum, What learning, gosh, what industry. academiae Britannicae socium, apud aerumnis hominum parvum vel nihil Great is the mass of evidence, the tale grim, universitatem Cantabrigiensem quondam scire; at si revera sedem editam et sapientia but he leads the reader through the labyrinth historiae Professorem Regium et adhuc munitam occupant, immensitatem campi with a sure step. -
Logic, Diophantine Geometry, and Transcendence Theory
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 49, Number 1, January 2012, Pages 51–71 S 0273-0979(2011)01354-4 Article electronically published on October 24, 2011 COUNTING SPECIAL POINTS: LOGIC, DIOPHANTINE GEOMETRY, AND TRANSCENDENCE THEORY THOMAS SCANLON Abstract. We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier. 1. Introduction Over the past decade and a half, starting with Hrushovski’s proof of the func- tion field Mordell-Lang conjecture [12], some of the more refined theorems from model theory in the sense of mathematical logic have been applied to problems in diophantine geometry. In most of these cases, the technical results underlying the applications concern the model theory of fields considered with some additional distinguished structure, and the model theoretic ideas fuse algebraic model theory (the study of algebraic structures with a special emphasis on questions of defin- ability) and stability theory (the development of abstract notions of dimension, dependence, classification, etc.) for the purpose of analyzing the class of models of a theory. Over this period, there has been a parallel development of the model theory of theories more suited for real analysis carried out under the rubric of o-minimality, but this theory did not appear to have much to say about number theory. Some spectacular recent theorems demonstrate the error of this impression. In the paper [30], Pila presents an unconditional proof of a version of the so- called Andr´e-Oort conjecture about algebraic relations amongst the j-invariants of elliptic curves with complex multiplication using a novel technique that comes from model theory.