Paths To, from and in Renormalization at the Confluence of Rough Paths, Algebra, Analysis and Geometry
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June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings for MATHEMATICS 2014 and Events Following a Very Generous Tions Open in Late 2014
LONDONLONDON MATHEMATICALMATHEMATICAL SOCIETYSOCIETY NEWSLETTER No. 437 June 2014 Society Meetings Society and Events SHEPHARD PRIZE: NEW PRIZE Meetings FOR MATHEMATICS 2014 and Events Following a very generous tions open in late 2014. The prize Monday 16 June donation made by Professor may be awarded to either a single Midlands Regional Meeting, Loughborough Geoffrey Shephard, the London winner or jointly to collaborators. page 11 Mathematical Society will, in 2015, The mathematical contribution Friday 4 July introduce a new prize. The prize, to which an award will be made Graduate Student to be known as the Shephard must be published, though there Meeting, Prize will be awarded bienni- is no requirement that the pub- London ally. The award will be made to lication be in an LMS-published page 8 a mathematician (or mathemati- journal. Friday 4 July cians) based in the UK in recog- Professor Shephard himself is 1 Society Meeting nition of a specific contribution Professor of Mathematics at the Hardy Lecture to mathematics with a strong University of East Anglia whose London intuitive component which can be main fields of interest are in page 9 explained to those with little or convex geometry and tessella- Wednesday 9 July no knowledge of university math- tions. Professor Shephard is one LMS Popular Lectures ematics, though the work itself of the longest-standing members London may involve more advanced ideas. of the LMS, having given more page 17 The Society now actively en- than sixty years of membership. Tuesday 19 August courages members to consider The Society wishes to place on LMS Meeting and Reception nominees who could be put record its thanks for his support ICM 2014, Seoul forward for the award of a in the establishment of the new page 11 Shephard Prize when nomina- prize. -
Arxiv:1710.07481V1 [Q-Fin.PR] 20 Oct 2017 Appendix A
A REGULARITY STRUCTURE FOR ROUGH VOLATILITY C. BAYER, P. K. FRIZ, P. GASSIAT, J. MARTIN, B. STEMPER Abstract. A new paradigm recently emerged in financial modelling: rough (stochastic) volatility, first observed by Gatheral et al. in high-frequency data, subsequently derived within market microstructure models, also turned out to capture parsimoniously key stylized facts of the entire implied volatility surface, including extreme skews that were thought to be outside the scope of stochastic volatility. On the mathematical side, Markovianity and, partially, semi-martingality are lost. In this paper we show that Hairer's regularity structures, a major extension of rough path theory, which caused a revolution in the field of stochastic partial differential equations, also provides a new and powerful tool to analyze rough volatility models. Dedicated to Professor Jim Gatheral on the occasion of his 60th birthday. Contents 1. Introduction 2 1.1. Markovian stochastic volatility models 3 1.2. Complications with rough volatility 3 1.3. Description of main results 4 1.4. Lessons from KPZ and singular SPDE theory 8 2. Reduction of Theorems 1.1 and 1.3 10 3. The rough pricing regularity structure 11 3.1. Basic pricing setup 11 3.2. Approximation and renormalization theory 18 3.3. The case of the Haar basis 23 4. The full rough volatility regularity structure 24 4.1. Basic setup 24 4.2. Small noise model large deviation 25 5. Rough Volterra dynamics for volatility 26 5.1. Motivation from market micro-structure 26 5.2. Regularity structure approach 27 5.3. Solving for rough volatility 28 6. -
Press Release
Press release 13 August 2014 Two Fields Medals 2014 awarded to ERC laureates The 2014 Fields Medals were awarded today to four outstanding mathematicians, of whom two are grantees of the European Research Council (ERC): Prof. Artur Avila (Brazil-France), an ERC Starting grant holder since 2010, and Prof. Martin Hairer (Austria) has been selected for funding under an ERC Consolidator grant in 2013. They received the prize respectively for their work on dynamical systems and probability, and on stochastic analysis. The other two laureates are Prof. Manjul Barghava (Canada-US) and Prof. Maryam Mirzakhani (Iran). The Medals were announced at the International Congress of Mathematicians (ICM) taking place from 13 – 21 August in Seoul, South Korea. On the occasion of the announcement, ERC President Prof. Jean-Pierre Bourguignon, a mathematician himself, said: “On behalf of the ERC Scientific Council, I would like to congratulate warmly all four Fields Medallists for their outstanding contributions to the field of mathematics. My special congratulations go to Artur Avila and Martin Hairer, who are both brilliant scientists supported by the ERC. We are happy to see that their remarkable talent in the endless frontiers of science has been recognised. The Fields Medals awarded today are also a sign that the ERC continues to identity and fund the most promising researchers across Europe; this is true not only in mathematics but in all scientific disciplines.” EU Commissioner for Research, Innovation and Science, Máire Geoghegan-Quinn, said: “I would like to congratulate the four laureates of the Fields Medal announced today. The Fields Medal, the highest international distinction for young mathematicians, is a well- deserved honour for hardworking and creative young researchers who push the boundaries of knowledge. -
Annual Report 2017-2018
Annual Review 2017 | 2018 ONTENTS C 1 Overview 1 2 Profile 4 3 Research 6 4 Events 9 5 Personnel 13 6 Mentoring 17 7 Structures 18 APPENDICES R1 Highlighted Papers 20 R2 Complete List of Papers 23 E1 HIMR-run Events 29 E2 HIMR-sponsored Events 31 E3 Focused Research Events 39 E4 Future Events 54 P1 Fellows Joining in 2017|2018 59 P2 Fellows Leaving since September 2017 60 P3 Fellows Moving with 3-year Extensions 62 P4 Future Fellows 63 M1 Mentoring Programme 64 1. Overview This has been another excellent year for the Heilbronn Institute, which is now firmly established as a major national mathematical research centre. HIMR has developed a strong brand and is increasingly influential in the UK mathematics community. There is currently an outstanding cohort of Heilbronn Research Fellows doing first-rate research. Recruitment of new Fellows has been most encouraging, as is the fact that many distinguished academic mathematicians continue to work with the Institute. The research culture at HIMR is excellent. Members have expressed a high level of satisfaction. This is especially the case with the Fellows, many of whom have chosen to continue their relationships with the Institute. Our new Fellows come from leading mathematics departments and have excellent academic credentials. Those who left have moved to high-profile groups, including several to permanent academic positions. We currently have 29 Fellows, hosted by 6 universities. We are encouraged by the fact that of the 9 Fellows joining us this year, 5 are women. The achievements of our Fellows this year again range from winning prestigious prizes to publishing in the elite mathematical journals and organising major mathematical meetings. -
PDF in English
:RUOG6FLHQWLÀF Newsletter No. 39 • October 2014 World Scientific publishes acclaimed new book Fields Medallists’ Lectures, 3rd Edition edited by Sir Michael Atiyah (University of Edinburgh, UK), Daniel Iagolnitzer (CEA-Saclay, France), Chitat Chong (National University of Singapore) John W. MilnorEnrico Bombieri Gerd Faltings Andrei Okounkov Terence Tao Cédric Villani Elon Lindenstrauss Ngô Båo Châu Stanislav Smirnov Manjul Bhargava Martin Hairer lthough the Fields Medal does not have the same public The third edition of Fieldsds recognition as the Nobel Prize, they share a similar Medallists’ Lectures featuress Aintellectual standing. It is restricted to one field — that additional contributions from: of mathematics. The medal is awarded to the best mathematicians John W. Milnor (1962), Enricoo who are 40 or younger, every four years. Bombieri (1974), Gerd Faltingsgs A list of Fields Medallists and their contributions provides (1986), Andrei Okounkov (2006), TTerence TTao (2006)(2006), CédCédrici a bird’s eye view of the major developments in mathematics Villani (2010), Elon Lindenstrauss (2010), Ngô Båo Châu over the past 80 years. It highlights the areas in which, at (2010), Stanislav Smirnov (2010), Manjul Bhargava (2014) and various times, the greatest progress has been made. Martin Hairer (2014). At approximately 1000 pages, this new edition will be published in two volumes. The Lives and Works of 33 Nobel Laureates in Crystallography presented in new book From a Grain of Salt to the Ribosome his book is published to Sweden), Anders Liljas (Lund University, Sweden), Sven Lidin celebrate the Interna- (Lund University, Sweden), From a Grain of Salt to the T tional Year of Crystall- Ribosome: The History of Crystallography as Seen Through the ography 2014, as proclaimed by Lens of the Nobel Prize describes the lives and works of 33 Nobel the United Nations. -
Stochastic Pdes, Regularity Structures, and Interacting Particle Systems
ANNALES DE LA FACULTÉ DES SCIENCES Mathématiques AJAY CHANDRA AND HENDRIK WEBER Stochastic PDEs, Regularity structures, and interacting particle systems Tome XXVI, no 4 (2017), p. 847-909. <http://afst.cedram.org/item?id=AFST_2017_6_26_4_847_0> © Université Paul Sabatier, Toulouse, 2017, tous droits réservés. L’accès aux articles de la revue « Annales de la faculté des sci- ences de Toulouse Mathématiques » (http://afst.cedram.org/), implique l’accord avec les conditions générales d’utilisation (http://afst.cedram. org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l’utilisation à fin strictement personnelle du copiste est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/ Annales de la faculté des sciences de Toulouse Volume XXVI, no 4, 2017 pp. 847-909 Stochastic PDEs, Regularity structures, and interacting particle systems Ajay Chandra (1) and Hendrik Weber (2) ABSTRACT.— These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Mat- sumoto, and Darmstadt. The main aim is to explain some aspects of the theory of “Regularity structures” developed recently by Hairer in [27]. This theory gives a way to study well-posedness for a class of stochastic PDEs that could not be treated previously. Prominent examples include 4 the KPZ equation as well as the dynamic Φ3 model. Such equations can be expanded into formal perturbative expansions. -
Journals/Notices/202003/ “Hyphen Classes” of the Form XX–00 General Refer- Rnoti-P410.Pdf Ence Works, XX–01 Introductory Expositions, XX–02
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY S E European March 2020 M M Mathematical Issue 115 E S Society ISSN 1027-488X Features Renormalisation of Stochastic PDEs Approximate Groups Interviews Freeman Dyson David Ruelle Obituary Hagen Neidhardt Freeman Dyson (photo: Dan Komoda/ IAS, Princeton, NJ USA) New books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. K3 Surfaces (EMS Tracts in Mathematics, Vol. 32) Shigeyuki Kondo– (Nagoya University, Japan) ISBN 978-3-03719-208-5. 2020. 252 pages. Hardcover. 17 x 24 cm. 78.00 Euro K 3 surfaces are a key piece in the classification of complex analytic or algebraic surfaces. The term was coined by A. Weil in 1958 – a result of the initials Kummer, Kähler, Kodaira, and the mountain K2 found in Karakoram. The most famous example is the Kummer surface discovered in the 19th century. K 3 surfaces can be considered as a 2-dimensional analogue of an elliptic curve, and the theory of periods – called the Torelli-type theorem for K 3 surfaces – was established around 1970. Since then, several pieces of research on K 3 sur- faces have been undertaken and more recently K 3 surfaces have even become of interest in theoretical physics. The main purpose of this book is an introduction to the Torelli-type theorem for complex analytic K 3 surfaces, and its applications. -
Stochastic Quantization Equations
Stochastic quantization equations Hao Shen (Columbia University) February 23, 2016 Page 1/25 1 2 I Ornstein-Uhlenbeck (d=0): S(X )= 2 X dX = X dt + dB t − t t 4 1 2 1 4 d I Φ model: S(φ)= 2 ( φ(x)) + 4 φ(x) d x ´ r @ φ =∆φ φ3 + ⇠ t − 1 2 2 I Sine-Gordon (d=2): S(φ)= 2β ( φ(x)) + cos(φ(x))d x ´ r 1 @t u = ∆u + sin(βu)+⇠ 2 Stochastic quantization Stochastic quantization: consider a Euclidean quantum field theory measure as a stationary distribution of a stochastic process. exp( S(φ)) φ/Z @ φ = δS(φ)/δφ + ⇠ − D ) t − where ⇠ is space-time white noise E[⇠(x, t)⇠(¯x, t¯)] = δ(d)(x x¯)δ(t t¯). − − Page 2/25 Stochastic quantization Stochastic quantization: consider a Euclidean quantum field theory measure as a stationary distribution of a stochastic process. exp( S(φ)) φ/Z @ φ = δS(φ)/δφ + ⇠ − D ) t − where ⇠ is space-time white noise E[⇠(x, t)⇠(¯x, t¯)] = δ(d)(x x¯)δ(t t¯). − − 1 2 I Ornstein-Uhlenbeck (d=0): S(X )= 2 X dX = X dt + dB t − t t 4 1 2 1 4 d I Φ model: S(φ)= 2 ( φ(x)) + 4 φ(x) d x ´ r @ φ =∆φ φ3 + ⇠ t − 1 2 2 I Sine-Gordon (d=2): S(φ)= 2β ( φ(x)) + cos(φ(x))d x ´ r 1 @t u = ∆u + sin(βu)+⇠ 2 Page 2/25 I The solution to the linear equation (when d 2) is a.s. -
NEWSLETTER Issue: 492 - January 2021
i “NLMS_492” — 2020/12/21 — 10:40 — page 1 — #1 i i i NEWSLETTER Issue: 492 - January 2021 RUBEL’S MATHEMATICS FOUR PROBLEM AND DECADES INDEPENDENCE ON i i i i i “NLMS_492” — 2020/12/21 — 10:40 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Eleanor Lingham (Sheeld Hallam University) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when EDITORIAL BOARD reproducing whole articles. Contributions to the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or David Chillingworth (University of Southampton) photographer for the rights to reproduce. Jessica Enright (University of Glasgow) The LMS cannot accept responsibility for the Jonathan Fraser (University of St Andrews) accuracy of information in the Newsletter. Views Jelena Grbic´ (University of Southampton) expressed do not necessarily represent the Cathy Hobbs (UWE) views or policy of the Editorial Team or London Christopher Hollings (Oxford) Mathematical Society. Robb McDonald (University College London) Adam Johansen (University of Warwick) Susan Oakes (London Mathematical Society) ISSN: 2516-3841 (Print) Andrew Wade (Durham University) ISSN: 2516-385X (Online) Mike Whittaker (University of Glasgow) DOI: 10.1112/NLMS Andrew Wilson (University of Glasgow) Early Career Content Editor: Jelena Grbic´ NEWSLETTER WEBSITE News Editor: Susan Oakes Reviews Editor: Christopher Hollings The Newsletter is freely available electronically at lms.ac.uk/publications/lms-newsletter. CORRESPONDENTS AND STAFF LMS/EMS Correspondent: David Chillingworth MEMBERSHIP Policy Digest: John Johnston Joining the LMS is a straightforward process. For Production: Katherine Wright membership details see lms.ac.uk/membership. -
Mathematical Olympiad & Other Scholarship, Research Programmes
DEPARTMENT OF MATHEMATICS COCHIN UNIVERSITY OF SCIENCE AND TECHNOLOGY COCHIN - 682 022 The erstwhile University of Cochin founded in 1971 was reorganised and converted into a full fledged University of Science and Technology in 1986 for the promotion of Graduate and Post Graduate studies and advanced research in Applied Sciences, Technology, Commerce, Management and Social Sciences. The combined Department of Mathematics and Statistics came into existence in 1976, which was bifurcated to form the Department of Mathematics in 1996. Apart from offering M.Sc, and M. Phil. degree courses in Mathematics it has active research programmes in, Algebra, Operations Research, Stochastic Processes, Graph Theory, Wavelet Analysis and Operator Theory. The Department has been coordinating the Mathematical olympiad - a talent search programme for high school students since 1990. It also organizes Mathematics Enrichment Programmes for students and teachers to promote the cause of Mathematics and attract young minds to choose a career in Mathematics. It also co-ordinates the national level tests of NBHM for M.Sc and Ph.D scholarship. The department also organized the ‘International Conference on Recent Trends in Graph Theory and Combinatorics’ as a satellite conference of the International Congress of Mathematicians (ICM) during August 2010. “Tejasvinavadhithamastu” May learning illumine us both, The teacher and the taught. In the ‘SILVER JUBILEE YEAR’ of the RMO Co-ordination, we plan a reunion of the ‘INMO Awardees’ during 1991-2014. Please contact the Regional Co-ordinator ([email protected].) -1- PREFACE This brochure contains information on various talent search and research programmes in basic sciences in general and mathematics in particular and is meant for the students of Xth standard and above. -
Martin Hairer
MARTIN HAIRER Mathematics Department Phone: ++44 20 7589 5111 (dept) Imperial College London Email: [email protected] London SW7 2AZ Web: http://www.hairer.org/ United Kingdom Last update of this document: January 20, 2018 Career history from 10/2017 CHAIR IN PROBABILITY AND STOCHASTIC ANALYSIS Imperial College London. 04/2014 – 10/2017 REGIUS PROFESSOR OF MATHEMATICS The University of Warwick. 01/2010 – 04/2014 FULL PROFESSOR The University of Warwick. 01/2009 – 01/2010 ASSOCIATE PROFESSOR New York University (Courant institute). 09/2007 – 01/2009 ASSOCIATE PROFESSOR (READER) The University of Warwick. 09/2006 – 09/2007 ASSOCIATE PROFESSOR The University of Warwick. 10/2004 – 09/2006 LECTURER /ASSISTANT PROFESSOR The University of Warwick. 10/2003 – 10/2004 ADVANCED FELLOWSHIP (from the Swiss NSF) Mathematics Research Centre, University of Warwick. 10/2002 – 10/2003 POSTDOCTORAL FELLOWSHIP (from the Swiss NSF) Mathematics Research Centre, University of Warwick. Education November 2001 PHD IN PHYSICS – University of Geneva. October 1998 MSC IN PHYSICS – University of Geneva. July 1998 BSC IN MATHEMATICS – University of Geneva. June 1994 HIGH SCHOOL DIPLOMA – College` Claparede,` Geneva. Honours and awards • 2008 LMS Whitehead prize • 2008 Philip Leverhulme Prize • 2009 Royal Society Wolfson Research Merit Award • 2013 Fermat prize • Fellow of the Royal Society (since 2014) • 2014 Frohlich¨ prize • 2014 Fields medal • Fellow of the AMS (since 2015) • Member of the Austrian Academy of Sciences (since 2015) • Member of the German National Academy of Sciences Leopoldina (since 2015) • Member of the Berlin-Brandenburg Academy of Sciences and Humanities (since 2016) • Honorary degree in science from HKBU (2016) • Honorary Knight Commander of the British Empire (KBE, since 2016) Past and current PhD students A. -
Arxiv:2109.00399V1 [Math.AP] 1 Sep 2021 Esi H Atta Renormalization That Fact the in Cess This Setting
Locality for singular stochastic PDEs I. BAILLEUL1 & Y. BRUNED Abstract. We develop in this note the tools of regularity structures to deal with singular stochastic PDEs that involve non-translation invariant differential operators. We describe in particular the renormalised equation for a very large class of spacetime dependent renormalization schemes. 1 – Introduction In contrast to paracontrolled calculus [18, 1, 3] that was developed in a manifold, hence non- translation invariant setting, after being set first in the Euclidean torus, the theory of regularity structures [20, 12, 15, 10] has so far been developed in the translation invariant setting of locally Euclidean spaces and its analytic side was devised for the analysis of equations involving constant coefficients differential operators. The extension of the theory to a manifold setting calls for a development of the theory to deal in a first step with non-translation invariant differential operators in a locally Euclidean setting. It is the purpose of the present note to make that first step, assuming from the reader that she/he is already acquainted with the fundamentals of the theory of regularity structures, such as exposed for instance in Hairer’s lecture notes [21, 22], the book [17] by Friz & Hairer, or Chandra & Weber’s article [16], where accessible accounts of part of the theory of regularity structures. Bailleul & Hoshino’s ‘Tourist Guide’ [8] provides a dense self-contained presentation of the analytic and algebraic sides of the theory. Denote by (x0, x1) ∈ R × T a typical spacetime point over the one dimensional periodic torus T. (We choose for convenience of notations to work on the one dimensional torus rather than on a multidimensional torus.) Let i i 2 i Lx1 v := a (·)∂x1 v + b (·)∂x1 v, (1 ≤ i ≤ k0), stand for a finite family of second order differential operators with smooth coefficients.