DOCSLIB.ORG

NEWSLETTER Issue: 482 - May 2019

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
NEWSLETTER Issue: 482 - May 2019 i “NLMS_482” — 2019/5/7 — 15:39 — page 1 — #1 i i i NEWSLETTER Issue: 482 - May 2019 RANDOM GROWTH: FROM GAMBLING COLOURING FROM LICHEN TO RANDOM WITHOUT TO LIGHTNING MODELLING COLOURS i i i i i “NLMS_482” — 2019/5/7 — 15:39 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbic´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) Andrew Wade (Durham University) NEWSLETTER WEBSITE Early Career Content Editor: Vicky Neale The Newsletter is freely available electronically News Editor: Susan Oakes at lms.ac.uk/publications/lms-newsletter. Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process. For LMS/EMS Correspondent: David Chillingworth membership details see lms.ac.uk/membership. Policy Roundup: John Johnston Production: Katherine Wright Printing: Holbrooks Printers Ltd SUBMISSIONS The Newsletter welcomes submissions of fea- EDITORIAL OFFICE ture content, including mathematical arti- cles, career related articles, and microtheses London Mathematical Society from members and non-members. Submis- De Morgan House sion guidelines and LaTeX templates can be 57–58 Russell Square found at lms.ac.uk/publications/submit-to-the- London, WC1B 4HS lms-newsletter. [email protected] Feature content should be submitted to the Charity registration number: 252660 editor-in-chief at [email protected]. News items should be sent to [email protected]. Notices of events should be prepared us- ing the template at lms.ac.uk/publications/lms- COVER IMAGE newsletter and sent to [email protected]. Diusion-limited aggregation grown by compos- For advertising rates and guidelines see ing conformal mappings using the Hastings– lms.ac.uk/publications/advertise-in-the-lms- Levitov construction. See page 19. newsletter. i i i i i “NLMS_482” — 2019/5/7 — 15:39 — page 3 — #3 i i i CONTENTS NEWS The latest from the LMS and elsewhere 4 LMS BUSINESS Reports from the LMS 11 FEATURES From Lichen to Lightning: Understanding Random Growth 14 From Gambling to Random Modelling 20 Colouring Without Colours: Graphs and Matroids 25 The Nigerian Mathematical Society 30 EARLY CAREER Microthesis: Timescales of Inuence on Unobserved Graphs 31 REVIEWS From the bookshelf 34 OBITUARIES In memoriam 39 EVENTS Latest announcements 45 CALENDAR All forthcoming events 50 i i i i i “NLMS_482” — 2019/5/7 — 15:39 — page 4 — #4 i i i 4 NEWS LMS NEWS LMS General Meeting its owners University College London, and will be the sixth journal published in partnership with Wiley, There will be a General Meeting of the Society on 28 along with the core journals of the LMS (the Bulletin, June 2019 at 3:30 pm, to be held at Mary Ward House, Journal, Proceedings and Transactions) and the Journal Tavistock Square, London. The business shall be: 1) of Topology. the appointment of the Scrutineers; 2) announce- ment of Council’s recommendation for election to Honorary Membership; 3) announcement of LMS William Chen, Frank Smith, Alexander Sobolev prize winners for 2019. Managing Editors The General Meeting, at which Professor Bakh Khous- sainov (University of Auckland) will give the Aitken Forthcoming LMS Events Lecture, will be followed by a Society Meeting. It is hoped that as many members as possible will be The following events will take place in the next two able to attend. months: Mathematika partnering with Wiley LMS Education Day: 13 May, De Morgan House, Lon- From January 2020, the don (tinyurl.com/y65p23kk) LMS will partner with Invited Lecture Series: 20–24 May, ICMS, Edinburgh John Wiley & Sons Ltd (tinyurl.com/yb7v47yu) for the production and Northern Regional Meeting: 28–29 May, Newcastle distribution of the jour- University (tinyurl.com/y9d49s5t) nal Mathematika. The de- cision to move to Wi- Popular Lectures: 26 June, Institute of Education, ley was taken jointly London (tinyurl.com/hu58wjk) by the Managing Editors Graduate Student Meeting, General Meeting and of Mathematika and the Aitken Lecture: 28 June, Mary Ward House, London LMS Publications Com- (tinyurl.com/y3umhyjl) mittee and Council after a thorough review process. Mathematika is published A full listing of upcoming LMS events can be found by the London Mathematical Society on behalf of on page 50. OTHER NEWS Karen Uhlenbeck awarded the 2019 tal impact of her work on analysis, geometry and Abel Prize mathematical physics’. She is the rst woman to be awarded the prestigious honour. Professor Uhlenbeck This year’s Abel Prize will be presented with the Prize by His Majesty King has been awarded to Harald V at an award ceremony in Oslo on 21 May the US mathematician 2019. The Prize carries a cash award of NOK 6 million Professor Karen Uhlen- (about €650,000 or about US$730,000). beck, Princeton Univer- Professor Uhlenbeck is a founder of modern Geo- sity, for her ‘pioneer- metric Analysis. Her perspective has permeated the ing achievements in geo- eld and led to some of the most dramatic advances metric partial dierential in mathematics in the past 40 years. Geometric anal- equations, gauge theory ysis is a eld of mathematics where techniques of and integrable systems, analysis and dierential equations are interwoven and for the fundamen- i i i i i “NLMS_482” — 2019/5/7 — 15:39 — page 5 — #5 i i i NEWS 5 with the study of geometrical and topological prob- neural networks a critical component of computing,” lems, specically, studies on objects such as curves, and recognises work carried out both independently surfaces, connections and elds, which are critical and together by the three winners. Widely consid- points of functionals representing geometric quanti- ered as the highest distinction in computer science, ties such as energy and volume. For example, minimal the award comes with a $1 million prize. surfaces are critical points of the area and harmonic maps are critical points of the Dirichlet energy. The “Articial neural networks” are inspired by the human winner’s major contributions include foundational brain, and enable computers to solve tasks such as results on minimal surfaces and harmonic maps, object recognition, without explicit step-by-step in- Yang-Mills theory, and integrable systems. structions. This idea goes back to the early 1980s, when Hinton — who had previously studied at the Professor Uhlenbeck has received many honours Universities of Cambridge and Edinburgh — was an during a distinguished career and was elected an early advocate of this approach. The three winners Honorary Member of the LMS in 2008. were part of a small group of researchers who per- severed with this “machine learning” approach to For the rst time the announcement was transmitted articial intelligence during the next three decades; live to an audience at the Science Gallery in Lon- today this methodology has been incorporated into don, with the LMS working in collaboration with the technology used by billions of people, as well as being Norwegian Academy of Science and Letters and the dominant across most areas of scientic research. Norwegian Embassy in London. After the announce- ment, a panel including LMS President Professor Car- ACM President Cherri M. Pancake said: “Articial in- oline Series FRS, past-LMS President Professor Nigel telligence is now one of the fastest-growing areas Hitchin FRS, Professor Mark Haskins and Professor in all of science and one of the most talked-about Peter Topping discussed the winner’s life and work. topics in society. The growth of and interest in AI is The panel was moderated by the Science Gallery’s due, in no small part, to the recent advances in deep founding Director Daniel Glaser. learning for which Bengio, Hinton and LeCun laid the foundation.” Professor Caroline Series FRS, President of the LMS, said: “I have always been a great admirer of Karen’s. She is a powerful and distinguished mathematician L’Oréal–UNESCO Prize for Women whose foundational work in geometric analysis has and Science had far reaching ramications. Throughout her ca- reer she has also been a great leader and mentor, The 21st International Prize for Women in Science and I am sure that many others besides myself will L’Oréal-UNESCO, on 11 February, awarded honours be absolutely delighted that she has been recognised to ve outstanding women scientists from dierent by the award of the Abel Prize, one of the highest parts of the world, for excellence in their work in the awards in mathematics”. elds of material science, mathematics and computer science. Among the ve international prizes two are More information is available at abelprize.no/. mathematicians, Ingrid Daubechies and Claire Voisin, both Honorary Members of the LMS. Turing Award announced Professor Daubechies was awarded for her “ground- breaking work on wavelet theory, which has trans- As the Newsletter was going to press, the Association formed the numerical treatment of images and sig- for Computing Machinery (ACM) has announced the nal processing, providing standard and exible al- joint winners of the ACM A.M.
Load more

Recommended publications
  • Caucher Birkar — from Asylum Seeker to Fields Medal Winner at Cambridge
    MATHS, 1 Caucher Birkar, 41, at VERSION Cambridge University, photographed by Jude Edginton REPR O OP HEARD THE ONE ABOUT THE ASYLUM SEEKER SUBS WHO WANDERED INTO A BRITISH UNIVERSITY... A RT AND CAME OUT A MATHS SUPERSTAR? PR ODUCTION CLIENT Caucher Birkar grew up in a Kurdish peasant family in a war zone and arrived in Nottingham as a refugee – now he has received the mathematics equivalent of the Nobel prize. By Tom Whipple BLACK YELLOW MAGENTA CYAN 91TTM1940232.pgs 01.04.2019 17:39 MATHS, 2 VERSION ineteen years ago, the mathematics Caucher Birkar in Isfahan, Receiving the Fields Medal If that makes sense, congratulations: you department at the University of Iran, in 1999 in Rio de Janeiro, 2018 now have a very hazy understanding of Nottingham received an email algebraic geometry. This is the field that from an asylum seeker who Birkar works in. wanted to talk to someone about The problem with explaining maths is REPR algebraic geometry. not, or at least not always, the stupidity of his They replied and invited him in. listeners. It is more fundamental than that: O OP N So it was that, shortly afterwards, it is language. Mathematics is not designed Caucher Birkar, the 21-year-old to be described in words. It is designed to be son of a Kurdish peasant family, described in mathematics. This is the great stood in front of Ivan Fesenko, a professor at triumph of the subject. It was why a Kurdish Nottingham, and began speaking in broken asylum seeker with bad English could convince SUBS English.
    [Show full text]
  • Birational Geometry of Algebraic Varieties
    Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol. 1 (563–588) BIRATIONAL GEOMETRY OF ALGEBRAIC VARIETIES Caucher Birkar 1 Introduction This is a report on some of the main developments in birational geometry in recent years focusing on the minimal model program, Fano varieties, singularities and related topics, in characteristic zero. This is not a comprehensive survey of all advances in birational geometry, e.g. we will not touch upon the positive characteristic case which is a very active area of research. We will work over an algebraically closed field k of characteristic zero. Varieties are all quasi-projective. Birational geometry, with the so-called minimal model program at its core, aims to classify algebraic varieties up to birational isomorphism by identifying “nice” elements in each birational class and then classifying such elements, e.g study their moduli spaces. Two varieties are birational if they contain isomorphic open subsets. In dimension one, a nice element in a birational class is simply a smooth and projective element. In higher dimension though there are infinitely many such elements in each class, so picking a rep- resentative is a very challenging problem. Before going any further lets introduce the canonical divisor. 1.1 Canonical divisor. To understand a variety X one studies subvarieties and sheaves on it. Subvarieties of codimension one and their linear combinations, that is, divisors play a crucial role. Of particular importance is the canonical divisor KX . When X is smooth this is the divisor (class) whose associated sheaf OX (KX ) is the canonical sheaf !X := det ΩX where ΩX is the sheaf of regular differential forms.
    [Show full text]
  • Arxiv:1609.05543V2 [Math.AG] 1 Dec 2020 Ewrs Aovreis One Aiis Iersystem Linear Families, Bounded Varieties, Program
    Singularities of linear systems and boundedness of Fano varieties Caucher Birkar Abstract. We study log canonical thresholds (also called global log canonical threshold or α-invariant) of R-linear systems. We prove existence of positive lower bounds in different settings, in particular, proving a conjecture of Ambro. We then show that the Borisov- Alexeev-Borisov conjecture holds, that is, given a natural number d and a positive real number ǫ, the set of Fano varieties of dimension d with ǫ-log canonical singularities forms a bounded family. This implies that birational automorphism groups of rationally connected varieties are Jordan which in particular answers a question of Serre. Next we show that if the log canonical threshold of the anti-canonical system of a Fano variety is at most one, then it is computed by some divisor, answering a question of Tian in this case. Contents 1. Introduction 2 2. Preliminaries 9 2.1. Divisors 9 2.2. Pairs and singularities 10 2.4. Fano pairs 10 2.5. Minimal models, Mori fibre spaces, and MMP 10 2.6. Plt pairs 11 2.8. Bounded families of pairs 12 2.9. Effective birationality and birational boundedness 12 2.12. Complements 12 2.14. From bounds on lc thresholds to boundedness of varieties 13 2.16. Sequences of blowups 13 2.18. Analytic pairs and analytic neighbourhoods of algebraic singularities 14 2.19. Etale´ morphisms 15 2.22. Toric varieties and toric MMP 15 arXiv:1609.05543v2 [math.AG] 1 Dec 2020 2.23. Bounded small modifications 15 2.25. Semi-ample divisors 16 3.
    [Show full text]
  • Number-Theory Prodigy Among Winners of Coveted Maths Prize Fields Medals Awarded to Researchers in Number Theory, Geometry and Differential Equations
    NEWS IN FOCUS nature means these states are resistant to topological states. But in 2017, Andrei Bernevig, Bernevig and his colleagues also used their change, and thus stable to temperature fluctua- a physicist at Princeton University in New Jersey, method to create a new topological catalogue. tions and physical distortion — features that and Ashvin Vishwanath, at Harvard University His team used the Inorganic Crystal Structure could make them useful in devices. in Cambridge, Massachusetts, separately pio- Database, filtering its 184,270 materials to find Physicists have been investigating one class, neered approaches6,7 that speed up the process. 5,797 “high-quality” topological materials. The known as topological insulators, since the prop- The techniques use algorithms to sort materi- researchers plan to add the ability to check a erty was first seen experimentally in 2D in a thin als automatically into material’s topology, and certain related fea- sheet of mercury telluride4 in 2007 and in 3D in “It’s up to databases on the basis tures, to the popular Bilbao Crystallographic bismuth antimony a year later5. Topological insu- experimentalists of their chemistry and Server. A third group — including Vishwa- lators consist mostly of insulating material, yet to uncover properties that result nath — also found hundreds of topological their surfaces are great conductors. And because new exciting from symmetries in materials. currents on the surface can be controlled using physical their structure. The Experimentalists have their work cut out. magnetic fields, physicists think the materials phenomena.” symmetries can be Researchers will be able to comb the databases could find uses in energy-efficient ‘spintronic’ used to predict how to find new topological materials to explore.
    [Show full text]
  • Public Recognition and Media Coverage of Mathematical Achievements
    Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Sepulcre, J. "Public Recognition and Media Coverage of Mathematical Achievements," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 93-129. DOI: 10.5642/ jhummath.201902.08 . Available at: https://scholarship.claremont.edu/jhm/vol9/iss2/8 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre Department of Mathematics, University of Alicante, Alicante, SPAIN [email protected] Synopsis This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathemat- ics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians.
    [Show full text]
  • NEWSLETTER Issue: 481 - March 2019
    i “NLMS_481” — 2019/2/13 — 11:04 — page 1 — #1 i i i NEWSLETTER Issue: 481 - March 2019 HILBERT’S FRACTALS CHANGING SIXTH AND A-LEVEL PROBLEM GEOMETRY STANDARDS i i i i i “NLMS_481” — 2019/2/13 — 11:04 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbic´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) David Singerman (University of Southampton) Andrew Wade (Durham University) NEWSLETTER WEBSITE The Newsletter is freely available electronically Early Career Content Editor: Vicky Neale at lms.ac.uk/publications/lms-newsletter. News Editor: Susan Oakes Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process.
    [Show full text]
  • Mathematics People
    NEWS Mathematics People or up to ten years post-PhD, are eligible. Awardees receive Braverman Receives US$1 million distributed over five years. NSF Waterman Award —From an NSF announcement Mark Braverman of Princeton University has been selected as a Prizes of the Association cowinner of the 2019 Alan T. Wa- terman Award of the National Sci- for Women in Mathematics ence Foundation (NSF) for his work in complexity theory, algorithms, The Association for Women in Mathematics (AWM) has and the limits of what is possible awarded a number of prizes in 2019. computationally. According to the Catherine Sulem of the Univer- prize citation, his work “focuses on sity of Toronto has been named the Mark Braverman complexity, including looking at Sonia Kovalevsky Lecturer for 2019 by algorithms for optimization, which, the Association for Women in Math- when applied, might mean planning a route—how to get ematics (AWM) and the Society for from point A to point B in the most efficient way possible. Industrial and Applied Mathematics “Algorithms are everywhere. Most people know that (SIAM). The citation states: “Sulem every time someone uses a computer, algorithms are at is a prominent applied mathemati- work. But they also occur in nature. Braverman examines cian working in the area of nonlin- randomness in the motion of objects, down to the erratic Catherine Sulem ear analysis and partial differential movement of particles in a fluid. equations. She has specialized on “His work is also tied to algorithms required for learning, the topic of singularity development in solutions of the which serve as building blocks to artificial intelligence, and nonlinear Schrödinger equation (NLS), on the problem of has even had implications for the foundations of quantum free surface water waves, and on Hamiltonian partial differ- computing.
    [Show full text]
  • NEWSLETTER Issue: 478 - September 2018
    i “NLMS_478” — 2018/8/17 — 16:44 — page 1 — #1 i i i NEWSLETTER Issue: 478 - September 2018 APOLLONIUS GRAPH THEORY MATHEMATICS CIRCLE AND BOVINE OF LANGUAGE COUNTING EPIDEMIOLOGY AND GRAMMAR i i i i i “NLMS_478” — 2018/8/17 — 16:44 — page 2 — #2 i i i EDITOR-IN-CHIEF COPYRIGHT NOTICE Iain Moatt (Royal Holloway, University of London) News items and notices in the Newsletter may [email protected] be freely used elsewhere unless otherwise stated, although attribution is requested when reproducing whole articles. Contributions to EDITORIAL BOARD the Newsletter are made under a non-exclusive June Barrow-Green (Open University) licence; please contact the author or photog- Tomasz Brzezinski (Swansea University) rapher for the rights to reproduce. The LMS Lucia Di Vizio (CNRS) cannot accept responsibility for the accuracy of Jonathan Fraser (University of St Andrews) information in the Newsletter. Views expressed Jelena Grbin´ (University of Southampton) do not necessarily represent the views or policy Thomas Hudson (University of Warwick) of the Editorial Team or London Mathematical Stephen Huggett (University of Plymouth) Society. Adam Johansen (University of Warwick) Bill Lionheart (University of Manchester) ISSN: 2516-3841 (Print) Mark McCartney (Ulster University) ISSN: 2516-385X (Online) Kitty Meeks (University of Glasgow) DOI: 10.1112/NLMS Vicky Neale (University of Oxford) Susan Oakes (London Mathematical Society) David Singerman (University of Southampton) Andrew Wade (Durham University) NEWSLETTER WEBSITE The Newsletter is freely available electronically Early Career Content Editor: Vicky Neale at lms.ac.uk/publications/lms-newsletter. News Editor: Susan Oakes Reviews Editor: Mark McCartney MEMBERSHIP CORRESPONDENTS AND STAFF Joining the LMS is a straightforward process.
    [Show full text]
  • Emissary | Fall 2018
    Fall 2018 EMISSARY M a t h ema t i cal Sc ien c es R e sea r c h Insti tute www.msri.org Hamiltonian Systems, from Topology to Applications through Analysis Philip J. Morrison and Sergei Tabachnikov Overview The special historic form of dynamical systems credited to Hamil- ton encompasses a vast array of fundamental and applied research. It is a basic form for physical law that has engendered development in many areas of mathematics, including analysis of ordinary and partial differential equations, topology, and geometry. Our jumbo program at MSRI has brought together a broad spectrum of math- ematicians and scientists with research spanning emphasis on the applied to the rigorous. It is hard to choose a starting point in the long history of Hamil- tonian dynamics and its concomitant variational principles. One can go as far back as ancient Greece (Euclid, Heron), onward to the inspirational work of Fermat’s principle of geometric optics (17th century), and up to the voluminous works of Lagrange (18th century). Fermat stated that the path taken by light going from one point to another in some medium is the path that minimizes (or, more accurately, extremizes) the travel time. This implies the law of optical reflection (the angle of incidence equals the angle of reflection) and Snell’s law of refraction. William Rowan Hamilton (19th century) studied the propagation of the phase in optical systems guided by Fermat’s principle and real- ized that one could generalize it and adapt it to particle mechanics. Here is a very brief description of Hamiltonian mechanics.
    [Show full text]
  • Arxiv:2102.09405V2 [Math.AG] 29 Mar 2021 Fhge Rtoa)Rn Hc Iiiefntoso H Pc Fvalu of Space Qua the on for Functions Rings Minimize Theory
    FINITE GENERATION FOR VALUATIONS COMPUTING STABILITY THRESHOLDS AND APPLICATIONS TO K-STABILITY YUCHEN LIU, CHENYANG XU, AND ZIQUAN ZHUANG Abstract. We prove that on any log Fano pair of dimension n whose stability threshold n+1 is less than n , any valuation computing the stability threshold has a finitely generated associated graded ring. Together with earlier works, this implies: (a) a log Fano pair is uniformly K-stable (resp. reduced uniformly K-stable) if and only if it is K-stable (resp. K-polystable); (b) the K-moduli spaces are proper and projective; and combining with the previously known equivalence between the existence of K¨ahler-Einstein metric and reduced uniform K-stability proved by the variational approach, (c) the Yau-Tian- Donaldson conjecture holds for general (possibly singular) log Fano pairs. 1. Introduction In recent years, the algebro-geometric study of the K-stability of Fano varieties has made remarkable progress. See [Xu20] for a comprehensive up-to-date survey. The theory has naturally driven people’s attention to valuations which are not neces- sarily divisorial. In fact, to further advance the theory, one main question is to show the finite generation property of the associated graded rings for quasi-monomial valuations of higher (rational) rank which minimize functions on the space of valuations arisen from K-stability theory. While the finite generation property for divisorial valuations follows from [BCHM10], the higher rank case posts a completely new problem. In fact, there were very few stud- ies on higher rank quasi-monomial valuations from the viewpoint of the minimal model program (MMP), which is our fundamental tool to study K-stability.
    [Show full text]
  • Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante
    Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Sepulcre, J. "Public Recognition and Media Coverage of Mathematical Achievements," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 93-129. DOI: 10.5642/jhummath.201902.08 . Available at: https://scholarship.claremont.edu/jhm/vol9/ iss2/8 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The de itorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre Department of Mathematics, University of Alicante, Alicante, SPAIN [email protected] Synopsis This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathemat- ics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians.
    [Show full text]
  • Sir Roger Penrose Wins Nobel Prize
    The Oxford Mathematics Annual Newsletter 2021 Sir Roger Penrose wins Nobel Prize Oxford Mathematics and the coronavirus Ideas for a complex world Equality, diversity and inclusion Can maths help us to win at Fantasy Football? Ideas for a Head of Department’s letter 3 Contents complex world 7 Interview with Jon Keating 9 Ulrike Tillmann, Fernando Alday, Bryan Birch 11 Appointments and achievements 15 The past year in Oxford Mathematics 17 Oxford Mathematics Obituary: Peter M. Neumann OBE 18 in the time of the coronavirus A world history of mathematics 21 12 Sir Roger Penrose wins Nobel Prize What’s on in Oxford Mathematics? 5 400 years of the Sedleian Professors 22 Equality, diversity and inclusion in New books by Oxford Mathematicians 24 Oxford Mathematics 20 Helping future students Undergraduate lectures for the world 25 Social media #WhatsonYourMind Can maths help us to win at Fantasy Football? Public Lectures 26 23 Our Graduate Student Campaign A final thought 27 2 Oxford Mathematics Annual Newsletter 2021 I am writing this in early 2021, and like everyone concerned about how that would work in practice, else I am hoping this will be a better year than but our students at home coped amazingly well 2020. The coronavirus pandemic has been an with the challenges of using their mobile phones to enormous challenge for all of us. With the benefit of photograph and upload their examination scripts, hindsight, there are definitely some things I would and surprisingly few had major internet problems. have done differently over the past 10 months.
    [Show full text]