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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. -
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. -
The Life and Works of Sadid Al-Din Kazeroni: an Iranian Physician and Anatomist
ORerimgiinnaisl cAernticcele Middle East Journal of Cancer; JOuclyto 2b0e1r 52 061(38);: 9(4): 323-327 The Life and Works of Sadid al-Din Kazeroni: An Iranian Physician and Anatomist Seyyed Alireza Golshani* ♦, Seyyed Ehsan Golshan**, Mohammad Ebrahim Zohalinezhad*** *Department of History, Ferdowsi University of Mashhad, Mashhad, Iran **Department of Foreign Languages, Marvdasht Azad University, Marvdasht, Iran ***Assistant Professor, Persian Medicine, Shiraz University of Medical Sciences, Shiraz, Iran; Eessence of Parsiyan Wisdom Institute, Traditional Medicine and Medicinal Plant Incubator, Shiraz University of Medical Sciences, Shiraz, Iran Abstract Background: One of the great physicians in Iran who had expertise in medicine, surgery, and pharmacy was Sadid al-Din Kazeroni. He was a 14 th century physician. No information is available on his birth and death – only “Al-Mughni”, a book, has been left to make him famous in surgical and medical knowledge. Methods: We used desk and historical research methods in this research, with a historical approach. This commonly used research method in human sciences was used to criticize and study the birthplace and works of Sadid al-Din Kazeroni. Results and Conclusion: Sadid al-Din Kazeroni discussed the exact issues in the field of anatomy, surgery, and gynecology. He was fluent in pharmacology. In his pharmacology book, for the first time, he named drugs considered necessary before and after surgery. In this study, we reviewed the biography and introduction of the works and reviewed “Al-Mughni”, a book on breast cancer. Keywords: Sadid al-Din Kazeroni, Breast cancer, Anatomical illustration, Al-Mughni, Persian medicine ♦Corresponding Author: Seyyed Alireza Golshani, PhD Student Introduction the Nobel Prize in Math. -
Arxiv:2009.11923V1 [Math.GT] 24 Sep 2020 Manifolds One Is Interested in Studying
A MODEL FOR RANDOM THREE{MANIFOLDS BRAM PETRI AND JEAN RAIMBAULT Abstract. We study compact three-manifolds with boundary obtained by randomly gluing together truncated tetrahedra along their faces. We prove that, asymptotically almost surely as the number of tetrahedra tends to infinity, these manifolds are connected and have a single boundary component. We prove a law of large numbers for the genus of this boundary component, we show that the Heegaard genus of these manifolds is linear in the number of tetrahedra and we bound their first Betti number. We also show that, asymptotically almost surely as the number of tetrahedra tends to infinity, our manifolds admit a unique hyperbolic metric with totally geodesic boundary. We prove a law of large numbers for the volume of this metric, prove that the associated Laplacian has a uniform spectral gap and show that the diameter of our manifolds is logarithmic as a function of their volume. Finally, we determine the Benjamini{Schramm limit of our sequence of random manifolds. 1. Introduction 1.1. Context. Random constructions of compact manifolds can be seen as an analogue of the well-established theory of random graphs and serve similar purposes. First of all, they make the notion of a \typical" manifold rigorous. Secondly, they can be used as a testing ground for conjectures of which the proof is still out of reach. Finally, there is what is often called the probabilistic method { using probability theory to prove the existence of objects with extremal properties. In this paper we are mostly interested in the first aspect. -
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. -
Interview with Research Fellow Maryam Mirzakhani
Profile Interview with Research Fellow Maryam Mirzakhani Could you talk about your mathematical education? What experiences and people were especially influential? I was very lucky in many ways. The war ended when I finished elementary school; I couldn’t have had the great opportunities that I had if I had been born ten years earlier. I went to a great high school in Tehran, Farzanegan, and had very good teachers. I met my friend Roya Beheshti the first week after entering middle school. It is invaluable to have a friend who shares your interests, and helps you stay motivated. Our school was close to a street full of bookstores in Tehran. I remember how walking along this crowded street, and going to the bookstores, was so exciting for us. We couldn’t skim through the books like people usually do here in a bookstore, so we would end up buying a lot of random books. Maryam Mirzakhani, a native of Iran, is currently a professor of mathematics at Stanford. She Also, our school principal was a strong-willed completed her Ph.D. at Harvard in 2004 under the woman who was willing to go a long way to provide direction of Curtis T. McMullen. In her thesis she us with the same opportunities as the boys’ school. showed how to compute the Weil-Petersson volume Later, I got involved in Math Olympiads that made of the moduli space of bordered Riemann surfaces. me think about harder problems. As a teenager, I Her research interests include Teichmüller theory, enjoyed the challenge. -
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. -
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. -
International Congress of Mathematicians
International Congress of Mathematicians Hyderabad, August 19–27, 2010 Abstracts Plenary Lectures Invited Lectures Panel Discussions Editor Rajendra Bhatia Co-Editors Arup Pal G. Rangarajan V. Srinivas M. Vanninathan Technical Editor Pablo Gastesi Contents Plenary Lectures ................................................... .. 1 Emmy Noether Lecture................................. ................ 17 Abel Lecture........................................ .................... 18 Invited Lectures ................................................... ... 19 Section 1: Logic and Foundations ....................... .............. 21 Section 2: Algebra................................... ................. 23 Section 3: Number Theory.............................. .............. 27 Section 4: Algebraic and Complex Geometry............... ........... 32 Section 5: Geometry.................................. ................ 39 Section 6: Topology.................................. ................. 46 Section 7: Lie Theory and Generalizations............... .............. 52 Section 8: Analysis.................................. .................. 57 Section 9: Functional Analysis and Applications......... .............. 62 Section 10: Dynamical Systems and Ordinary Differential Equations . 66 Section 11: Partial Differential Equations.............. ................. 71 Section 12: Mathematical Physics ...................... ................ 77 Section 13: Probability and Statistics................. .................. 82 Section 14: Combinatorics........................... -
Mathematics Education in Iran from Ancient to Modern
Mathematics Education in Iran From Ancient to Modern Yahya Tabesh Sharif University of Technology Shima Salehi Stanford University 1. Introduction Land of Persia was a cradle of science in ancient times and moved to the modern Iran through historical ups and downs. Iran has been a land of prominent, influential figures in science, arts and literature. It is a country whose impact on the global civilization has permeated centuries. Persian scientists contributed to the understanding of nature, medicine, mathematics, and philosophy, and the unparalleled names of Ferdowsi, Rumi, Rhazes, al-Biruni, al-Khwarizmi and Avicenna attest to the fact that Iran has been perpetually a land of science, knowledge and conscience in which cleverness grows and talent develops. There are considerable advances through education and training in various fields of sciences and mathematics in the ancient and medieval eras to the modern and post-modern periods. In this survey, we will present advancements of mathematics and math education in Iran from ancient Persia and the Islamic Golden Age toward modern and post-modern eras, we will have some conclusions and remarks in the epilogue. 2. Ancient: Rise of the Persian Empire The Land of Persia is home to one of the world's oldest civilizations, beginning with its formation in 3200–2800 BC and reaching its pinnacle of its power during the Achaemenid Empire. Founded by Cyrus the Great in 550 BC, the Achaemenid Empire at its greatest extent comprised major portions of the ancient world. Persian Empire 1 Governing such a vast empire was, for sure in need of financial and administration systems. -
RM Calendar 2019
Rudi Mathematici x3 – 6’141 x2 + 12’569’843 x – 8’575’752’975 = 0 www.rudimathematici.com 1 T (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 2 W (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 F (1643) Isaac Newton RM071 5 S (1723) Nicole-Reine Étable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2004, A1 (1871) Federigo Enriques RM084 Basketball star Shanille O’Keal’s team statistician (1871) Gino Fano keeps track of the number, S( N), of successful free 6 S (1807) Jozeph Mitza Petzval throws she has made in her first N attempts of the (1841) Rudolf Sturm season. Early in the season, S( N) was less than 80% of 2 7 M (1871) Felix Edouard Justin Émile Borel N, but by the end of the season, S( N) was more than (1907) Raymond Edward Alan Christopher Paley 80% of N. Was there necessarily a moment in between 8 T (1888) Richard Courant RM156 when S( N) was exactly 80% of N? (1924) Paul Moritz Cohn (1942) Stephen William Hawking Vintage computer definitions 9 W (1864) Vladimir Adreievich Steklov Advanced User : A person who has managed to remove a (1915) Mollie Orshansky computer from its packing materials. 10 T (1875) Issai Schur (1905) Ruth Moufang Mathematical Jokes 11 F (1545) Guidobaldo del Monte RM120 In modern mathematics, algebra has become so (1707) Vincenzo Riccati important that numbers will soon only have symbolic (1734) Achille Pierre Dionis du Sejour meaning. -
Volumes and Random Matrices
Volumes And Random Matrices Edward Witten Institute for Advanced Study Einstein Drive, Princeton, NJ 08540 USA Abstract This article is an introduction to newly discovered relations between volumes of moduli spaces of Riemann surfaces or super Riemann surfaces, simple models of gravity or supergravity in two dimensions, and random matrix ensembles. (The article is based on a lecture at the conference on the Mathematics of Gauge Theory and String Theory, University of Auckland, January 2020. It has been submitted to a special issue of the Quarterly Journal of Mathematics in memory of Michael Atiyah.) arXiv:2004.05183v2 [math.SG] 6 Jul 2020 Contents 1 Introduction 1 2 Universal Teichm¨ullerSpace 4 3 Quantum Gravity In Two Dimensions 5 4 A Random Matrix Ensemble 9 5 Matrix Ensembles and Volumes of Super Moduli Spaces 14 1 Introduction In this article, I will sketch some recent developments involving the volume of the moduli space Mg of Riemann surfaces of genus g, and also the volume of the corresponding moduli space Mg of super Riemann surfaces. The discussion also encompasses Riemann surfaces with punctures and/or boundaries. The main goal is to explain how these volumes are related to random matrix ensembles. This is an old story with a very contemporary twist. What is meant by the volume of Mg? One answer is that Mg for g > 1 has a natural Weil- Petersson symplectic form. A Riemann surface Σ of genus g > 1 can be regarded as the quotient ∼ of the upper half plane H = PSL(2; R)=U(1) by a discrete group.