Jacob Fox Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139 (860) 881-9870 [email protected] Math.Mit.Edu/∼Fox
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Geometry © 2003 Springer-Verlag New York Inc
Discrete Comput Geom 30:311–320 (2003) Discrete & Computational DOI: 10.1007/s00454-003-0012-9 Geometry © 2003 Springer-Verlag New York Inc. Unavoidable Configurations in Complete Topological Graphs∗ J´anos Pach,1,2 J´ozsef Solymosi,2,3 and G´eza T´oth2 1Courant Institute, New York University, New York, NY 10012, USA [email protected] 2R´enyi Institute, Hungarian Academy of Sciences, Pf 127, H-1364 Budapest, Hungary {pach, solymosi, geza}@renyi.hu 3Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z4 Abstract. A topological graph is a graph drawn in the plane so that its vertices are represented by points, and its edges are represented by Jordan curves connecting the corre- sponding points, with the property that any two curves have at most one point in common. We define two canonical classes of topological complete graphs, and prove that every topo- logical complete graph with n vertices has a canonical subgraph of size at least c log1/8 n, which belongs to one of these classes. We also show that every complete topological graph with n vertices has a non-crossing subgraph isomorphic to any fixed tree with at most c log1/6 n vertices. 1. Introduction, Results A topological graph G is a graph drawn in the plane by Jordan curves, any two of which have at most one point in common. That is, it is defined as a pair (V (G), E(G)), where V (G) is a set of points in the plane and E(G) is a set of simple continuous arcs ∗ J´anos Pach was supported by NSF Grant CCR-00-98246 and PSC-CUNY Research Award 64421- 0034. -
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Arxiv:1909.00223V1 [Cs.CG] 31 Aug 2019
Simple k-Planar Graphs are Simple (k + 1)-Quasiplanar∗ Patrizio Angeliniy Michael A. Bekosy Franz J. Brandenburgz Giordano Da Lozzox Giuseppe Di Battistax Walter Didimo{ Michael Hoffmannk Giuseppe Liotta{ Fabrizio Montecchiani{ Ignaz Rutterz Csaba D. T´oth∗∗ yy y Universit¨atT¨ubingen,T¨ubingen,Germany fangelini,[email protected] z University of Passau, Passau, Germany fbrandenb,[email protected] x Roma Tre University, Rome, Italy fgiordano.dalozzo,[email protected] { Universit´adegli Studi di Perugia, Perugia, Italy fwalter.didimo,giuseppe.liotta,[email protected] k Department of Computer Science, ETH Z¨urich, Z¨urich, Switzerland [email protected] ∗∗ California State University Northridge, Los Angeles, CA, USA [email protected] yy Tufts University, Medford, MA, USA Abstract A simple topological graph is k-quasiplanar (k ≥ 2) if it contains no k pairwise crossing edges, and k-planar if no edge is crossed more than k times. In this paper, we explore the relationship between k-planarity and k-quasiplanarity to show that, for k ≥ 2, every k-planar simple topological graph can be transformed into a (k + 1)-quasiplanar simple topological graph. arXiv:1909.00223v1 [cs.CG] 31 Aug 2019 ∗Preliminary versions of the results presented in this paper appeared at WG 2017 [6] and MFCS 2017 [19]. 1 (a) (b) (c) (d) Figure 1: (a) A crossing configuration that is forbidden in a 3-planar topological graph. (b) A 3-planar topological graph. (c) A crossing configuration that is forbidden in a 4-quasiplanar topological graph. (d) A 4-quasiplanar topological graph obtained from the one of Figure (b) by suitably rerouting the thick edge. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
CV Updated: August 16, 2021
http://yufeizhao.com [email protected] MIT Department of Mathematics Yufei Zhao 77 Massachusetts Ave, Room 2-271 Cambridge, MA 02139, USA Department of Mathematics, Massachusetts Institute of Technology Cambridge, MA Assistant Professor of Mathematics 2017— Class of 1956 Career Development Assistant Professor 2018—2021 Previous and Visiting Academic Positions Department of Mathematics, Stanford University Stanford, CA Visiting Assistant Professor Spring 2020 Simons Institute for the Theory of Computing, UC Berkeley Berkeley, CA Simons-Berkeley Research Fellow Spring 2017 New College, University of Oxford Oxford, UK Esmée Fairbairn Junior Research Fellow in Mathematics 2015—2017 Education Massachusetts Institute of Technology Cambridge, MA Ph.D. Mathematics. Advisor: Jacob Fox 2011—2015 University of Cambridge Cambridge, UK M.A.St. Mathematics with Distinction 2010—2011 Massachusetts Institute of Technology Cambridge, MA S.B. Mathematics, with minor in Economics 2006—2010 S.B. Computer Science and Engineering Selected Awards and Honors NSF CAREER award, 2021 MIT UROP Outstanding Mentor Award for Faculty, 2020 MIT First Year Advisor Award—Innovative Seminar, 2019 Sloan Research Fellowship, 2019 MIT Future of Science award, 2018 SIAM Dénes König Prize, 2018 Johnson Prize, MIT Mathematics Department, 2015 Microsoft Research PhD Fellowship, 2013–2015 Morgan Prize Honorable Mention, 2011 Gates Cambridge Scholarship, 2010–2011 MIT Jon A. Bucsela Prize in Mathematics, 2010 Putnam Math Competition: Three-time Putnam Fellow (top five rank) 2006, 2008, -
Mathematisches Forschungsinstitut Oberwolfach Combinatorics
Mathematisches Forschungsinstitut Oberwolfach Report No. 1/2006 Combinatorics Organised by L´aszl´oLov´asz (Redmond) Hans J¨urgen Pr¨omel (Berlin) January 1st – January 7th, 2006 Abstract. This is the report on the Oberwolfach workshop on Combina- torics, held 1–7 January 2006. Combinatorics is a branch of mathematics studying families of mainly, but not exclusively, finite or countable struc- tures – discrete objects. The discrete objects considered in the workshop were graphs, set systems, discrete geometries, and matrices. The programme consisted of 15 invited lectures, 18 contributed talks, and a problem ses- sion focusing on recent developments in graph theory, coding theory, discrete geometry, extremal combinatorics, Ramsey theory, theoretical computer sci- ence, and probabilistic combinatorics. Mathematics Subject Classification (2000): 05Cxx, 05Dxx, 52Bxx, 68Rxx. Introduction by the Organisers The workshop Combinatorics organised by L´aszl´oLov´asz (Redmond) and Hans J¨urgen Pr¨omel (Berlin) was held January 1st–January 7th, 2006. This meeting was very well attended with 48 participants from many different countries. The pro- gramme consisted of 15 plenary lectures, accompanied by 18 shorter contributions and a vivid problem session led by Vera T. S´os. The plenary lectures provided a very good overview over the current develop- ments in several areas of combinatorics and discrete mathematics. We were very fortunate that some of the speaker reported on essential progress on longstanding open problems. In particular, Ajtai, Koml´os, Simonovits, and Szemer´edi solved the Erd˝os–T. S´os conjecture on trees (for large trees) and Tao and Vu greatly improved the asymptotic upper bound on the probability that a Bernoulli ma- trix is singular. -
The Theory of Combinatorial Maps and Its Use in the Graph-Topological Computations
The theory of combinatorial maps and its use in the graph-topological computations. Dainis Zeps To cite this version: Dainis Zeps. The theory of combinatorial maps and its use in the graph-topological computations.. Mathematics [math]. Institute of Mathematics and Computer Science. University of Latvia, 1998. English. tel-00417773 HAL Id: tel-00417773 https://tel.archives-ouvertes.fr/tel-00417773 Submitted on 18 Sep 2009 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. University of Latvia The theory of combinatorial maps and its use in the graph-topological computations Dr. Math. Dissertation Dainis Zeps Institute of Mathematics and Computer Science University of Latvia Rai»nabulv., 29, R¹³ga,LV-1459 Latvia R¹³ga,1997 Dainis ZEPS 2 The theory of combinatorial maps and its use in the graph-topological computations. Dainis ZEPS ¤ y ¤This research is supported by the grant 96.0247 of Latvian Council of Science. yAuthor's address: Institute of Mathematics and Computer Science, University of Latvia, 29 Rainis blvd., Riga, Latvia. [email protected] 1 Abstract In this work we investigate combinatorial maps, see [2, 11, 12, 18, 19, 22, 23], applying the ge- ometrical idea of considering the corners between the edges in the embedding of the graph on the surface to be the elements on which the permutations act [58]. -
Prizes and Awards
DENVER • JAN 15–18, 2020 January 2020 Prizes and Awards 4:25 PM, Thursday, January 16, 2020 PROGRAM OPENING REMARKS Michael Dorff, Mathematical Association of America AWARD FOR DISTINGUISHED PUBLIC SERVICE American Mathematical Society BÔCHER MEMORIAL PRIZE American Mathematical Society CHEVALLEY PRIZE IN LIE THEORY American Mathematical Society FRANK NELSON COLE PRIZE IN NUMBER THEORY American Mathematical Society LEONARD EISENBUD PRIZE FOR MATHEMATICS AND PHYSICS American Mathematical Society LEVI L. CONANT PRIZE American Mathematical Society JOSEPH L. DOOB PRIZE American Mathematical Society LEROY P. S TEELE PRIZE FOR MATHEMATICAL EXPOSITION American Mathematical Society LEROY P. S TEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH American Mathematical Society LEROY P. S TEELE PRIZE FOR LIFETIME ACHIEVEMENT American Mathematical Society LOUISE HAY AWARD FOR CONTRIBUTION TO MATHEMATICS EDUCATION Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE WOMEN IN MATHEMATICS Association for Women in Mathematics MICROSOFT RESEARCH PRIZE IN ALGEBRA AND NUMBER THEORY Association for Women in Mathematics SADOSKY RESEARCH PRIZE IN ANALYSIS Association for Women in Mathematics FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY AN UNDERGRADUATE STUDENT American Mathematical Society Mathematical Association of America Society for Industrial and Applied Mathematics COMMUNICATIONS AWARD Joint Policy Board for Mathematics CHAUVENET PRIZE Mathematical Association of America DAVID P. R OBBINS PRIZE Mathematical Association of America EULER BOOK PRIZE Mathematical Association of America DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS Mathematical Association of America YUEH-GIN GUNG AND DR.CHARLES Y. HU AWARD FOR DISTINGUISHED SERVICE TO MATHEMATICS Mathematical Association of America CLOSING REMARKS Jill C. -
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. -
Prize Is Awarded Every Three Years at the Joint Mathematics Meetings
AMERICAN MATHEMATICAL SOCIETY LEVI L. CONANT PRIZE This prize was established in 2000 in honor of Levi L. Conant to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding fi ve years. Levi L. Conant (1857–1916) was a math- ematician who taught at Dakota School of Mines for three years and at Worcester Polytechnic Institute for twenty-fi ve years. His will included a bequest to the AMS effective upon his wife’s death, which occurred sixty years after his own demise. Citation Persi Diaconis The Levi L. Conant Prize for 2012 is awarded to Persi Diaconis for his article, “The Markov chain Monte Carlo revolution” (Bulletin Amer. Math. Soc. 46 (2009), no. 2, 179–205). This wonderful article is a lively and engaging overview of modern methods in probability and statistics, and their applications. It opens with a fascinating real- life example: a prison psychologist turns up at Stanford University with encoded messages written by prisoners, and Marc Coram uses the Metropolis algorithm to decrypt them. From there, the article gets even more compelling! After a highly accessible description of Markov chains from fi rst principles, Diaconis colorfully illustrates many of the applications and venues of these ideas. Along the way, he points to some very interesting mathematics and some fascinating open questions, especially about the running time in concrete situ- ations of the Metropolis algorithm, which is a specifi c Monte Carlo method for constructing Markov chains. The article also highlights the use of spectral methods to deduce estimates for the length of the chain needed to achieve mixing. -
Combinatorial Topology
Topological Graph Theory 3 Basic Definitions 3 Some Common Graphs Kn 8 Connectivity 9 Mader's Theorem v 12 Menger's Theorem 15 Minors and Topological Minors Kn 19 Application: Reliability Polynomial 21 The Cycle Space 30 Inclusion-Exclusion The Dumbbell Graph 32 Some Applications to 3-connected Graphs 33 Tutte's Lemma A graph is a set of vertices 40 Betti Numbers 9 Trees which are connected by edges. Bottlenecks and Connectivity This is a simple example of Theorems and Lemmas 12 a topological space. Two 13 Mader's Theorem topological characteristics of 5 Average vertex degree 14 Dumbbell Graph graphs are the number of con- 6 An Even number of odd vertices 23 K5 Subdivision nected components, and the 16 Adding paths preserves ·(G) 2 26 Peterson Graph number of cycles they contain. ¸ 17 Menger's Theorem 27 Application: Reliability Polynomial 18 Characterization of 2-connected graphs 28 How to count cycles Homeomorphic Faces as Basis Definitions 24 47 29 Graphs a 1-complexes 51 Tutte Counterexample 1 Graph 36 Identifying Paths 52 Tutte's Lemma 4 Neighborhood 37 Identifying Cycles 7 Paths and Cycles 42 Definitions of Maps 11 Vertex Connectedness 44 Induced Map on Cycle Spaces 15 k-path connected 46 Inclusion-Exclusion 21 Graph Isomorphism 50 Tutte 22 Subdivision 53 Characterization of ·(G) 3 ¸ 25 Contraction Examples 30 Linearizeation of Sets 32 Summing the Target 2 Friends in the Order 33 Summing the Domain 3 Some Common Graphs 38 Cycle Space 8 Paths and Cycles Basic Definitions 1 A graph is a mathematical representation of network. -
Geometric Intersection Patterns and the Theory of Topological Graphs
Geometric Intersection Patterns and the Theory of Topological Graphs J´anosPach∗ Abstract. The intersection graph of a set system S is a graph on the vertex set S, in which two vertices are connected by an edge if and only if the corresponding sets have nonempty intersection. It was shown by Tietze (1905) that every finite graph is the intersection graph of 3-dimensional convex polytopes. The analogous statement is false in any fixed dimension if the polytopes are allowed to have only a bounded number of faces or are replaced by simple geometric objects that can be described in terms of a bounded number of real parameters. Intersection graphs of various classes of geometric objects, even in the plane, have interesting structural and extremal properties. We survey problems and results on geometric intersection graphs and, more gener- ally, intersection patterns. Many of the questions discussed were originally raised by Berge, Erd}os,Gr¨unbaum, Hadwiger, Tur´an,and others in the context of classical topol- ogy, graph theory, and combinatorics (related, e.g., to Helly's theorem, Ramsey theory, perfect graphs). The rapid development of computational geometry and graph drawing algorithms in the last couple of decades gave further impetus to research in this field. A topological graph is a graph drawn in the plane so that its vertices are represented by points and its edges by possibly intersecting simple continuous curves connecting the corresponding point pairs. We give applications of the results concerning intersection patterns in the theory of topological graphs. Mathematics Subject Classification (2010). Primary 05C35; Secondary 05C62, 52C10. -
AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student
comm-morgan.qxp 4/22/98 8:19 AM Page 323 AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student The new Frank and Brennie Morgan Prize stands dergraduate at the to recognize and encourage outstanding math- University of Michi- ematical research by undergraduate students. gan, he had been Undergraduates are working on problems of pursuing a program current research interest, proving theorems, of research in ana- writing up results for publication, and giving lytic number theory talks on their work. There is undergraduate re- and has made out- search today at the highest standards of pro- standing contribu- fessional excellence. The prize was endowed by tions to that field. Mrs. Frank Morgan and also carries the name of A year ago he her late husband. (Their son, Frank Morgan of solved a long-stand- ing and much stud- Williams College, is on the prize selection com- ied conjecture of mittee.) Kannan Soundararajan Ron Graham, jointly The first Frank and Brennie Morgan Prize was with R. Balasubra- awarded at the Joint Meetings in Orlando in Jan- manian. When at Bell Labs two years ago, he es- Kannan Soundararajan uary 1996 to of tablished asymptotic formulae for the distribu- Princeton University. An Honorable Mention was tion of “smooth polynomials”. Especially in the awarded to Kiran Kedlaya of Harvard Univer- last two undergraduate years he has had great sity. The prize selection committee consisted of success in establishing properties of the Rie- Kelly J. Black, Gulbank D. Chakerian, Frank mann zeta function on the line Rs =1/2.