Ciprian Manolescu Curriculum Vitae
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Ciprian Manolescu
A combinatorial approach to Heegaard Floer invariants Ciprian Manolescu UCLA July 5, 2012 Ciprian Manolescu (UCLA) Combinatorial HF Theory July 5, 2012 1 / 34 Motivation (4D) Much insight into smooth 4-manifolds comes from PDE techniques: gauge theory and symplectic geometry. Donaldson (1980’s): used the Yang-Mills equations to get constraints on the intersection forms of smooth 4-manifolds, etc. Solution counts −→ Donaldson invariants, able to detect exotic smooth structures on closed 4-manifolds. Seiberg-Witten (1994): discovered the monopole equations, which can replace Yang-Mills for most applications, and are easier to study. Solution counts −→ Seiberg-Witten invariants. Ozsv´ath-Szab´o (2000’s): developed Heegaard Floer theory, based on counts of holomorphic curves in symplectic manifolds. Their mixed HF invariants of 4-manifolds are conjecturally the same as the Seiberg-Witten invariants, and can be used for the same applications (in particular, to detect exotic smooth structures). Ciprian Manolescu (UCLA) Combinatorial HF Theory July 5, 2012 2 / 34 Motivation (3D) All three theories (Yang-Mills, Seiberg-Witten, Heegaard-Floer) also produce invariants of closed 3-manifolds, in the form of graded Abelian groups called Floer homologies. These have applications of their own, e.g.: What is the minimal genus of a surface representing a given homology class in a 3-manifold? (Kronheimer-Mrowka, Ozsv´ath-Szab´o) Does a given 3-manifold fiber over the circle? (Ghiggini, Ni) In dimension 3, the Heegaard-Floer and Seiberg-Witten Floer homologies are known to be isomorphic: work of Kutluhan-Lee-Taubes and Colin-Ghiggini-Honda, based on the relation to Hutchings’s ECH. -
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, -
EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M. -
FLOER THEORY and ITS TOPOLOGICAL APPLICATIONS 1. Introduction in Finite Dimensions, One Way to Compute the Homology of a Compact
FLOER THEORY AND ITS TOPOLOGICAL APPLICATIONS CIPRIAN MANOLESCU Abstract. We survey the different versions of Floer homology that can be associated to three-manifolds. We also discuss their applications, particularly to questions about surgery, homology cobordism, and four-manifolds with boundary. We then describe Floer stable homotopy types, the related Pin(2)-equivariant Seiberg-Witten Floer homology, and its application to the triangulation conjecture. 1. Introduction In finite dimensions, one way to compute the homology of a compact, smooth manifold is by Morse theory. Specifically, we start with a a smooth function f : X ! R and a Riemannian metric g on X. Under certain hypotheses (the Morse and Morse-Smale conditions), we can form a complex C∗(X; f; g) as follows: The generators of C∗(X; f; g) are the critical points of f, and the differential is given by X (1) @x = nxy · y; fyjind(x)−ind(y)=1g where nxy 2 Z is a signed count of the downward gradient flow lines of f connecting x to y. The quantity ind denotes the index of a critical point, that is, the number of negative eigenvalues of the Hessian (the matrix of second derivatives of f) at that point. The homology H∗(X; f; g) is called Morse homology, and it turns out to be isomorphic to the singular homology of X [Wit82, Flo89b, Bot88]. Floer homology is an adaptation of Morse homology to infinite dimensions. It applies to certain classes of infinite dimensional manifolds X and functions f : X ! R, where at critical points of f the Hessian has infinitely many positive and infinitely many negative eigenvalues. -
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. -
Ciprian Manolescu Interview Conducted by Alexander Diaz-Lopez
THE GRADUATE STUDENT SECTION Ciprian Manolescu Interview Conducted by Alexander Diaz-Lopez Diaz-Lopez: When did you know you wanted to be a math- ematician? Manolescu: As a kid I liked math puzzles and games. I remember being particularly fond of a book by Martin Gardner (in Romanian translation). In middle school, I started participating in math olympiads, and by then I figured I wanted to do mathematics in some form when I grew up. At the time I did not know any research math- ematicians personally, but I read a couple of books popu- larizing mathematical research and news articles about Wiles’ proof of Fermat’s Last Theorem. It all sounded very exciting. Diaz-Lopez: Who encouraged or inspired you? Manolescu: My parents have been extremely support- ive, and I was fortunate to have good teachers—especially my high school math teacher Stefan Alexe, who lent me a large part of his collection of problem books to prepare for the olympiads. Clearly, however, my greatest math- ematical debt is to my college and PhD advisor, Peter Kronheimer. We had weekly meetings for several years, and I learned a great deal of mathematics from him. Diaz-Lopez: How would you describe your work to a graduate student? Manolescu: I work in topology, where the main motivat- ing problem is the classification of smooth shapes (mani- folds). There is a theorem that a complete classification is not possible in dimensions four or higher, because we run into group-theoretic difficulties. However, one can focus on manifolds with a reasonable fundamental group, and Ciprian Manolescu is professor of mathematics at then the problem becomes tractable in dimensions five the University of California, Los Angeles, working in or higher. -
On the Khovanov and Knot Floer Homologies of Quasi-Alternating Links
ON THE KHOVANOV AND KNOT FLOER HOMOLOGIES OF QUASI-ALTERNATING LINKS CIPRIAN MANOLESCU AND PETER OZSVATH´ Abstract. Quasi-alternating links are a natural generalization of alternating links. In this paper, we show that quasi-alternating links are “homologically thin” for both Khovanov homology and knot Floer homology. In particular, their bigraded homology groups are determined by the signature of the link, together with the Euler characteristic of the respective homology (i.e. the Jones or the Alexander polynomial). The proofs use the exact triangles relating the homology of a link with the homologies of its two resolutions at a crossing. 1. Introduction In recent years, two homological invariants for oriented links L ⊂ S3 have been studied extensively: Khovanov homology and knot Floer homology. Our purpose here is to calculate these invariants for the class of quasi-alternating links introduced in [19], which generalize alternating links. The first link invariant we will consider in this paper is Khovanov’s reduced homology ([5],[6]). This invariant takes the form of a bigraded vector space over Z/2Z, denoted i,j Kh (L), whose Euler characteristic is the Jones polynomial in the following sense: i j i,j g (−1) q rank Kh (L)= VL(q), − i∈Z,j∈Z+ l 1 X 2 g where l is the number of components of L. The indices i and j are called the homological and the Jones grading, respectively. (In our convention j is actually half the integral grading j from [5].) The indices appear as superscripts because Khovanov’s theory is conventionally defined to be a cohomology theory. -
TRIANGULATIONS of MANIFOLDS in Topology, a Basic Building Block for Spaces Is the N-Simplex. a 0-Simplex Is a Point, a 1-Simplex
TRIANGULATIONS OF MANIFOLDS CIPRIAN MANOLESCU In topology, a basic building block for spaces is the n-simplex. A 0-simplex is a point, a 1-simplex is a closed interval, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron. In general, an n-simplex is the convex hull of n + 1 vertices in n-dimensional space. One constructs more complicated spaces by gluing together several simplices along their faces, and a space constructed in this fashion is called a simplicial complex. For example, the surface of a cube can be built out of twelve triangles|two for each face, as in the following picture: Apart from simplicial complexes, manifolds form another fundamental class of spaces studied in topology. An n-dimensional topological manifold is a space that looks locally like the n-dimensional Euclidean space; i.e., such that it can be covered by open sets (charts) n homeomorphic to R . Furthermore, for the purposes of this note, we will only consider manifolds that are second countable and Hausdorff, as topological spaces. One can consider topological manifolds with additional structure: (i)A smooth manifold is a topological manifold equipped with a (maximal) open cover by charts such that the transition maps between charts are smooth (C1); (ii)A Ck manifold is similar to the above, but requiring that the transition maps are only Ck, for 0 ≤ k < 1. In particular, C0 manifolds are the same as topological manifolds. For k ≥ 1, it can be shown that every Ck manifold has a unique compatible C1 structure. Thus, for k ≥ 1 the study of Ck manifolds reduces to that of smooth manifolds. -
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.