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Curriculum Vitae
Curriculum Vitae Larry Guth Education B.S. Mathematics, Yale University, 2000 PhD Mathematics, MIT, 2005 Employment Samelson Fellow, Stanford University 2005-6 Szego Assistant Professor, Stanford University, 2006 - 2008 National Science Foundation Postdoctoral Fellow, 2006 - 2008 Tenure-stream Assistant Professor, University of Toronto, 2008 - 2011 Member, Institute for Advanced Study, 2010 - 2011 Professor, New York University, 2011 - 2012 Professor, MIT, 2012 - Fellowships National Science Foundation Graduate Fellowship, 2001 - 2003 National Science Foundation Postdoctoral Fellowship , 2006 - 2008 Alfred P. Sloan Research Fellowship, 2010 - 2014 Simons Investigator, 2014 - Honors Salem prize 2013 Invited talks Invited sectional speaker at the 2010 International Congress of Mathematics Marston Morse lectures, IAS, 2013 Namboodiri lectures, University of Chicago, 2015 1 Selected publications 1. Lipshitz maps from surfaces, Geom. Funct. Anal. 15 (2005), no. 5, 1052-109 2. The width-volume inequality, Geom. Funct. Anal. 17 (2007) no. 4, 1139-1179 3. Notes on Gromov's systolic estimate, Geom. Dedicata 123 (2006) 113-129 4. Symplectic embeddings of polydisks, Invent. Math. 172 (2008) no. 3, 477-489 5. Minimax problems related to cup powers and Steenrod squares, Geom. Funct. Anal. 18 (2009), no. 6, 1917{1987 6. The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture, Acta Math. 205 (2010), no. 2, 263-286. 7. Systolic inequalities and minimal hypersurfaces, Geom. Funct. Anal. 19 (2010), no. 6, 1688-1692. 8. Volumes of balls in large Riemannian manifolds, Ann. of Math. (2) 173 (2011), no. 1, 5176. 9. Area-expanding embeddings of rectangles, preprint 10. Algebraic methods in discrete analogs of the Kakeya problem (joint with Nets Katz), Adv. -
Department of Mathematics
Department of Mathematics The Department of Mathematics seeks to maintain its top ranking in mathematics research and education in the United States. The department is a key part of MIT’s educational mission at both the undergraduate and graduate levels and produces the most sought-after young researchers. Key to the department’s success is recruitment of the best faculty members, postdoctoral associates, and graduate students in an ever more competitive environment. The department strives to be diverse at all levels in terms of race, gender, and ethnicity. It continues to serve the varied needs of its graduate students, undergraduate students majoring in mathematics, and the broader MIT community. Awards and Honors The faculty received numerous distinctions this year. Professor Victor Kac received the Leroy P. Steele Prize for Lifetime Achievement, for “groundbreaking contributions to Lie Theory and its applications to Mathematics and Mathematical Physics.” Larry Guth (together with Netz Katz of the California Institute of Technology) won the Clay Mathematics Institute Research Award. Tomasz Mrowka was elected as a member of the National Academy of Sciences and William Minicozzi was elected as a fellow of the American Academy of Arts and Sciences. Alexei Borodin received the 2015 Loève Prize in Probability, given by the University of California, Berkeley, in recognition of outstanding research in mathematical probability by a young researcher. Alan Edelman received the 2015 Babbage Award, given at the IEEE International Parallel and Distributed Processing Symposium, for exceptional contributions to the field of parallel processing. Bonnie Berger was elected vice president of the International Society for Computational Biology. -
2017-2018 Annual Report
Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2017 – April 30, 2018 Brendan Hassett, Director Mathew Borton, IT Director Jeff Brock, Associate Director Ruth Crane, Assistant Director Sigal Gottlieb, Deputy Director Elisenda Grigsby, Deputy Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Associate Director Jill Pipher, Consulting Associate Director Bjorn Sandstede, Associate Director Homer Walker, Consulting Associate Director Ulrica Wilson, Associate Director for Diversity and Outreach Table of Contents Mission ....................................................................................................................................... 6 Core Programs and Events ......................................................................................................... 6 Participant Summaries by Program Type ................................................................................... 9 ICERM Funded Participants ................................................................................................................. 9 All Participants (ICERM funded and Non-ICERM funded) .................................................................. 10 ICERM Funded Speakers ................................................................................................................... 11 All Speakers (ICERM funded and Non-ICERM funded) ...................................................................... 12 ICERM Funded Postdocs .................................................................................................................. -
Polynomial Methods in Combinatorics
UNIVERSITY LECTURE SERIES VOLUME 64 Polynomial Methods in Combinatorics Larry Guth American Mathematical Society https://doi.org/10.1090//ulect/064 Polynomial Methods in Combinatorics UNIVERSITY LECTURE SERIES VOLUME 64 Polynomial Methods in Combinatorics Larry Guth American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Jordan S. Ellenberg Robert Guralnick William P. Minicozzi II (Chair) Tatiana Toro 2010 Mathematics Subject Classification. Primary 05D99. For additional information and updates on this book, visit www.ams.org/bookpages/ulect-64 Library of Congress Cataloging-in-Publication Data Names: Guth, Larry, 1977– Title: Polynomial methods in combinatorics / Larry Guth. Description: Providence, Rhode Island : American Mathematical Society, [2016] | Series: Univer- sity lecture series ; volume 64 | Includes bibliographical references. Identifiers: LCCN 2016007729 | ISBN 9781470428907 (alk. paper) Subjects: LCSH: Combinatorial geometry. | Polynomials. | Geometry, Algebraic. | AMS: Combina- torics – Extremal combinatorics – None of the above, but in this section. msc Classification: LCC QA167 .G88 2016 | DDC 511/.66–dc23 LC record available at http://lccn.loc. gov/2016007729 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Permissions to reuse portions of AMS publication content are handled by Copyright Clearance Center’s RightsLink service. For more information, please visit: http://www.ams.org/rightslink. -
Helmut Hofer Publication List
Helmut Hofer Publication List Journal Articles: (1) A multiplicity result for a class of nonlinear problems with ap- plications to a nonlinear wave equation. Jour. of Nonlinear Analysis, Theory, Methods and Applications, 5, No. 1 (1981), 1-11 (2) Existence and multiplicity result for a class of second order el- liptic equations. Proc. of the Royal Society of Edinburgh, 88A (1981), 83-92 (3) A new proof for a result of Ekeland and Lasry concerning the number of periodic Hamiltonian trajectories on a prescribed energy surface. Bolletino UMI 6, 1-B (1982), 931-942 (4) A variational approach to a wave equation problem at resonance. Metodi asintoctici e topologici in problemi differenziali non lin- eari; ed. L. Boccardo, A.M. Micheletti, Collano Atti di Con- gressi, Pitagora Editrice, Bologna (1981), 187-200 (5) On the range of a wave operator with nonmonotone nonlinear- ity. Math. Nachrichten 106 (1982), 327-340 (6) Variational and topological methods in partially ordered Hilbert spaces. Math. Annalen 261 (1982), 493-514 (7) On strongly indefinite funtionals with applications. Transactions of the AMS 275, No. 1 (1983), 185-213 (8) A note on the topological degree at a critical point of moun- tainpass-type. Proc. of the AMS 90, No. 2 (1984), 309-315 (9) Homoclinic, heteroclinic and periodic orbits for indefinite Hamil- tonian systems (with J. Toland). Math. Annalen 268 (1984), 387-403 (10) The topological degree at a critical point of mountainpasstype. AMS Proceedings of Symposia in Pure Math. 45, Part 1 (1986) 501-509 (11) A geometric description of the neighborhood of a critical point given by the mountainpass-theorem. -
Mathematical Research in High School: the PRIMES Experience
Mathematical Research in High School: The PRIMES Experience The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Etingof, Pavel, Slava Gerovitch, and Tanya Khovanova. “Mathematical Research in High School: The PRIMES Experience.” Notices of the American Mathematical Society 62, no. 08 (September 1, 2015): 910–918. © American Mathematical Society (AMS) As Published http://dx.doi.org/10.1090/noti1270 Publisher American Mathematical Society (AMS) Version Final published version Citable link http://hdl.handle.net/1721.1/110267 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Mathematical Research in High School: The PRIMES Experience Pavel Etingof, Slava Gerovitch, and Tanya Khovanova Consider a finite set of lines in 3-space. A joint is a point where three of these lines (not lying in the same plane) intersect. If there are L lines, what is the largest possible number of joints? Well, let’s try our luck and randomly choose k planes. Any pair of planes produces a line, and any triple of planes, a joint. Thus, they produce L := k(k − 1)/2 lines and J :=p k(k − 1)(k − 2)/6 joints. If k is large, J is 2 3=2 about 3 L . For many years it was conjectured that one cannot do much better than that, in the 3=2 sense that if L is large, thenp J ≤ CL , where C is a constant (clearly, C ≥ 2 ). -
LARRY GUTH Curriculum Vitae Department Of
LARRY GUTH Curriculum Vitae Department of Mathematics 617-253-4326 Room 2-278 [email protected] 77 Massachusetts Avenue Cambridge, MA 02139 Degrees: B.S. Mathematics, Yale University, 2000 Ph.D. Mathematics, MIT, 2005 Employment: Samelson Fellow, Stanford University, 2005-2006 Szego Assistant Professor, Stanford University, 2006-2008 National Science Foundation Postoctoral Fellow, 2006-2008 Tenure-stream Assistant Professor, University of Toronto, 2008-2011 Member, Institute for Advanced Study, 2010-2011 Professor, New York University, 2011-2012 Professor, MIT, Department of Mathematics, 2012- Claude Shannon Professor of Mathematics, MIT, 2019- Fellowships: National Science Foundation Graduate Fellowship, 2001-2003 National Science Foundation Postdoctoral Fellowship, 2006-2008 Alfred P. Sloan Research Fellowship, 2010-2014 Simons Investigator, 2014- Honors: Sloan Research Fellowship, 2010 Salem Prize, 2013 Simons Investigator, Simons Fnd, 2014 Clay Research Award, 2015 School of Science Prize for Excellence in Graduate Teaching, 2015 New Horizons in Mathematics Breakthrough Prize, 2015 Fellow of the American Academy of Arts and Sciences, 2018 Best Paper Award, International Consortium of Chinese Math., 2018 Fellow of the American Mathematical Society, 2019 B^ocher Memorial Prize, 2020 Maryam Mirzakhani Prize in Mathematics, 2020 Margaret MacVicar Faculty Fellow, MIT, 2021 Member of the National Academy of Sciences, 2021 1 B.S. Student Thesis Supervised (University of Toronto): Lisha (Janet) Li: University of Toronto: Received a 2017 PhD in Statistics & Machine Learning, from U.C. Berkeley; currently at Amplify Partners, S.F. Bay Area Graduate Students Supervised: University of Toronto: Dominic Dotterrer: PhD, University of Toronto, 2013: Dickson Instr., University of Chicago, 2013-2016; currently: Senior Research Scientist, Goldman Sachs, 2019-. -
Instantons, Knots and Knotted Graphs
Annual McKnight-Zame Lecture INSTANTONS, KNOTS AND KNOTTED GRAPHS Thursday February 27th, 2020 5:30 PM Newman Alumni Center 6200 San Amaro Drive Coral Gables, FL 33146 RSVP ummcknight-zame2020.eventbrite.com Tomasz Mrowka, Ph.D. Professor of Mathematics, MIT Member of the National Academy of Sciences Fellow of the American Academy of Arts & Sciences 2007 Veblen Prize in Geometry Recipient Over the past four decades, input from geometry and analysis has been central to progress in the ield of low-dimensional topology. This talk will focus on one aspect of these developments, namely, the use of Yang-Mills theory, or gauge theory. These techniques were pioneered by Simon Donaldson in his work on 4-manifolds beginning in 1982. The past ten years have seen new applications of gauge theory and new interactions with more recent threads in the subject, particularly in 3-dimensional topology and knot theory. In our exploration of this subject, a recurring question will be, "How can we detect knottedness?" Many mathematical techniques have found application to this question, but gauge theory in particular has provided its own collection of answers, both directly and through its connection with other tools. Beyond classical knots, we will also take a look at the nearby but less-explored world of spatial graphs. Hosted by Department of Mathematics UNIVERSITY OF MIAMI The McKnight-Zame Distinguished Lecture Series is made possible by a COLLEGE of generous donation from Dr. Jery Fuqua (Ph.D., UM, 1972). These annual lectures ARTS & SCIENCES are named in honor of Professor James McKnight, who directed Dr. -
2016-2017 Annual Report
Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2016 – April 30, 2017 Brendan Hassett, Director Mathew Borton, IT Director Jeff Brock, Associate Director Ruth Crane, Assistant Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Associate Director Jill Pipher, Consulting Associate Director Sinai Robins, Deputy Director Bjorn Sandstede, Associate Director Homer Walker, Deputy Director Ulrica Wilson, Associate Director for Diversity and Outreach 1 Table of Contents Mission ......................................................................................................................................................... 5 Core Programs and Events ............................................................................................................................. 5 Participant Summaries by Program Type ....................................................................................................... 8 ICERM Funded Participants .................................................................................................................................................................................. 8 All Participants (ICERM funded and Non-ICERM funded) ....................................................................................................................... 9 ICERM Funded Speakers .................................................................................................................................................................................... -
January 2007 Prizes and Awards
January 2007 Prizes and Awards 4:25 P.M., Saturday, January 6, 2007 MATHEMATICAL ASSOCIATION OF AMERICA DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY TEACHING OF MATHEMATICS In 1991, the Mathematical Association of America instituted the Deborah and Franklin Tepper Haimo Awards for Distinguished College or University Teaching of Mathematics in order to honor college or university teachers who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions. Deborah Tepper Haimo was president of the Association, 1991–1992. Citation Jennifer Quinn Jennifer Quinn has a contagious enthusiasm that draws students to mathematics. The joy she takes in all things mathematical is reflected in her classes, her presentations, her publications, her videos and her on-line materials. Her class assignments often include nonstandard activities, such as creating time line entries for historic math events, or acting out scenes from the book Proofs and Refutations. One student created a children’s story about prime numbers and another produced a video documentary about students’ perceptions of math. A student who had her for six classes says, “I hope to become a teacher after finishing my master’s degree and I would be thrilled if I were able to come anywhere close to being as great a teacher as she is.” Jenny developed a variety of courses at Occidental College. Working with members of the physics department and funded by an NSF grant, she helped develop a combined yearlong course in calculus and mechanics. She also developed a course on “Mathematics as a Liberal Art” which included computer discussions, writing assignments, and other means to draw technophobes into the course. -
Instanton and the Depth of Taut Foliations
Instanton and the depth of taut foliations Zhenkun Li Abstract Sutured instanton Floer homology was introduced by Kronheimer and Mrowka in [8]. In this paper, we prove that for a taut balanced sutured man- ifold with vanishing second homology, the dimension of the sutured instanton Floer homology provides a bound on the minimal depth of all possible taut foliations on that balanced sutured manifold. The same argument can be adapted to the monopole and even the Heegaard Floer settings, which gives a partial answer to one of Juhasz’s conjectures in [5]. Using the nature of instanton Floer homology, on knot complements, we can construct a taut foliation with bounded depth, given some information on the representation varieties of the knot fundamental groups. This indicates a mystery relation between the representation varieties and some small depth taut foliations on knot complements, and gives a partial answer to one of Kronheimer and Mrowka’s conjecture in [8]. 1 Introduction Sutured manifolds and sutured manifold hierarchies were introduced by Gabai in 1983 in [2] and subsequent papers. They are powerful tools in the study of 3-dimensional topology. A sutured manifold is a compact oriented 3-manifold with boundary, together with an oriented closed 1-submanifold γ on BM, which is called the suture. If S Ă M is a properly embedded surface inside M, which satisfies some milt conditions, then we can perform a decomposition of pM, γq along S and obtain a new sutured manifold pM 1, γ1q. We call this process a sutured manifold decomposition and write S 1 1 arXiv:2003.02891v1 [math.GT] 5 Mar 2020 pM, γq pM , γ q. -
1 Institute for Pure and Applied Mathematics, UCLA Preliminary
Institute for Pure and Applied Mathematics, UCLA Preliminary Report on Funding Year 2014-2015 June 19, 2015 The current funding period ends on August 31, 2015. This is a preliminary report. The full report will be submitted next year. IPAM held two long programs. Each long program included tutorials, four workshops, and a culminating retreat. Between workshops, the participants planned a series of talks and focus groups. Mathematics of Turbulence (fall 2014) Broad Perspectives and New Directions in Financial Mathematics (spring 2015) Workshops in the past year included: Multiple Sequence Alignment Symmetry and Topology in Quantum Matter Computational Photography and Intelligent Cameras Zariski-dense Subgroups Machine Learning for Many-Particle Systems IPAM held two diversity conferences in the past year: Blackwell-Tapia Conference and Awards Ceremony Latinos/as in the Mathematical Sciences Conference The Blackwell-Tapia Conference was supported by the NSF Math Institutes’ Diversity Grant and a grant from the Sloan Foundation. The NSA and Raytheon Corporation sponsored the Latinos in Math Conference. An undergraduate event entitled “Grad School and Beyond: Advice for the Aspiring Mathematician” was held the day before the Blackwell-Tapia Conference and featured some of the conference speakers and participants. IPAM held “reunion conferences” for four long programs: Plasma Physics, Materials Defects, Interaction between Analysis and Geometry, and Materials for Sustainable Energy Three summer research programs will take place this summer: RIPS-Hong Kong, RIPS-LA and Graduate-level RIPS in Berlin. The graduate summer school “Games and Contracts for Cyber-Physical Security” will take place in July 2015. The Green Family Lecture Series this year featured Andrew Lo, director of MIT’s Laboratory for Financial Engineering.