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Mechanical Aspire
Newsletter Volume 6, Issue 11, November 2016 Mechanical Aspire Achievements in Sports, Projects, Industry, Research and Education All About Nobel Prize- Part 35 The Breakthrough Prize Inspired by Nobel Prize, there have been many other prizes similar to that, both in amount and in purpose. One such prize is the Breakthrough Prize. The Breakthrough Prize is backed by Facebook chief executive Mark Zuckerberg and Google co-founder Sergey Brin, among others. The Breakthrough Prize was founded by Brin and Anne Wojcicki, who runs genetic testing firm 23andMe, Chinese businessman Jack Ma, and Russian entrepreneur Yuri Milner and his wife Julia. The Breakthrough Prizes honor important, primarily recent, achievements in the categories of Fundamental Physics, Life Sciences and Mathematics . The prizes were founded in 2012 by Sergey Brin and Anne Wojcicki, Mark Zuckerberg and Priscilla Chan, Yuri and Julia Milner, and Jack Ma and Cathy Zhang. Committees of previous laureates choose the winners from candidates nominated in a process that’s online and open to the public. Laureates receive $3 million each in prize money. They attend a televised award ceremony designed to celebrate their achievements and inspire the next generation of scientists. As part of the ceremony schedule, they also engage in a program of lectures and discussions. Those that go on to make fresh discoveries remain eligible for future Breakthrough Prizes. The Trophy The Breakthrough Prize trophy was created by Olafur Eliasson. “The whole idea for me started out with, ‘Where do these great ideas come from? What type of intuition started the trajectory that eventually becomes what we celebrate today?’” Like much of Eliasson's work, the sculpture explores the common ground between art and science. -
Algebra & Number Theory Vol. 7 (2013)
Algebra & Number Theory Volume 7 2013 No. 3 msp Algebra & Number Theory msp.org/ant EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Raman Parimala Emory University, USA John H. Coates University of Cambridge, UK Jonathan Pila University of Oxford, UK J-L. Colliot-Thélène CNRS, Université Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hélène Esnault Freie Universität Berlin, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universität, Germany Joseph H. Silverman Brown University, USA Edward Frenkel University of California, Berkeley, USA Michael Singer North Carolina State University, USA Andrew Granville Université de Montréal, Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Virginia, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale University, USA Ravi Vakil Stanford University, -
Chapter 1 Introduction 1.1 Algebraic Setting
Towards a Functor Between Affine and Finite Hecke Categories in Type A by Kostiantyn Tolmachov Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2018 Massachusetts Institute of Technology 2018. All rights reserved. -Signature redacted A uthor .. ....................... Department of Mathematics May 1, 2018 Certified by. Signature redacted.................... Roman Bezrukavnikov Professor of Mathematics Thesis Supervisor Accepted by. Signature redacted ................ -.. - -William Minicozzi G duate Co-Chair Department of Mathematics MASSACHUlS INSITUTE OF TECHNOLOGY MAY 3 0 2018 LIBRARIES fRCHIVES Towards a Functor Between Affine and Finite Hecke Categories in Type A by Kostiantyn Tolmachov Submitted to the Department of Mathematics on May 1, 2018, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis we construct a functor from the perfect subcategory of the coherent version of the affine Hecke category in type A to the finite constructible Hecke ca- tegory, partly categorifying a certain natural homomorphism of the corresponding Hecke algebras. This homomorphism sends generators of the Bernstein's commutative subalgebra inside the affine Hecke algebra to Jucys-Murphy elements in the finite Hecke algebra. Construction employs the general strategy devised by Bezrukavnikov to prove the equivalence of coherent and constructible variants of the affine Hecke category. Namely, we identify an action of the category Rep(GL,) on the finite Hecke category, and lift this action to a functor from the perfect derived category of the Steinberg variety, by equipping it with various additional data. Thesis Supervisor: Roman Bezrukavnikov Title: Professor of Mathematics 3 4 Acknowledgments I would like to thank my advisor, Roman Bezrukavnikov, for his support and guidance over these years, as well as for many helpful discussions and sharing his expertise. -
Mathematics Calendar
Mathematics Calendar Please submit conference information for the Mathematics Calendar through the Mathematics Calendar submission form at http:// www.ams.org/cgi-bin/mathcal-submit.pl. The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/. June 2014 Information: http://www.tesol.org/attend-and-learn/ online-courses-seminars/esl-for-the-secondary- 1–7 Modern Time-Frequency Analysis, Strobl, Austria. (Apr. 2013, mathematics-teacher. p. 429) * 2–30 Algorithmic Randomness, Institute for Mathematical Sciences, 2–5 WSCG 2014 - 22nd International Conference on Computer National University of Singapore, Singapore. Graphics, Visualization and Computer Vision 2014, Primavera Description: Activities 1. Informal Collaboration: June 2–8, 2014. 2. Hotel and Congress Centrum, Plzen (close to Prague), Czech Repub- Ninth International Conference on Computability, Complexity and lic. (Jan. 2014, p. 90) Randomness (CCR 2014): June 9–13, 2014. The conference series 2–6 AIM Workshop: Descriptive inner model theory, American “Computability, Complexity and Randomness” is centered on devel- Institute of Mathematics, Palo Alto, California. (Mar. 2014, p. 312) opments in Algorithmic Randomness, and the conference CCR 2014 2–6 Computational Nonlinear Algebra, Institute for Computational will be part of the IMS programme. The CCR has previously been held and Experimental Research in Mathematics, (ICERM), Brown Univer- in Cordoba 2004, in Buenos Aires 2007, in Nanjing 2008, in Luminy sity, Providence, Rhode Island. (Nov. 2013, p. 1398) 2009, in Notre Dame 2010, in Cape Town 2011, in Cambridge 2012, and in Moscow 2013; it will be held in Heidelberg 2015. 3. Informal 2–6 Conference on Ulam’s type stability, Rytro, Poland. -
3-Manifold Groups
3-Manifold Groups Matthias Aschenbrenner Stefan Friedl Henry Wilton University of California, Los Angeles, California, USA E-mail address: [email protected] Fakultat¨ fur¨ Mathematik, Universitat¨ Regensburg, Germany E-mail address: [email protected] Department of Pure Mathematics and Mathematical Statistics, Cam- bridge University, United Kingdom E-mail address: [email protected] Abstract. We summarize properties of 3-manifold groups, with a particular focus on the consequences of the recent results of Ian Agol, Jeremy Kahn, Vladimir Markovic and Dani Wise. Contents Introduction 1 Chapter 1. Decomposition Theorems 7 1.1. Topological and smooth 3-manifolds 7 1.2. The Prime Decomposition Theorem 8 1.3. The Loop Theorem and the Sphere Theorem 9 1.4. Preliminary observations about 3-manifold groups 10 1.5. Seifert fibered manifolds 11 1.6. The JSJ-Decomposition Theorem 14 1.7. The Geometrization Theorem 16 1.8. Geometric 3-manifolds 20 1.9. The Geometric Decomposition Theorem 21 1.10. The Geometrization Theorem for fibered 3-manifolds 24 1.11. 3-manifolds with (virtually) solvable fundamental group 26 Chapter 2. The Classification of 3-Manifolds by their Fundamental Groups 29 2.1. Closed 3-manifolds and fundamental groups 29 2.2. Peripheral structures and 3-manifolds with boundary 31 2.3. Submanifolds and subgroups 32 2.4. Properties of 3-manifolds and their fundamental groups 32 2.5. Centralizers 35 Chapter 3. 3-manifold groups after Geometrization 41 3.1. Definitions and conventions 42 3.2. Justifications 45 3.3. Additional results and implications 59 Chapter 4. The Work of Agol, Kahn{Markovic, and Wise 63 4.1. -
Meetings & Conferences of The
Meetings & Conferences of the AMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting. abstract submission form found at http://www.ams.org/ Knoxville, Tennessee cgi-bin/abstracts/abstract.pl. University of Tennessee, Knoxville Algebraic Methods in Graph Theory and Combinator- ics (Code: SS 7A), Felix Lazebnik, University of Delaware, March 21–23, 2014 Andrew Woldar, Villanova University, and Bangteng Xu, Friday – Sunday Eastern Kentucky University. Arithmetic of Algebraic Curves (Code: SS 9A), Lubjana Meeting #1097 Beshaj, Oakland University, Caleb Shor, Western New Eng- Southeastern Section land University, and Andreas Malmendier, Colby College. Associate secretary: Brian D. Boe Commutative Ring Theory (in honor of the retirement Announcement issue of Notices: January 2014 of David E. Dobbs) (Code: SS 1A), David Anderson, Uni- Program first available on AMS website: February 6, 2014 versity of Tennessee, Knoxville, and Jay Shapiro, George Program issue of electronic Notices: March 2014 Mason University. Issue of Abstracts: Volume 35, Issue 2 Completely Integrable Systems and Dispersive Nonlinear Deadlines Equations (Code: SS 12A), Robert Buckingham, University of Cincinnati, and Peter Perry, University of Kentucky. For organizers: Expired Complex Analysis, Probability, and Metric Geometry For abstracts: January 28, 2014 (Code: SS 11A), Matthew Badger, Stony Brook University, Jim Gill, St. -
January 2013 Prizes and Awards
January 2013 Prizes and Awards 4:25 P.M., Thursday, January 10, 2013 PROGRAM SUMMARY OF AWARDS OPENING REMARKS FOR AMS Eric Friedlander, President LEVI L. CONANT PRIZE: JOHN BAEZ, JOHN HUERTA American Mathematical Society E. H. MOORE RESEARCH ARTICLE PRIZE: MICHAEL LARSEN, RICHARD PINK DEBORAH AND FRANKLIN TEPPER HAIMO AWARDS FOR DISTINGUISHED COLLEGE OR UNIVERSITY DAVID P. ROBBINS PRIZE: ALEXANDER RAZBOROV TEACHING OF MATHEMATICS RUTH LYTTLE SATTER PRIZE IN MATHEMATICS: MARYAM MIRZAKHANI Mathematical Association of America LEROY P. STEELE PRIZE FOR LIFETIME ACHIEVEMENT: YAKOV SINAI EULER BOOK PRIZE LEROY P. STEELE PRIZE FOR MATHEMATICAL EXPOSITION: JOHN GUCKENHEIMER, PHILIP HOLMES Mathematical Association of America LEROY P. STEELE PRIZE FOR SEMINAL CONTRIBUTION TO RESEARCH: SAHARON SHELAH LEVI L. CONANT PRIZE OSWALD VEBLEN PRIZE IN GEOMETRY: IAN AGOL, DANIEL WISE American Mathematical Society DAVID P. ROBBINS PRIZE FOR AMS-SIAM American Mathematical Society NORBERT WIENER PRIZE IN APPLIED MATHEMATICS: ANDREW J. MAJDA OSWALD VEBLEN PRIZE IN GEOMETRY FOR AMS-MAA-SIAM American Mathematical Society FRANK AND BRENNIE MORGAN PRIZE FOR OUTSTANDING RESEARCH IN MATHEMATICS BY ALICE T. SCHAFER PRIZE FOR EXCELLENCE IN MATHEMATICS BY AN UNDERGRADUATE WOMAN AN UNDERGRADUATE STUDENT: FAN WEI Association for Women in Mathematics FOR AWM LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION LOUISE HAY AWARD FOR CONTRIBUTIONS TO MATHEMATICS EDUCATION: AMY COHEN Association for Women in Mathematics M. GWENETH HUMPHREYS AWARD FOR MENTORSHIP OF UNDERGRADUATE -
ANNEXURE 1 School of Mathematics Sciences —A Profile As in March 2010
University Yearbook (Academic Audit Report 2005-10) ANNEXURE 1 School of Mathematics Sciences —A Profile as in March 2010 Contents 1. Introduction 1 1.1. Science Education: A synthesis of two paradigms 2 2. Faculty 3 2.1. Mathematics 4 2.2. Physics 12 2.3. Computer Science 18 3. International Links 18 3.1. Collaborations Set Up 18 3.2. Visits by our faculty abroad for research purposes 19 3.3. Visits by faculty abroad to Belur for research purposes 19 4. Service at the National Level 20 4.1. Links at the level of faculty 20 5. Student Placement 21 5.1. 2006-8 MSc Mathematics Batch 21 5.2. 2008-10 MSc Mathematics Batch 22 6. Research 23 1. Introduction Swami Vivekananda envisioned a University at Belur Math, West Bengal, the headquarters of the Ramakrishna Mission. In his conversation with Jamshedji Tata, it was indicated that the spirit of austerity, service and renun- ciation, traditionally associated with monasticism could be united with the quest for Truth and Universality that Science embodies. An inevitable fruit of such a synthesis would be a vigorous pursuit of science as an aspect of Karma Yoga. Truth would be sought by research and the knowledge obtained disseminated through teach- ing, making knowledge universally available. The VivekanandaSchool of Mathematical Sciences at the fledgling Ramakrishna Mission Vivekananda University, headquartered at Belur, has been set up keeping these twin ide- als in mind. We shall first indicate that at the National level, a realization of these objectives would fulfill a deeply felt National need. 1.1. -
Preface Issue 4-2014
Jahresber Dtsch Math-Ver (2014) 116:199–200 DOI 10.1365/s13291-014-0108-4 PREFACE Preface Issue 4-2014 Hans-Christoph Grunau © Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg 2014 The last few years have been a good time for solving long standing geometrical- topological conjectures. This issue reports on the solution of the Willmore conject-√ ure—the “best” topological torus is a “real” torus with ratio of radii equal to 2— and one of Thurston’s conjectures—every hyperbolic 3-manifold can be fibered over a circle, up to passing to a finite cover. Starting in the 1960s, Thomas Willmore studied the integral of the squared mean curvature of surfaces in R3 as the simplest but most interesting frame invariant elas- tic bending energy. This energy had shown up already in the early 19th century—too early for a rigorous investigation. Willmore asked: What is the shape of a compact surface of fixed genus minimising the Willmore energy in this class? (In the 1990s, existence of minimisers was proved by Leon Simon, with a contribution by Matthias Bauer and Ernst Kuwert.) Willmore already knew that the genus-0-minimiser is a sphere. Assuming that symmetric surfaces require less energy than asymmetric ones (which has not been proved, yet) he studied families√ of geometric tori with the smaller radius 1 fixed and found that the larger radius 2 would yield the minimum in this very special family. He conjectured that this particular torus would be the genus- 1-minimiser. Almost 50 years later Fernando Marques and André Neves found and published a 100-page-proof. -
The Work of Robert Macpherson 1
The work of Robert MacPherson 1 along with a huge supporting cast of coauthors: Paul Baum, Sasha Beilinson, Walter Borho, Tom Braden, JeanPaul Brasselet, JeanLuc Brylinski, Jeff Cheeger, Robert Coveyou, Corrado DeConcini, Pierre Deligne, Bill Fulton, Israel Gelfand, Sergei Gelfand, Mark Goresky, Dick Hain, Masaki Hanamura, Gunter Harder, Lizhen Ji, Steve Kleiman, Bob Kot twitz, George Lusztig, Mark MacConnell, Arvind Nair, Claudio Procesi, Vadim Schechtman, Vera Serganova, Frank Sottile, Berndt Sturmfels, and Kari Vilonen 2 and students: Paul Dippolito (Brown 1974), Mark Goresky (B 1976), Thomas DeLio (B 1978—in music!), David Damiano (B 1980), Kari Vilonen (B 1983), Kevin Ryan (B 1984), Allen Shepard (B 1985), Mark McConnell (B 1987), Masaki Hanamura (B 1988), Wolfram Gerdes (MIT 1989), David Yavin (M 1991), Yi Hu (M 1991), Richard Scott (M 1993), Eric Babson (M 1994), Paul Gunnells (M 1994), Laura Anderson (M 1994), Tom Braden (M 1995), Mikhail Grinberg (Harvard 1997), Francis Fung (Princeton 1997), Jared Anderson (P 2000), David Nadler (P 2001), Julianna Tymoczko (P 2003), Brent Doran (P 2003), Aravind Asok (P 2004) 3 and I suppose a good bunch of these eager critics are sitting in this room today. 4 5 Born — Lakewood, Ohio — May 25, 1944 B.A. — Swarthmore College 1966 Ph.D. — Harvard University 1970 Brown University — 1970 – 1987 M.I.T. — 1987 – 1994 I.A.S. — 1994 – 6 BA PhD Brown MIT IAS 1950 1960 1970 1980 1990 2000 7 Publication record (colour coded by the number of authors) 8 Part I. Test for random number generators [105] Fourier Analysis of Uniform Random Number Generators, with R. -
Fundamental Local Equivalences in Quantum Geometric Langlands
FUNDAMENTAL LOCAL EQUIVALENCES IN QUANTUM GEOMETRIC LANGLANDS JUSTIN CAMPBELL, GURBIR DHILLON, AND SAM RASKIN Abstract. In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory{Lurie proposed a conjectural substitute, later termed the fundamental local equivalence. With a few exceptions, we prove this conjecture and its extension to the affine flag variety by using what amount to Soergel module techniques. Contents 1. Introduction 1 2. Preliminary material 6 3. Fundamental local equivalences 10 Appendix A. Proof in the general case 27 References 29 1. Introduction 1.1. In the early days of the geometric Langlands program, experts observed that the fundamental objects of study deform over the space of levels κ for the reductive group G. For example, if G is simple, this is a 1-dimensional space. Moreover, levels admit duality as well: a level κ for G gives rise to a dual level1 κˇ for the Langlands dual group Gˇ. This observation suggested the existence of a quantum geometric Langlands program, deforming the usual Langlands program. The first triumph of this idea appeared in the work of Feigin{Frenkel [FF91], where they proved duality of affine W-algebras: WG,κ ' WG;ˇ κˇ. We emphasize that this result is quantum in its nature: the level κ appears. For the critical level κ = κc, which corresponds to classical geometric Langlands, Beilinson{Drinfeld [BDdf] used Feigin{Frenkel duality to give a beautiful construction of Hecke eigensheaves for certain irreducible local systems. 1.2. The major deficiency of the quantum geometric Langlands was understood immediately: the Satake equivalence is more degenerate. -
HODGE THEORY and UNITARY REPRESENTATIONS of REDUCTIVE LIE GROUPS 3 Most Important
AMS/IP Studies in Advanced Mathematics Hodge theory and unitary representations of reductive Lie groups Wilfried Schmid and Kari Vilonen Abstract. We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof. 1. Introduction In this paper we state a conjecture on the unitary dual of reductive Lie groups and formulate certain foundational results towards it. We are currently working towards a proof. The conjecture does not give an explicit description of the uni- tary dual. Rather, it provides a strong functorial framework for studying unitary representations. Our main tool is M. Saito’s theory of mixed Hodge modules [19], applied to the Beilinson-Bernstein realization of Harish Chandra modules [4] Our paper represents an elaboration of the first named author’s lecture at the Sanya Inauguration conference. Like that lecture, it aims to provide an expository account of the present state of our work. We consider a linear reductive Lie group GR with maximal compact subgroup KR. The complexification G of GR contains a unique compact real form UR such that KR = GR ∩ UR. We denote the Lie algebras of GR, UR, KR by the subscripted Gothic letters gR, uR, and kR ; the first two of these lie as real forms in g, the Lie algebra of the complex group G, and similarly kR is a realform of k, the Lie algebra of arXiv:1206.5547v1 [math.RT] 24 Jun 2012 the complexification K of the group KR.