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Karen Uhlenbeck Awarded the 2019 Abel Prize
RESEARCH NEWS Karen Uhlenbeck While she was in Urbana-Champagne (Uni- versity of Illinois), Karen Uhlenbeck worked Awarded the 2019 Abel with a postdoctoral fellow, Jonathan Sacks, Prize∗ on singularities of harmonic maps on 2D sur- faces. This was the beginning of a long journey in geometric analysis. In gauge the- Rukmini Dey ory, Uhlenbeck, in her remarkable ‘removable singularity theorem’, proved the existence of smooth local solutions to Yang–Mills equa- tions. The Fields medallist Simon Donaldson was very much influenced by her work. Sem- inal results of Donaldson and Uhlenbeck–Yau (amongst others) helped in establishing gauge theory on a firm mathematical footing. Uhlen- beck’s work with Terng on integrable systems is also very influential in the field. Karen Uhlenbeck is a professor emeritus of mathematics at the University of Texas at Austin, where she holds Sid W. Richardson Foundation Chair (since 1988). She is cur- Karen Uhlenbeck (Source: Wikimedia) rently a visiting associate at the Institute for Advanced Study, Princeton and a visiting se- nior research scholar at Princeton University. The 2019 Abel prize for lifetime achievements She has enthused many young women to take in mathematics was awarded for the first time up mathematics and runs a mentorship pro- to a woman mathematician, Professor Karen gram for women in mathematics at Princeton. Uhlenbeck. She is famous for her work in ge- Karen loves gardening and nature hikes. Hav- ometry, analysis and gauge theory. She has ing known her personally, I found she is one of proved very important (and hard) theorems in the most kind-hearted mathematicians I have analysis and applied them to geometry and ever known. -
Twenty Female Mathematicians Hollis Williams
Twenty Female Mathematicians Hollis Williams Acknowledgements The author would like to thank Alba Carballo González for support and encouragement. 1 Table of Contents Sofia Kovalevskaya ................................................................................................................................. 4 Emmy Noether ..................................................................................................................................... 16 Mary Cartwright ................................................................................................................................... 26 Julia Robinson ....................................................................................................................................... 36 Olga Ladyzhenskaya ............................................................................................................................. 46 Yvonne Choquet-Bruhat ....................................................................................................................... 56 Olga Oleinik .......................................................................................................................................... 67 Charlotte Fischer .................................................................................................................................. 77 Karen Uhlenbeck .................................................................................................................................. 87 Krystyna Kuperberg ............................................................................................................................. -
Copyright by Magdalena Czubak 2008 the Dissertation Committee for Magdalena Czubak Certifies That This Is the Approved Version of the Following Dissertation
Copyright by Magdalena Czubak 2008 The Dissertation Committee for Magdalena Czubak certifies that this is the approved version of the following dissertation: Well-posedness for the space-time Monopole Equation and Ward Wave Map. Committee: Karen Uhlenbeck, Supervisor William Beckner Daniel Knopf Andrea Nahmod Mikhail M. Vishik Well-posedness for the space-time Monopole Equation and Ward Wave Map. by Magdalena Czubak, B.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2008 Dla mojej Mamy. Well-posedness for the space-time Monopole Equation and Ward Wave Map. Publication No. Magdalena Czubak, Ph.D. The University of Texas at Austin, 2008 Supervisor: Karen Uhlenbeck We study local well-posedness of the Cauchy problem for two geometric wave equations that can be derived from Anti-Self-Dual Yang Mills equations on R2+2. These are the space-time Monopole Equation and the Ward Wave Map. The equations can be formulated in different ways. For the formulations we use, we establish local well-posedness results, which are sharp using the iteration methods. v Table of Contents Abstract v Chapter 1. Introduction 1 1.1 Space-time Monopole and Ward Wave Map equations . 1 1.2 Chapter Summaries . 7 Chapter 2. Preliminaries 9 2.1 Notation . 9 2.2 Function Spaces & Inversion of the Wave Operator . 10 2.3 Estimates Used . 12 2.4 Classical Results . 16 2.5 Null Forms . 18 2.5.1 Symbols . -
Karen Keskulla Uhlenbeck
2019 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2019 to Karen Keskulla Uhlenbeck University of Texas at Austin “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Karen Keskulla Uhlenbeck is a founder of modern by earlier work of Morse, guarantees existence of Geometric Analysis. Her perspective has permeated minimisers of geometric functionals and is successful the field and led to some of the most dramatic in the case of 1-dimensional domains, such as advances in mathematics in the last 40 years. closed geodesics. Geometric analysis is a field of mathematics where Uhlenbeck realised that the condition of Palais— techniques of analysis and differential equations are Smale fails in the case of surfaces due to topological interwoven with the study of geometrical and reasons. The papers of Uhlenbeck, co-authored with topological problems. Specifically, one studies Sacks, on the energy functional for maps of surfaces objects such as curves, surfaces, connections and into a Riemannian manifold, have been extremely fields which are critical points of functionals influential and describe in detail what happens when representing geometric quantities such as energy the Palais-Smale condition is violated. A minimising and volume. For example, minimal surfaces are sequence of mappings converges outside a finite set critical points of the area and harmonic maps are of singular points and by using rescaling arguments, critical points of the Dirichlet energy. Uhlenbeck’s they describe the behaviour near the singularities major contributions include foundational results on as bubbles or instantons, which are the standard minimal surfaces and harmonic maps, Yang-Mills solutions of the minimising map from the 2-sphere to theory, and integrable systems. -
Surveys in Differential Geometry
Surveys in Differential Geometry Vol. 1: Lectures given in 1990 edited by S.-T. Yau and H. Blaine Lawson Vol. 2: Lectures given in 1993 edited by C.C. Hsiung and S.-T. Yau Vol. 3: Lectures given in 1996 edited by C.C. Hsiung and S.-T. Yau Vol. 4: Integrable systems edited by Chuu Lian Terng and Karen Uhlenbeck Vol. 5: Differential geometry inspired by string theory edited by S.-T. Yau Vol. 6: Essays on Einstein manifolds edited by Claude LeBrun and McKenzie Wang Vol. 7: Papers dedicated to Atiyah, Bott, Hirzebruch, and Singer edited by S.-T. Yau Vol. 8: Papers in honor of Calabi, Lawson, Siu, and Uhlenbeck edited by S.-T. Yau Vol. 9: Eigenvalues of Laplacians and other geometric operators edited by A. Grigor’yan and S-T. Yau Vol. 10: Essays in geometry in memory of S.-S. Chern edited by S.-T. Yau Vol. 11: Metric and comparison geometry edited by Jeffrey Cheeger and Karsten Grove Vol. 12: Geometric flows edited by Huai-Dong Cao and S.-T. Yau Vol. 13: Geometry, analysis, and algebraic geometry edited by Huai-Dong Cao and S.-T.Yau Vol. 14: Geometry of Riemann surfaces and their moduli spaces edited by Lizhen Ji, Scott A. Wolpert, and S.-T. Yau Vol. 15: Perspectives in mathematics and physics: Essays dedicated to Isadore Singer edited by Tomasz Mrowka and S.-T. Yau Vol. 16: Geometry of special holonomy and related topics edited by Naichung Conan Leung and S.-T. Yau Vol. 17: In Memory of C. C. -
Karen Uhlenbeck Awarded Abel Prize
COMMUNICATION Karen Uhlenbeck Awarded Abel Prize The Norwegian Academy of Science and Letters has awarded the Abel Prize for 2019 to Karen Keskulla Uhlenbeck of the University of Texas at Austin, “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” The Abel Prize recognizes contributions of extraordinary depth and influence in the mathematical sciences and has been awarded annually since 2003. It carries a cash award of six million Norwegian krone (approximately US$700,000). Citation detail what happens when the Palais–Smale condition is Karen Keskulla Uhlenbeck is a violated. A minimizing sequence of mappings converges founder of modern geometric outside a finite set of singular points, and, by using resca- analysis. Her perspective has ling arguments, they describe the behavior near the singu- permeated the field and led larities as bubbles or instantons, which are the standard to some of the most dramatic solutions of the minimizing map from the 2-sphere to the advances in mathematics in the target manifold. last forty years. In higher dimensions, Uhlenbeck in collaboration with Geometric analysis is a field Schoen wrote two foundational papers on minimizing of mathematics where tech- harmonic maps. They gave a profound understanding niques of analysis and differ- of singularities of solutions of nonlinear elliptic partial ential equations are interwoven differential equations. The singular set, which in the case Karen Keskulla Uhlenbeck with the study of geometrical of surfaces consists only of isolated points, is in higher and topological problems. -
Spring 2019 Fine Letters
Spring 2019 • Issue 8 Department of MATHEMATICS Princeton University From the Chair Professor Allan Sly Receives MacArthur Fellowship Congratulations to Sly works on an area of probability retical computer science, where a key the Class of 2019 theory with applications from the goal often is to understand whether and all the finishing physics of magnetic materials to it is likely or unlikely that a large set graduate students. computer science and information of randomly imposed constraints on a Congratulations theory. His work investigates thresh- system can be satisfied. Sly has shown to the members of olds at which complex networks mathematically how such systems of- class of 2018 and suddenly change from having one ten reach a threshold at which solving new Ph. D.s who set of properties to another. Such a particular problem shifts from likely are reading Fine Letters for the first questions originally arose in phys- or unlikely. Sly has used a party invi- time as alumni. As we all know, the ics, where scientists observed such tation list as an analogy for the work: Math major is a great foundation for shifts in the magnetism of certain As you add interpersonal conflicts a diverse range of endeavors. This metal alloys. Sly provided a rigorous among a group of potential guests, it is exemplified by seventeen '18's who mathematical proof of the shift and can suddenly become effectively im- have gone to industry and seventeen a framework for identifying when possible to create a workable party. to grad school; ten to advanced study such shifts occur. -
Printed Program and Abstracts
Printed Program and Abstracts Sponsored by the SIAM Activity Group on Algebraic Geometry The purpose of the SIAM Activity Group on Algebraic Geometry is to bring together researchers who use algebraic geometry in industrial and applied mathematics. “Algebraic geometry” is interpreted broadly to include at least: algebraic geometry, commutative algebra, noncommutative algebra, symbolic and numeric computation, algebraic and geometric combinatorics, representation theory, and algebraic topology. These methods have already seen applications in: biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear partial differential equations, optimization, robotics, and statistics. We welcome participation from both theoretical mathematical areas and application areas not on this list which fall under this broadly interpreted notion of algebraic geometry and its applications. Society for Industrial and Applied Mathematics 3600 Market Street, 6th Floor Philadelphia, PA 19104-2688 USA Telephone: +1-215-382-9800 Fax: +1-215-386-7999 Conference E-mail: [email protected] Conference Web: www.siam.org/meetings/ Membership and Customer Service: (800) 447-7426 (USA & Canada) or +1-215-382-9800 (worldwide) www.siam.org/meetings/ag17 2 SIAM Conference on Applied Algebraic Geometry Table of Contents SIAM Registration Desk Corporate/Institutional Members The Aerospace Corporation The SIAM registration desk is located Air Force Office of Scientific Research Program-At-A-Glance… in the Skiles Building - Bottom (0-th) Amazon ................................ Separate handout Floor. It is open during the following General Information .............................. 2 hours: Aramco Services Company Get-togethers ......................................... 4 Monday, July 31 Bechtel Marine Propulsion Laboratory Invited Plenary Presentations ................ 5 7:00 AM – 4:00 PM The Boeing Company Prize .................................................... -
April 2017 Table of Contents
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society April 2017 Volume 64, Number 4 AMS Prize Announcements page 311 Spring Sectional Sampler page 333 AWM Research Symposium 2017 Lecture Sampler page 341 Mathematics and Statistics Awareness Month page 362 About the Cover: How Minimal Surfaces Converge to a Foliation (see page 307) MATHEMATICAL CONGRESS OF THE AMERICAS MCA 2017 JULY 2428, 2017 | MONTREAL CANADA MCA2017 will take place in the beautiful city of Montreal on July 24–28, 2017. The many exciting activities planned include 25 invited lectures by very distinguished mathematicians from across the Americas, 72 special sessions covering a broad spectrum of mathematics, public lectures by Étienne Ghys and Erik Demaine, a concert by the Cecilia String Quartet, presentation of the MCA Prizes and much more. SPONSORS AND PARTNERS INCLUDE Canadian Mathematical Society American Mathematical Society Pacifi c Institute for the Mathematical Sciences Society for Industrial and Applied Mathematics The Fields Institute for Research in Mathematical Sciences National Science Foundation Centre de Recherches Mathématiques Conacyt, Mexico Atlantic Association for Research in Mathematical Sciences Instituto de Matemática Pura e Aplicada Tourisme Montréal Sociedade Brasileira de Matemática FRQNT Quebec Unión Matemática Argentina Centro de Modelamiento Matemático For detailed information please see the web site at www.mca2017.org. AMERICAN MATHEMATICAL SOCIETY PUSHING LIMITS From West Point to Berkeley & Beyond PUSHING LIMITS FROM WEST POINT TO BERKELEY & BEYOND Ted Hill, Georgia Tech, Atlanta, GA, and Cal Poly, San Luis Obispo, CA Recounting the unique odyssey of a noted mathematician who overcame military hurdles at West Point, Army Ranger School, and the Vietnam War, this is the tale of an academic career as noteworthy for its o beat adventures as for its teaching and research accomplishments. -
Xssociation for Goomen in (At Matics
,_Xssociationfor gOomenin (at matics Volume 20, Number 4 NEWSLETTER July-August 1990 ****************************************************************** PRESIDENT'S REPORT I am looking forward to a lively and interesting panel, "Enrichment programs in urban public schools," this summer in Columbus. The panelists will include Jacqueline Rivers, who runs The Algebra Project in Boston, Paul Sally, who directs the University of Chicago summer program for mathematically talented youth, and Harvey Keynes, who has been involved in an effort to increase the number of girls participating in the University of Minnesota Talented Youth Mathematics Program (UMTYMP). An article by Keynes describing the intervention program appeared in the last issue of the AWM Newsletter. While the latter two programs deal with mathematically talented youth, The Algebra Project, started by Bob Moses in Cambridge, Massachusetts, uses mathematics as a vehicle to raise the level of academic performance in general of inner city youth. Remember, there will be an award ceremony for the Schafer Prize winners at the beginning of the Business Meeting in Columbus, so please come to meet and applaud these talented young women. We would like to increase the endowment so that the prize can be self-supporting, and I hope that you will all help us in this task. I am delighted to congratulate two of our members: Cathleen Morawetz on her election to the National Academy of Sciences, and Lee Lorch on the receipt of an honorary degree from the City University of New York. Rogers Newman, President of the National Association of Mathematicians, sent me a very nice note thanking the AWM for our congratulatory letter on the occasion of their 20th anniversary. -
Karen Uhlenbeck Wins Abel Prize Aren Uhlenbeck Is the 2019 Recipient of the Abel Prize
Karen Uhlenbeck wins Abel Prize aren Uhlenbeck is the 2019 recipient of the Abel Prize. Already in the case dim M = 2, the problem posed considerable The citation awards the prize ‘for her pioneering achieve- challenges: the Palais–Smale condition fails for F, moreover, Kments in geometric partial differential equations, gauge the Euler–Lagrange equation does not enter the framework of theory and integrable systems, and for the fundamental impact classical elliptic partial differential equations. of her work on analysis, geometry and mathematical physics.’ In the 70s, while at Urbana–Champaign, Uhlenbeck devised, She was one of the founders of geometric analysis: how did this in a ground-breaking paper [1] co-authored with J. Sacks, come about? an alternative method to detect harmonic maps (in the case In the mid 60s, Uhlenbeck (then Karen Keskulla) began dim M = 2) by approximation: the key was to consider a se- graduate school at Brandeis University, with Palais as her quence of energies F (u)= u 2. |∇ | adviser; this naturally led her to the calculus of variations. A M fundamental question in this field (among Hilbert’s famous 2 α problems from 1904) is to prove the existence of critical points Fα(u)= (1 + u ) , |∇ | of certain energies (area, elastic energy, etc.). A critical point is M an equilibrium configuration with respect to the given energy; the equilibrium condition is expressed mathematically via the for a > 1; these energies satisfy the Palais–Smale condition Euler–Lagrange equation. and, as a ® 1, they approximate F. The Sacks–Uhlenbeck A classical example is a geodesic on a Riemannian mani- paper constructed a sequence ua of critical points of Fa and fold and, in order to prove the existence of geodesics, it proves effective to consider the energy as a functional on the (infinite-dimensional) ‘space of curves’. -
Notices of the American Mathematical Society
Society c :s ~ CALENDAR OF AMS MEETINGS THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meet ings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many depart ments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for abstracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meet· ing announcement and the Jist of organizers of special sessions. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 779 August 18-22, 1980 Ann Arbor,