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  1. Program Group Representation Theory and Applications

    Organizers: Robert Guralnick (University of Southern California), Alexander Kleshchev (University of Oregon), Gunter Malle (Universität Kaiserslautern), Gabriel Navarro (University of Valencia), Julia Pevtsova (University of Washington), Raphael Rouquier (University of California, Los Angeles), LEAD Pham Tiep (Rutgers University)

    Group Representation Theory is a central area of Algebra, with important and deep connections to areas as varied as topology, algebraic geometry, number theory, Lie theory, homological algebra, and mathematical physics. Born more than a century ago, the area still abounds with basic problems and fundamental conjectures, some of which have been open for over five decades. Very recent breakthroughs have led to the hope that some of these conjectures can finally be settled. In turn, recent results in group representation theory have helped achieve substantial progress in a vast number of applications.

    The goal of the program is to investigate all these deep problems and the wealth of new results and directions, to obtain major progress in the area, and to explore further applications of group representation theory to other branches of mathematics.

    Updated on Jan 12, 2018 04:00 PM PST
  2. Program Enumerative Geometry Beyond Numbers

    Organizers: Mina Aganagic (University of California, Berkeley), Denis Auroux (University of California, Berkeley), Jim Bryan (University of British Columbia), LEAD Andrei Okounkov (Columbia University), Balazs Szendroi (University of Oxford)

    Traditional enumerative geometry asks certain questions to which the expected answer is a number: for instance, the number of lines incident with two points in the plane (1, Euclid), or the number of twisted cubic curves on a quintic threefold (317 206 375). It has however been recognized for some time that the numerics is often just the tip of the iceberg: a deeper exploration reveals interesting geometric, topological, representation-, or knot-theoretic structures. This semester-long program will be devoted to these hidden structures behind enumerative invariants, concentrating on the core fields where these questions start: algebraic and symplectic geometry.

    Updated on Jan 16, 2018 10:12 AM PST
  1. Program Summer Research for Women in Mathematics

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute)

    The purpose of the MSRI's program, Summer Research for Women in Mathematics, is to provide space and funds to groups of women mathematicians to work on a research project at MSRI. Research projects can arise from work initiated at a Women's Conference, or can be freestanding activities.

    Updated on Feb 23, 2018 03:43 PM PST
  2. Summer Graduate School The ∂-Problem in the Twenty-First Century

    Organizers: Debraj Chakrabarti (Central Michigan University), Jeffery McNeal (Ohio State University)

    This Summer Graduate School will introduce students to the modern theory of the  inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum

    Updated on Apr 20, 2018 02:48 PM PDT
  3. Summer Graduate School Séminaire de Mathématiques Supérieures 2018: Derived Geometry and Higher Categorical Structures in Geometry and Physics

    Organizers: Anton Alekseev (Université de Genève), Ruxandra Moraru (University of Waterloo), Chenchang Zhu (Universität Göttingen)

    Higher categorical structures and homotopy methods have made significant influence on geometry in recent years. This summer school is aimed at transferring these ideas and fundamental technical tools to the next generation of mathematicians.

    The summer school will focus on the following four topics:  higher categorical structures in geometry, derived geometry, factorization algebras, and their application in physics.  There will be eight to ten mini courses on these topics, including mini courses led by Chirs Brav, Kevin Costello, Jacob Lurie, and Ezra Getzler. The prerequisites will be kept at a minimum, however, a introductory courses in differential geometry, algebraic topology and abstract algebra are recommended.

    Updated on Jan 07, 2018 12:47 PM PST
  4. MSRI-UP MSRI-UP 2018: The Mathematics of Data Science

    Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), LEAD Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Sam Houston State University), David Uminsky (University of San Francisco), Suzanne Weekes (Worcester Polytechnic Institute)

    The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

    In 2018, MSRI-UP will focus on the core role of (linear) algebra in current research and application areas of Data Science ranging from unsupervised learning, clustering and networks, to algebraic signal processing and feature extraction, to the central role linear algebra plays in deep machine learning.  The research program will be led by Dr. David Uminsky, Associate Professor of Mathematics and Statistics at the University of San Francisco.

    Updated on Feb 06, 2018 09:19 AM PST
  5. Summer Graduate School Mathematical Analysis of Behavior

    Organizers: Ann Hermundstad (Janelia Research Campus, HHMI), Vivek Jayaraman (Janelia Research Campus, HHMI), Eva Kanso (University of Southern California), L. Mahadevan (Harvard University)
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    Explore Outstanding Phenomena in Animal Behavior

    Jointly hosted by Janelia and the Mathematical Sciences Research Institute (MSRI), this program will bring together 15-20 advanced PhD students with complementary expertise who are interested in working at the interface of mathematics and biology. Emphasis will be placed on linking behavior to neural dynamics and exploring the coupling between these processes and the natural sensory environment of the organism. The aim is to educate a new type of global scientist that will work collaboratively in tackling complex problems in cellular, circuit and behavioral biology by combining experimental and computational techniques with rigorous mathematics and physics.

    Updated on Feb 01, 2018 01:16 PM PST
  6. Summer Graduate School Derived Categories

    Organizers: Nicolas Addington (University of Oregon), LEAD Alexander Polishchuk (University of Oregon)

    The goal of the school is to give an introduction to basic techniques for working with derived categories, with an emphasis on the derived categories of coherent sheaves on algebraic varieties. A particular goal will be to understand Orlov’s equivalence relating the derived category of a projective hypersurface with matrix factorizations of the corresponding polynomial.

    Updated on Jul 20, 2017 12:29 PM PDT
  7. Summer Graduate School H-principle

    Organizers: Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)
    072 04 small
    The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

    This two week summer school will introduce graduate students to the theory of h-principles.  After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, and foliation theory.

    Updated on Nov 02, 2017 10:19 AM PDT
  8. Summer Graduate School IAS/PCMI 2018: Harmonic Analysis

    Organizers: Carlos Kenig (University of Chicago), Fanghua Lin (New York University, Courant Institute), Svitlana Mayboroda (University of Minnesota, Twin Cities), Tatiana Toro (University of Washington)

    Harmonic analysis is a central field of mathematics with a number of applications to geometry, partial differential equations, probability, and number theory, as well as physics, biology, and engineering. The Graduate Summer School will feature mini-courses in geometric measure theory, homogenization, localization, free boundary problems, and partial differential equations as they apply to questions in or draw techniques from harmonic analysis. The goal of the program is to bring together students and researchers at all levels interested in these areas to share exciting recent developments in these subjects, stimulate further interactions, and inspire the new generation to pursue research in harmonic analysis and its applications.

    Updated on Nov 08, 2017 11:32 AM PST
  9. Summer Graduate School Representations of High Dimensional Data

    Organizers: Blake Hunter (Claremont McKenna College), Deanna Needell (University of California, Los Angeles)
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    In today's world, data is exploding at a faster rate than computer architectures can handle. This summer school will introduce students to modern and innovative mathematical techniques that address this phenomenon. Hands-on topics will include data mining, compression, classification, topic modeling, large-scale stochastic optimization, and more.

    Updated on Apr 26, 2018 02:07 PM PDT
  10. Summer Graduate School From Symplectic Geometry to Chaos

    Organizers: Marcel Guardia (Universitat Politecnica de Catalunya), Vadim Kaloshin (University of Maryland), Leonid Polterovich (Tel Aviv University)

    The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.

    Updated on May 18, 2018 03:05 PM PDT
  11. Program Hamiltonian systems, from topology to applications through analysis

    Organizers: Rafael de la Llave (Georgia Institute of Technology), LEAD Albert Fathi (Georgia Institute of Technology; École Normale Supérieure de Lyon), Vadim Kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley), Philip Morrison (University of Texas at Austin), Tere Seara (Universitat Politècnica de Catalunya), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)

    The interdisciplinary nature of Hamiltonian systems is deeply ingrained in its history. Therefore the program will bring together the communities of mathematicians with the community of practitioners, mainly engineers, physicists, and theoretical chemists who use Hamiltonian systems daily. The program will cover not only the mathematical aspects of Hamiltonian systems but also their applications, mainly in space mechanics, physics and chemistry.

    The mathematical aspects comprise celestial mechanics, variational methods, relations with PDE, Arnold diffusion and computation. The applications concern celestial mechanics, astrodynamics, motion of satellites, plasma physics, accelerator physics, theoretical chemistry, and atomic physics.

    The goal of the program is to bring to the forefront both the theoretical aspects and the applications, by making available for applications the latest theoretical developments, and also by nurturing the theoretical mathematical aspects with new problems that come from concrete problems of applications.

    Updated on Jul 13, 2017 12:19 PM PDT
  12. Program Complementary Program 2018-19

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Jan 02, 2018 10:45 AM PST
  13. Workshop Connections for Women: Hamiltonian Systems, from topology to applications through analysis

    Organizers: Marie-Claude Arnaud (Université d'Avignon), LEAD Basak Gurel (University of Central Florida), Tere Seara (Universitat Politècnica de Catalunya)
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    Representing the orbits of the standard map for K = 1.2

    This workshop will feature lectures on a variety of topics in Hamiltonian dynamics given by leading researchers in the area. The talks will focus on recent developments in subjects closely related to the program such as Arnold diffusion, celestial mechanics, Hamilton-Jacobi equations, KAM methods, Aubry-Mather theory and symplectic topological techniques, and on applications. The workshop is open to all mathematicians in areas related to the program.

    Updated on May 09, 2018 10:09 AM PDT
  14. Workshop Introductory Workshop: Hamiltonian systems, from topology to applications through analysis

    Organizers: Marie-Claude Arnaud (Université d'Avignon), Wilfrid Gangbo (University of California, Los Angeles), LEAD Vadim Kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley)

    The introductory workshop will cover the large variety of topics of the semester: weak KAM theory, Mather theory, Hamilton-Jacobi equations, integrable systems and integrable planar billiards, instability formation for nearly integrable systems, celestial mechanics, billiards, spectral rigidity, Astrodynamics, motion of satellites, Plasma Physics, Accelerator Physics, Theoretical Chemistry, and Atomic Physics.

    The workshop will consist of approximately 18 lectures to introduce the main topics relevant to the semester. That will leave time for discussions and exchange between the participants.

    Updated on Sep 26, 2017 09:18 AM PDT
  15. Workshop Hot Topics: Shape and Structure of Materials

    Organizers: Myfanwy Evans (TU Berlin), LEAD Frank Lutz (TU Berlin), Dmitriy Morozov (Lawrence Berkeley National Laboratory), James Sethian (University of California, Berkeley), Ileana Streinu (Smith College)
    Msri lbnl pic 3
    Tangled honeycomb networks | and the Advanced Light Source at LBNL

    The fascinating and complicated microstructures of materials that are now visible through advanced imaging techniques challenge the frontiers of characterisation and understanding. At the same time, developments in modern geometric and topological techniques are beginning to illuminate important features of material structures, while the microstructures themselves and the analysis and prediction of their macroscopic properties are inspiring new directions in pure and applied mathematics. In a collaboration with the Lawrence Berkeley National Laboratory (LBNL), this workshop aims at intensifying the interaction of mathematicians with material scientists, physicists and chemists on the structural description and design of materials.

    Updated on May 01, 2018 01:55 PM PDT
  16. Workshop Hamiltonian systems, from topology to applications through analysis I

    Organizers: Alessandra Celletti (University of Rome Tor Vergata), Rafael de la Llave (Georgia Institute of Technology), Diego Del-Castillo-Negrete (Oak Ridge National Laboratory), Lawrence Evans (University of California, Berkeley), LEAD Philip Morrison (University of Texas at Austin), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)
    Web image
    Depiction of the standard nontwist map (courtesy of G.Miloshevich).

    This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis” and is a companion to the workshop next month (November 26-30).  Both workshops will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications.  A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.),  techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

    Updated on Nov 02, 2017 09:56 AM PDT
  17. Workshop 2018 Modern Math Workshop

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), LEAD Elvan Ceyhan (SAMSI - Statistical and Applied Mathematical Sciences Institute), Leslie McClure (SAMSI - Statistical and Applied Mathematical Sciences Institute), Christian Ratsch (University of California, Los Angeles; Institute of Pure and Applied Mathematics (IPAM)), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))

    The Mathematical Sciences Diversity Initiative holds a Modern Math Workshop (MMW) prior to the SACNAS National Conference each year. The 2018 MMW will be hosted by SAMSI at the Henry B. Gonzalez Convention Center, San Antonio, Texas on October 10th and 11th, 2018. This workshop is intended to encourage undergraduates, graduate students and recent PhDs from underrepresented minority groups to pursue careers in the mathematical sciences and build research and mentoring networks. The Modern Math Workshop is a pre-conference event at the SACNAS National Conference. The MMW includes a keynote lecture, mini-courses, research talks, a question and answer session and a reception.

    Updated on Mar 15, 2018 12:33 PM PDT
  18. Workshop 2018 Blackwell-Tapia Conference and Award Banquet

    The NSF Mathematical Sciences Institutes Diversity Committee hosts the 2018 Blackwell-Tapia Conference and Awards Ceremony. This is the ninth conference since 2000, held every other year, with the location rotating among NSF Mathematics Institutes. The conference and prize honors David Blackwell, the first African-American member of the National Academy of Science, and Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who inspired a generation of African-American, Native American and Latino/Latina students to pursue careers in mathematics. The Blackwell-Tapia Prize recognizes a mathematician who has contributed significantly to research in his or her area of expertise, and who has served as a role model for mathematical scientists and students from underrepresented minority groups, or has contributed in other significant ways to addressing the problem of underrepresentation of minorities in math.

    The 2018 recipient of the Blackwell-Tapia Prize is Dr. Ronald E. Mickens, the Distinguished Fuller E. Callaway Professor in the Department of Physics at Clark Atlanta University.

    The conference will include scientific talks, poster presentations, panel discussions, ample opportunities for networking, and the awarding of the Blackwell-Tapia Prize. Participants are invited from all career stages and will represent institutions of all sizes across the country, including Puerto Rico.

    Updated on May 08, 2018 12:46 PM PDT
  19. Workshop Hamiltonian systems, from topology to applications through analysis II

    Organizers: Alessandra Celletti (University of Rome Tor Vergata), Rafael de la Llave (Georgia Institute of Technology), Diego Del-Castillo-Negrete (Oak Ridge National Laboratory), Lawrence Evans (University of California, Berkeley), Philip Morrison (University of Texas at Austin), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)
    Web image
    An invariant set inhibiting transport in a two degree-of-freedom Hamiltonian system (courtesy J. D. Szezech)

    This is a main workshop of the program “Hamiltonian systems, from topology to applications through analysis.”  It  will feature current developments pertaining to finite and infinite-dimensional Hamiltonian systems, with a mix of rigorous theory and applications.  A broad range of topics will be included, e.g., existence of and transport about invariant sets (Arnold diffusion, KAM, etc.),  techniques for projection/reduction of infinite to finite systems, and the role of topological invariants in applications.

    Updated on Nov 02, 2017 09:58 AM PDT
  20. Program Derived Algebraic Geometry

    Organizers: Julie Bergner (University of Virginia), LEAD Bhargav Bhatt (University of Michigan), Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Gabriele Vezzosi (Università di Firenze)

    Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating non-generic geometric situations (such as non-transverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the “moving” lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.

    Updated on Nov 02, 2016 04:30 PM PDT
  21. Program Birational Geometry and Moduli Spaces

    Organizers: Antonella Grassi (University of Pennsylvania), LEAD Christopher Hacon (University of Utah), Sándor Kovács (University of Washington), Mircea Mustaţă (University of Michigan), Martin Olsson (University of California, Berkeley)

    Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to  bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research.
     
    This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of Calabi-Yau Varieties in Geometry, Arithmetic and the Physics of String Theory

    Updated on Jan 31, 2017 07:46 PM PST
  22. Workshop Connections for Women: Derived Algebraic Geometry, Birational Geometry and Moduli Spaces

    Organizers: Julie Bergner (University of Virginia), LEAD Antonella Grassi (University of Pennsylvania), Bianca Viray (University of Washington), Kirsten Wickelgren (Georgia Institute of Technology)

    This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.

    Updated on Jul 30, 2017 11:34 PM PDT
  23. Workshop Introductory Workshop: Derived Algebraic Geometry and Birational Geometry and Moduli Spaces

    Organizers: Julie Bergner (University of Virginia), Bhargav Bhatt (University of Michigan), Christopher Hacon (University of Utah), LEAD Mircea Mustaţă (University of Michigan), Gabriele Vezzosi (Università di Firenze)

    The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository mini-courses and 7 separate lectures, each given by top experts in the field. 

    The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.
     

    Updated on Mar 06, 2018 03:29 PM PST
  24. Workshop Derived algebraic geometry and its applications

    Organizers: Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), LEAD Nikita Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Brooke Shipley (University of Illinois at Chicago)

    This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.    

    Updated on Apr 25, 2018 08:53 AM PDT
  25. Workshop Recent Progress in Moduli Theory

    Organizers: Lucia Caporaso (University of Rome, Roma 3), LEAD Sándor Kovács (University of Washington), Martin Olsson (University of California, Berkeley)
    Moduli b

    This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines. 

    Updated on Nov 02, 2017 09:59 AM PDT
  26. Summer Graduate School Random and arithmetic structures in topology

    Organizers: LEAD Alex Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science)
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    The study of locally symmetric manifolds, such as closed hyperbolic manifolds, involves geometry of the corresponding symmetric space, topology of towers of its finite covers, and number-theoretic aspects that are relevant to possible constructions.
    The workshop will provide an introduction to these and closely related topics such as lattices, invariant random subgroups, and homological methods.

    Updated on Apr 20, 2018 03:02 PM PDT
  27. Summer Graduate School Séminaire de Mathématiques Supérieures 2019: Current trends in Symplectic Topology

    Organizers: Octav Cornea (Université de Montréal), Yakov Eliashberg (Stanford University), Michael Hutchings (University of California, Berkeley), Egor Shelukhin (Université de Montréal)

    Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and four-dimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject. 

    Updated on Feb 21, 2018 11:27 AM PST
  28. Summer Graduate School Polynomial Method

    Organizers: Adam Sheffer (California Institute of Technology), LEAD Joshua Zahl (University of British Columbia)
    Twolines3d
    from distinct distances in the plane to line incidences in R^3

    In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments

    Updated on Apr 20, 2018 02:49 PM PDT
  29. Summer Graduate School Recent topics on well-posedness and stability of incompressible fluid and related topics

    Organizers: LEAD Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)
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    Fluid-flow stream function color-coded by vorticity in 3D flat torus calculated by K. Nakai (The University of Tokyo)

    The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

    Updated on May 02, 2018 10:57 AM PDT
  30. Summer Graduate School Toric Varieties in Taipei

    Organizers: David Cox (University of Massachusetts, Amherst), Henry Schenck
    Firstchoice cropped
    This simplicial fan in 3-dimensional space

    Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

    Updated on Apr 20, 2018 02:46 PM PDT
  31. Program Holomorphic Differentials in Mathematics and Physics

    Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at Urbana-Champaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg), Anton Zorich (Institut de Mathematiques de Jussieu)
    Quadmesh2
    Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

    Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

    It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our program will be of interest to those working in many different elds, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).

    Updated on Apr 10, 2018 10:50 AM PDT
  32. Program Microlocal Analysis

    Organizers: Pierre Albin (University of Illinois at Urbana-Champaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (École Normale Supérieure), LEAD Andras Vasy (Stanford University)
    315 image1

    Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This program will bring together researchers from various parts of the field to facilitate the transfer of ideas, and will also provide a comprehensive introduction to the field for postdocs and graduate students.

    Updated on Apr 13, 2018 11:42 AM PDT
  33. Workshop Connections for Women: Holomorphic Differentials in Mathematics and Physics

    Organizers: Laura Fredrickson (Stanford University), Lotte Hollands (Heriot-Watt University, Riccarton Campus), LEAD Qiongling Li (California Institute of Technology; Aarhus University), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg), Grace Work (University of Illinois at Urbana-Champaign)
    Quadmesh2
    Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

    This two-day workshop will consist of various talks given by prominent female mathematicians on topics of new developments in the role of holomorphic differentials on Riemann surfaces. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  

    This workshop is open to all mathematicians.

    Updated on May 10, 2018 09:01 AM PDT
  34. Workshop Introductory Workshop: Holomorphic Differentials in Mathematics and Physics

    Organizers: LEAD Jayadev Athreya (University of Washington), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)
    Quadmesh2
    Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

    Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.

    Updated on Nov 21, 2017 04:24 PM PST
  35. Workshop Connections for Women: Microlocal Analysis

    Organizers: Tanya Christiansen (University of Missouri), LEAD Raluca Felea (Rochester Institute of Technology)
    315 image1

    This workshop will provide a gentle introduction to a selection of applications of microlocal analysis.  These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems,  quantum chaos and relativity.  The workshop will also provide  a panel discussion, a poster session and an introduction/research session. 

    This workshop is open to all mathematicians.

    Updated on Jan 11, 2018 12:35 PM PST
  36. Workshop Introductory Workshop: Microlocal Analysis

    Organizers: Pierre Albin (University of Illinois at Urbana-Champaign), LEAD Raluca Felea (Rochester Institute of Technology), Andras Vasy (Stanford University)
    315 image1

    Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.

    Updated on Jan 11, 2018 01:28 PM PST
  37. Workshop Recent developments in microlocal analysis

    Organizers: LEAD Pierre Albin (University of Illinois at Urbana-Champaign), Colin Guillarmou (École Normale Supérieure), Andras Vasy (Stanford University)
    315 image1

    Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas. 

    Updated on May 08, 2018 03:21 PM PDT
  38. Workshop Holomorphic Differentials in Mathematics and Physics

    Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at Urbana-Champaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (University of Texas, Austin), Anton Zorich (Institut de Mathematiques de Jussieu)
    Sn image
    An example of a spectral network associated to the group SL(4).

    Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

    It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).

    Updated on May 14, 2018 02:00 PM PDT
  39. Program Quantum Symmetries

    Organizers: Vaughan Jones (Vanderbilt University), LEAD Scott Morrison (Australian National University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), Eric Rowell (Texas A & M University), LEAD Noah Snyder (Indiana University), Chelsea Walton (University of Illinois at Urbana-Champaign)
    Program picture
    The study of tensor categories involves the interplay of representation theory, combinatorics, number theory, and low dimensional topology (from a string diagram calculation, describing the 3-dimensional bordism 2-category [arXiv:1411.0945]).

    Symmetry, as formalized by group theory, is ubiquitous across mathematics and science. Classical examples include point groups in crystallography, Noether's theorem relating differentiable symmetries and conserved quantities, and the classification of fundamental particles according to irreducible representations of the Poincaré group and the internal symmetry groups of the standard model. However, in some quantum settings, the notion of a group is no longer enough to capture all symmetries. Important motivating examples include Galois-like symmetries of von Neumann algebras, anyonic particles in condensed matter physics, and deformations of universal enveloping algebras. The language of tensor categories provides a unified framework to discuss these notions of quantum symmetry.

    Updated on Mar 22, 2018 11:21 AM PDT
  40. Program Higher Categories and Categorification

    Organizers: David Ayala (Montana State University), Clark Barwick (Massachusetts Institute of Technology), David Nadler (University of California, Berkeley), LEAD Emily Riehl (Johns Hopkins University), Marcy Robertson (University of Melbourne), Peter Teichner (Max-Planck-Institut für Mathematik), Dominic Verity (Macquarie University)
    Higher adjunction axiom
    swallowtail identity

    Though many of the ideas in higher category theory find their origins in homotopy theory — for instance as expressed by Grothendieck’s “homotopy hypothesis” — the subject today interacts with a broad spectrum of areas of mathematical research. Unforeseen descent, or local-to-global formulas, for familiar objects can be articulated in terms of higher invertible morphisms. Compatible associative deformations of a sequence of maps of spaces, or derived schemes, can putatively be represented by higher categories, as Koszul duality for E_n-algebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as K-theory. Manifold theory is natively connected to higher category theory and adjunction data, a connection that is most famously articulated by the recently proven Cobordism Hypothesis.
    In parallel, the idea of "categorification'' is playing an increasing role in algebraic geometry, representation theory, mathematical physics, and manifold theory, and higher categorical structures also appear in the very foundations of mathematics in the form of univalent foundations and homotopy type theory. A central mission of this semester will be to mitigate the exorbitantly high "cost of admission'' for mathematicians in other areas of research who aim to apply higher categorical technology and to create opportunities for potent collaborations between mathematicians from these different fields and experts from within higher category theory.

    Updated on Apr 10, 2018 11:13 AM PDT
  41. Workshop Connections for Women: Quantum Symmetries

    Organizers: Emily Peters (Loyola University), LEAD Chelsea Walton (University of Illinois at Urbana-Champaign)
    Cfw image
    Photo by drmakete lab on Unsplash

    This workshop will feature several talks by experts, along with numerous 5-minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.

    Updated on Mar 26, 2018 12:18 PM PDT
  42. Workshop Introductory Workshop: Quantum Symmetries

    Organizers: Vaughan Jones (Vanderbilt University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), LEAD Noah Snyder (Indiana University)
    Jellyfish
    Jellyfish floating to the surface, as in the evaluation algorithm for certain planar algebras.

    This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter.  These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.

    Updated on Apr 09, 2018 02:20 PM PDT
  43. Program Random and Arithmetic Structures in Topology

    Organizers: Nicolas Bergeron (Université de Paris VI (Pierre et Marie Curie)), Jeffrey Brock (Brown University), Alex Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science), Ursula Hamenstädt (Rheinische Friedrich-Wilhelms-Universität Bonn), Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)), LEAD Alan Reid (Rice University)
    Msri image

    The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. The program will focus on invariants in topology, geometry, and the dynamics of group actions linked to random constructions.

    Updated on Nov 16, 2017 02:50 PM PST
  44. Program Decidability, definability and computability in number theory

    Organizers: Valentina Harizanov (George Washington University), Moshe Jarden (Tel-Aviv University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY), Jonathan Pila (University of Oxford), LEAD Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)

    This program is focused on the two-way interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.

    Updated on May 09, 2018 10:50 AM PDT
  45. Program Mathematical problems in fluid dynamics

    Organizers: Thomas Alazard (École Normale Supérieure; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Université Paris-Est Créteil Val-de-Marne; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)
    Barcuta

    Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.

    The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the well-known Euler equations for inviscid fluids, and the Navier-Stokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.

    Updated on Jan 24, 2018 10:14 AM PST

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