# Mathematical Sciences Research Institute

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1. # SeminarIntroduction to the middle K-theory of group rings and their relevance in topology, Part One: Introductory Talk

Created on Apr 14, 2014 11:17 AM PDT
2. # SeminarFinite Structures Seminar

Created on Apr 09, 2014 03:24 PM PDT
3. # SeminarBerkeley Model Theory Seminar: Pseudo Real Closed fields and NTP2

Updated on Apr 11, 2014 02:01 PM PDT
4. # SeminarBerkeley Model Theory Seminar: Higher amalgamation and polygroupoids.

Updated on Apr 11, 2014 02:06 PM PDT
5. # SeminarAlgebraic K- and L-theory of groups rings and their applications to topology and geometry, Part II: Main Talk

Created on Apr 14, 2014 11:19 AM PDT
6. # SeminarAT Research Seminar Pre-Talk: Module structures on Goodwillie derivatives

Updated on Apr 14, 2014 10:50 AM PDT
7. # SeminarAT Research Seminar: The classification of Taylor towers for functors from based spaces to spectra

Updated on Apr 14, 2014 11:20 AM PDT
8. # SeminarUnlikely intersections in semi-abelian schemes.

Created on Apr 11, 2014 02:11 PM PDT
9. # SeminarMSRI/Evans Lecture: A journey through motivic integration

Updated on Apr 11, 2014 03:43 PM PDT
10. # SeminarAlegbraic Topology Open Problems / Work in Progress Seminar

Created on Jan 30, 2014 08:24 AM PST
11. # SeminarConformal Field Theory

Created on Feb 19, 2014 08:18 AM PST
12. # SeminarModel Theory Day-Long Seminar

Created on Mar 04, 2014 02:57 PM PST
13. # SeminarEisenbud Seminar: Algebraic Geometry and Commutative Algebra

Created on Feb 10, 2014 08:42 AM PST
14. # SeminarAT Research Seminar Pre-Talk

Updated on Mar 06, 2014 02:34 PM PST
15. # SeminarAT Research Seminar

Created on Feb 14, 2014 08:55 AM PST
16. # SeminarMT Postdoc Seminar

Updated on Apr 15, 2014 02:45 PM PDT
17. # SeminarAT Postdoc Seminar

Created on Feb 07, 2014 09:36 AM PST
18. # SeminarConformal Field Theory

Created on Feb 19, 2014 08:18 AM PST
19. # SeminarAlegbraic Topology Open Problems / Work in Progress Seminar

Created on Jan 30, 2014 08:23 AM PST
20. # SeminarMSRI/Evans Lecture: The (un)reasonable effectiveness of model theory in mathematics

Updated on Apr 15, 2014 11:58 AM PDT
21. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Updated on Mar 24, 2014 11:20 AM PDT
22. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Created on Feb 04, 2014 09:06 AM PST
23. # SeminarEisenbud Seminar: Algebraic Geometry and Commutative Algebra

Created on Feb 10, 2014 08:42 AM PST
24. # SeminarAT Research Seminar

Created on Feb 14, 2014 08:56 AM PST
25. # SeminarAT Research Seminar Pre-Talk

Updated on Mar 06, 2014 02:41 PM PST
26. # SeminarMT Postdoc Seminar

Created on Feb 06, 2014 09:23 AM PST
27. # SeminarAT Postdoc Seminar

Created on Feb 07, 2014 09:36 AM PST
28. # SeminarConformal Field Theory

Created on Feb 19, 2014 08:18 AM PST
29. # SeminarAlegbraic Topology Open Problems / Work in Progress Seminar

Created on Jan 30, 2014 08:23 AM PST
30. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Updated on Mar 24, 2014 11:23 AM PDT
31. # SeminarEisenbud Seminar: Algebraic Geometry and Commutative Algebra

Created on Feb 10, 2014 08:43 AM PST
32. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Created on Feb 04, 2014 09:06 AM PST
33. # SeminarAT Research Seminar Pre-Talk

Updated on Mar 06, 2014 02:44 PM PST
34. # SeminarAT Research Seminar

Created on Feb 14, 2014 08:57 AM PST
35. # SeminarMT Postdoc Seminar

Created on Feb 06, 2014 09:23 AM PST
36. # SeminarAT Postdoc Seminar

Created on Feb 07, 2014 09:37 AM PST
37. # SeminarAT Seminar

Created on Apr 14, 2014 09:17 AM PDT
38. # SeminarConformal Field Theory

Created on Feb 19, 2014 08:23 AM PST
39. # SeminarAlegbraic Topology Open Problems / Work in Progress Seminar

Created on Jan 30, 2014 08:22 AM PST
40. # WorkshopModel Theory in Geometry and Arithmetic

Organizers: Raf Cluckers (Université de Lille I (Sciences et Techniques de Lille Flandres Artois)), LEAD Jonathan Pila (University of Oxford), Thomas Scanlon (University of California, Berkeley)

The workshop will feature talks in a range of topics where model theory interacts with other parts of mathematics, especially number theory and arithmetic geometry, including: motivic integration, algebraic dynamics, diophantine geometry, and valued fields.

Updated on Apr 03, 2014 09:21 AM PDT
41. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Updated on Mar 24, 2014 11:31 AM PDT
42. # SeminarEisenbud Seminar: Algebraic Geometry and Commutative Algebra

Created on Feb 10, 2014 08:43 AM PST
43. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Created on Feb 04, 2014 09:05 AM PST
44. # SeminarAT Research Seminar Pre-Talk

Updated on Mar 11, 2014 03:18 PM PDT
45. # SeminarAT Research Seminar

Created on Feb 14, 2014 08:57 AM PST
46. # SeminarConformal Field Theory

Created on Feb 19, 2014 08:24 AM PST
47. # SeminarAlegbraic Topology Open Problems / Work in Progress Seminar

Created on Jan 30, 2014 08:20 AM PST
48. # SeminarEisenbud Seminar: Algebraic Geometry and Commutative Algebra

Created on Feb 10, 2014 08:44 AM PST
49. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Updated on Mar 24, 2014 11:32 AM PDT
50. # SeminarModel Theory, Arithmetic Geometry and Number Theory Seminar

Created on Feb 04, 2014 08:54 AM PST
51. # SeminarAT Research Seminar

Created on Feb 14, 2014 08:58 AM PST
52. # SeminarAT Research Seminar Pre-Talk

Updated on Mar 06, 2014 02:51 PM PST
53. # Summer Graduate SchoolDispersive Partial Differential Equations

Organizers: Natasa Pavlovic (University of Texas), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)

The purpose of the workshop is to introduce graduate students to the recent developments in the area of dispersive partial di erential equations (PDE).

Dispersive equations have received a great deal of attention from mathematicians because of their applications to nonlinear optics, water wave theory and plasma physics. We will outline the basic tools of the theory that were developed with the help of multi-linear Harmonic Analysis techniques. The exposition will be as self-contained as possible.

Updated on Oct 17, 2013 03:37 PM PDT
54. # MSRI-UPMSRI-UP 2014: Arithmetic Aspects of Elementary Functions

Organizers: Duane Cooper (Morehouse College), Ricardo Cortez (Tulane University), LEAD Herbert Medina (Loyola Marymount University), Ivelisse M. Rubio (University of Puerto Rico), Suzanne Weekes (Worcester Polytechnic Institute)

The MSRI-UP summer program is designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply and the program cannot accept foreign students regardless of funding. The academic portion of the 2014 program will be led by Dr. Victor Moll from Tulane University.

Updated on Jan 07, 2014 01:54 PM PST
55. # Summer Graduate SchoolSeminaire de Mathematiques Superieures 2014: Counting Arithmetic Objects

Organizers: Henri Darmon (McGill University), Andrew Granville (University of Montreal), Benedict Gross (Harvard University)

Updated on Jan 16, 2014 08:48 AM PST
56. # Summer Graduate SchoolIAS/PCMI 2014: Mathematics and Materials

Organizers: Mark Bowick (Syracuse University), David Kinderlehrer (Carnegie-Mellon University), Govind Menon (Brown University), Charles Radin (University of Texas)

The program in 2014 will bring together a diverse group of mathematicians and scientists with interests in fundamental questions in mathematics and the behavior of materials. The meeting addresses several themes including computational investigations of material properties, the emergence of long- range order in materials and self-assembly, the geometry of soft condensed matter and the calculus of variations, phase transitions and statistical mechanics. The program will cover several topics in discrete and differential geometry that are motivated by questions in materials science. Many central topics, such as the geometry of packings, problems in the calculus of variations and phase transitions, will be discussed from the complementary points of view of mathematicians and physicists.

Updated on Mar 06, 2014 12:12 PM PST
57. # Summer Graduate SchoolAlgebraic Topology

Modern algebraic topology is a broad and vibrant field which has seen recent progress on classical problems as well as exciting new interactions with applied mathematics. This summer school will consist of a series of lecture by experts on major research directions, including several lectures on applied algebraic topology. Participants will also have the opportunity to have guided interaction with the seminal texts in the field, reading and speaking about the foundational papers.

Updated on Jan 16, 2014 08:46 AM PST
58. # Summer Graduate SchoolStochastic Partial Differential Equations

Organizers: Yuri Bakhtin (New York University, Courant Institute), LEAD Ivan Corwin (Columbia University), James Nolen (Duke University)

Stochastic Partial Differential Equations (SPDEs) serve as fundamental models of physical systems subject to random inputs, interactions or environments. It is a particular challenge to develop tools to construct solutions, prove robustness of approximation schemes, and study properties like ergodicity and fluctuation statistics for a wide variety of SPDEs.

The purpose of this two week workshop is to educate graduate students on the state-of-the-art methods and results in SPDEs. The three courses which will be run simultaneously will highlight different (though related) aspects of this area including (1) Fluctuation theory of PDEs with random coefficients (2) Ergodic theory of SPDEs and (3) Exact solvability of SPDEs

Updated on Nov 19, 2013 07:03 PM PST
59. # Summer Graduate SchoolGeometry and Analysis

Organizers: Hans-Joachim Hein (Imperial College, London), LEAD Aaron Naber (Massachusetts Institute of Technology)

Geometric and complex analysis is the application of tools from analysis to study questions from geometry and topology. This two week summer course will provide graduate students with the necessary background to begin studies in the area. The first week will consist of introductory courses on geometric analysis, complex analysis, and Riemann surfaces. The second week will consist of more advanced courses on the regularity theory of Einstein manifolds, Kahler-Einstein manifolds, and the analysis of Riemann surfaces.

Updated on Oct 18, 2013 08:32 AM PDT
60. # ProgramNew Geometric Methods in Number Theory and Automorphic Forms

Organizers: Pierre Colmez (L'Institut de Mathématiques de Jussieu), LEAD Wee Teck Gan (National University of Singapore), Michael Harris (Institut de Mathematiques de Jussieu), Elena Mantovan (California Institute of Technology), Ariane Mezard (Institut de Mathématiques de Jussieu), Akshay Venkatesh (Stanford University)

The branches of number theory most directly related to the arithmetic of automorphic forms have seen much recent progress, with the resolution of many longstanding conjectures. These breakthroughs have largely been achieved by the discovery of new geometric techniques and insights. The goal of this program is to highlight new geometric structures and new questions of a geometric nature which seem most crucial for further development. In particular, the program will emphasize geometric questions arising in the study of Shimura varieties, the p-adic Langlands program, and periods of automorphic forms.

Updated on Oct 11, 2013 02:02 PM PDT
61. # ProgramComplementary Program (2014-15)

Updated on Feb 27, 2014 09:09 AM PST
62. # WorkshopConnections for Women: New Geometric Methods in Number Theory and Automorphic Forms

Organizers: Wen-Ch'ing Li (Pennsylvania State University), LEAD Elena Mantovan (California Institute of Technology), Sophie Morel (Princeton University), Ramdorai Sujatha (University of British Columbia)

This 2-day workshop will showcase the contributions of female mathematicians to the three main themes of the associated MSRI program: Shimura varieties, p-adic automorphic forms, periods and L-functions. It will bring together women who are working in these areas in all stages of their careers, featuring lectures by both established leaders and emerging researchers. In addition, there will be a poster session open to all participants and an informal panel discussion on career issues.

Updated on Mar 17, 2014 09:50 AM PDT
63. # ProgramGeometric Representation Theory

Organizers: LEAD David Ben-Zvi (University of Texas), Ngô Bảo Châu (University of Chicago), Thomas Haines (University of Maryland), Florian Herzig (University of Toronto), Kevin McGerty (University of Oxford), David Nadler (University of California, Berkeley), Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn), Eva Viehmann (TU München)

The fundamental aims of geometric representation theory are to uncover the deeper geometric and categorical structures underlying the familiar objects of representation theory and harmonic analysis, and to apply the resulting insights to the resolution of classical problems. One of the main sources of inspiration for the field is the Langlands philosophy, a vast nonabelian generalization of the Fourier transform of classical harmonic analysis, which serves as a visionary roadmap for the subject and places it at the heart of number theory. A primary goal of the proposed MSRI program is to explore the potential impact of geometric methods and ideas in the Langlands program by bringing together researchers working in the diverse areas impacted by the Langlands philosophy, with a particular emphasis on representation theory over local fields.

Another focus comes from theoretical physics, where new perspectives on the central objects of geometric representation theory arise in the study supersymmetric gauge theory, integrable systems and topological string theory. The impact of these ideas is only beginning to be absorbed and the program will provide a forum for their dissemination and development.

Updated on Aug 12, 2013 03:02 PM PDT
64. # WorkshopIntroductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms

Organizers: Laurent Berger (École Normale Supérieure de Lyon), Ariane Mezard (Institut de Mathématiques de Jussieu), LEAD Akshay Venkatesh (Stanford University), Shou-Wu Zhang (Princeton University)

The goal of this workshop is to give a practical introduction to some of the main topics and techniques related to the August-December 2014 MSRI program, "New geometric methods in number theory and automorphic forms."   The workshop is aimed at graduate students and interested researchers in number theory or related fields.

There will be  lecture series on periods of automorphic forms, Shimura varieties, and representations of p-adic groups,as well as more advanced topics, including p-adic Hodge theory and the cohomology of arithmetic groups.

Updated on Mar 18, 2014 01:21 PM PDT
65. # WorkshopConnections for Women: Geometric Representation Theory

Organizers: LEAD Monica Vazirani (University of California, Davis), Eva Viehmann (TU München)

Within the broad range of geometric representation theory the Connections Workshop will focus on three research topics in which we expect particularly striking new developments within the next few years:
* Categorical and geometric structures in representation theory and Lie superalgebras
* Geometric construction of representations via Shimura varieties and related moduli spaces
* Hall algebras and representations

The workshop will bring together researchers from these different topics within geometric representation theory and will thus facilitate a successful start of the semester program. It will give junior researchers from each of these parts of geometric representation theory a broader picture of possible applications and of new developments, and will establish a closer contact between junior and senior researchers.
This workshop is aimed at encouraging and increasing the active participation of women and members of under-represented groups in the MSRI program.

Updated on Feb 07, 2014 08:03 PM PST
66. # WorkshopIntroductory Workshop: Geometric Representation Theory

Organizers: David Ben-Zvi (University of Texas), Kevin McGerty (University of Oxford)

Geometric Representation Theory is a very active field, at the center of recent advances in Number Theory and Theoretical Physics. The principal goal of the Introductory Workshop will be to provide a gateway for graduate students and new post-docs to the rich and exciting, but potentially daunting, world of geometric representation theory. The aim is to explore some of the fundamental tools and ideas needed to work in the subject, helping build a cohort of young researchers versed in the geometric and physical sides of the Langlands philosophy.

Updated on Feb 04, 2014 08:42 AM PST
67. # WorkshopCategorical Structures in Harmonic Analysis

Organizers: Thomas Haines (University of Maryland), Florian Herzig (University of Toronto), LEAD David Nadler (University of California, Berkeley)

The workshop will focus on the role of categorical structures in number theory and harmonic analysis, with an emphasis on the setting of the Langlands program. Celebrated examples of this theme range from Lusztig's character sheaves to Ngo's proof of the Fundamental Lemma. The workshop will be a forum for researchers from a diverse collection of fields to compare problems and strategies for solutions.

Updated on Feb 07, 2014 06:38 PM PST
68. # WorkshopAutomorphic forms, Shimura varieties, Galois representations and L-functions

Organizers: LEAD Pierre Colmez (L'Institut de Mathématiques de Jussieu), Stephen Kudla (University of Toronto), Elena Mantovan (California Institute of Technology), Ariane Mezard (Institut de Mathématiques de Jussieu), Richard Taylor (Institute for Advanced Study)

L-functions attached to Galois representations coming from algebraic geometry contain subtle arithmetic information (conjectures of Birch and Swinnerton-Dyer, Deligne, Beilinson, Bloch and Kato, Fontaine and Perrin-Riou). Langlands has predicted the existence of a correspondence relating these L-functions to L-functions of automorphic forms which are much better understood. The workshop will focus on recent developments related to Langlands correspondence (construction of Galois representations attached to automorphic forms via the cohomology of Shimura varieties, modularity of Galois representations...) and arithmetic of special values of L-functions.

It will be dedicated to Michael Harris as a tribute to his enormous influence on the themes of the workshop.

Updated on Jan 28, 2014 07:05 PM PST
69. # ProgramDynamics on Moduli Spaces of Geometric Structures

Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), François Labourie (Université Paris-Sud (Orsay)), LEAD Howard Masur (University of Chicago), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)

The program will focus on the deformation theory of geometric structures on manifolds, and the resulting geometry and dynamics. This subject is formally a subfield of differential geometry and topology, with a heavy infusion of Lie theory. Its richness stems from close relations to dynamical systems, algebraic geometry, representation theory, Lie theory, partial differential equations, number theory, and complex analysis.

Updated on Jul 29, 2013 03:58 PM PDT
70. # WorkshopConnections for Women: Dynamics on Moduli Spaces of Geometric Structures

Organizers: Virginie Charette (University of Sherbrooke), Fanny Kassel (Université de Lille I (Sciences et Techniques de Lille Flandres Artois)), Karin Melnick (University of Maryland), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)

This two-day workshop will consist of short courses given by prominent female mathematicians in the field.  These introductory courses will be appropriate for graduate students, post-docs, and researchers in areas related to the program.  The workshop will also include a panel discussion featuring successful women at various stages in their mathematical careers.

Updated on Jan 21, 2014 08:10 PM PST
71. # ProgramGeometric and Arithmetic Aspects of Homogeneous Dynamics

Organizers: LEAD Dmitry Kleinbock (Brandeis University), Elon Lindenstrauss (Hebrew University), Hee Oh (Yale University), Jean-François Quint (Université de Paris XIII (Paris-Nord)), Alireza Salehi Golsefidy (University of California, San Diego)

Homogeneous dynamics is the study of asymptotic properties of the action of subgroups of Lie groups on their homogeneous spaces. This includes many classical examples of dynamical systems, such as linear Anosov diffeomorphisms of tori and geodesic flows on negatively curved manifolds. This topic is related to many branches of mathematics, in particular, number theory and geometry. Some directions to be explored in this program include: measure rigidity of multidimensional diagonal groups; effectivization, sparse equidistribution and sieving; random walks, stationary measures and stiff actions; ergodic theory of thin groups; measure classification in positive characteristic. It is a companion program to “Dynamics on moduli spaces of geometric structures”.

Updated on Oct 11, 2013 02:07 PM PDT
72. # WorkshopIntroductory Workshop: Dynamics on Moduli Spaces of Geometric

Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), Ursula Hamenstaedt (Universität Bonn), Alessandra Iozzi (ETH Zürich)

The deformation theory of geometric structures on manifolds  is a subfield of differential geometry and topology, with a heavy infusion of Lie theory. Its richness stems from close relations to dynamical systems, algebraic geometry, representation theory, Lie theory, partial differential equations, number theory, and complex analysis.

The introductory workshop will serve  as an overview to the  program.   It aims to familiarize graduate students, post-docs, and other researchers to the major topics of the program. There will be a number of short courses.

Updated on Jan 28, 2014 05:57 PM PST
73. # WorkshopConnections for Women: Geometric and Arithmetic Aspects of Homogeneous Dynamics

Organizers: Elon Lindenstrauss (Hebrew University), Hee Oh (Yale University)

Updated on Jan 21, 2014 08:47 PM PST
74. # WorkshopIntroductory Workshop: Geometric and Arithmetic Aspects of Homogeneous Dynamics

Organizers: Manfred Einsiedler (ETH Zürich), Jean-François Quint (Université de Paris XIII (Paris-Nord)), Barbara Schapira (Université de Picardie (Jules Verne))

Updated on Jan 21, 2014 08:52 PM PST
75. # WorkshopDynamics on Moduli Spaces

Organizers: Markus Burger (ETH Zürich), David Dumas (University of Illinois at Chicago), Olivier Guichard (Université de Strasbourg I (Louis Pasteur)), François Labourie (Université Paris-Sud (Orsay)), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg)

The Research Workshop of the Dynamics on moduli spaces of geometric structures'' will concentrate on some of the following general interrelated themes:

(1) Geometric structures on the spaces of geometric structures which extend and generalize classical constructions on Teichmüller spaces, such as the Weil-Petersoon metric, the pressure metric, the Teichmüller metric and its geodesic flow, Fenchel-Nielsen coordinates, Fock-Goncharov Thurson-Penner coordinates, and the symplectic and Poisson  geometries

(2) Relations with harmonic maps, Riemann surfaces, complex geometry:  specifically Higgs  bundles, holomorphic differentials (quadratic, cubic, etc.) as parameters  for representations  of the fundamental group, hyperkähler and complex symplectic geometry of  moduli spaces,   lifts of Teichmüller geodesic flows to flat bundles of character varieties

(3) Asymptotic properties of higher Teichmüller spaces, including generalized measured geodesic laminations, Culler-Morgan-Shalen asymptotics of character varieties, degenerations of geometric structures and discrete subgroups

(4) Actions of mapping class groups and outer automorphism groups,  properness criteria for Anosov representations and their generalizations,  properness criteria for non-discrete representations, chaotic actions of  mapping class groups and the monodromy map from structures to  representations

(5) Classification of exotic geometric structures, tameness criteria, generalizations of ending lamination-type invariants to higher rank structures, rigidity and flexibility for thin subgroups, arithmeticity conditions, and geometric transitions

Updated on Jan 21, 2014 08:15 PM PST
76. # WorkshopAdvances in Homogeneous Dynamics

Organizers: LEAD Dmitry Kleinbock (Brandeis University), Hee Oh (Yale University), Alireza Salehi Golsefidy (University of California, San Diego), Ralf Spatzier (University of Michigan)

The Advances in Homogeneous Dynamics workshop will feature the speakers whose work is at the forefront of the eld. There will be a panel discussion accompanied by an open problem session to lay out possible directions for the research in homogeneous dynamics. Talks will be in a broad range of topics and this will help to build more connections between researchers interested in dynamical systems, number theory and geometry. For example we hope that the involvement of the participants of the other program held at MSRI during the same academic year (Dynamics on Moduli Spaces of Geometric Structures, Spring 2015) would create new connections between the topics. There will be shorter talks presented by early-career researchers

Updated on Jan 21, 2014 08:54 PM PST
77. # Summer Graduate SchoolGeometric Group Theory

Organizers: LEAD John Mackay, Anne Thomas, Kevin Wortman

Updated on Mar 18, 2014 06:51 PM PDT
78. # ProgramNew Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems

Organizers: Kay Kirkpatrick (University of Illinois at Urbana-Champaign), Yvan Martel (Université Versailles/Saint Quentin-en-Yvelines), Jonathan Mattingly (Duke University), Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice Sophia-Antipolis), Luc Rey-Bellet (University of Massachusetts, Amherst), LEAD Gigliola Staffilani (Massachusetts Institute of Technology), Daniel Tataru (University of California, Berkeley)

The fundamental aim of this program is to bring together a core group of mathematicians from the general communities of nonlinear dispersive and stochastic partial differential equations whose research contains an underlying and unifying problem: quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and non-deterministic evolution differential equations, or dynamical evolution of large physical systems, and in various regimes.

In recent years there has been spectacular progress within both communities in the understanding of this common problem. The main efforts exercised, so far mostly in parallel, have generated an incredible number of deep results, that are not just beautiful mathematically, but are  also important to understand the complex natural phenomena around us.  Yet, many open questions and challenges remain ahead of us. Hosting the proposed program at MSRI would be the most effective venue to explore the specific questions at the core of the unifying theme and to have a focused and open exchange of ideas, connections and mathematical tools leading to potential new paradigms.  This special program will undoubtedly produce new and fundamental results in both areas, and possibly be the start of a new generation of researchers comfortable on both languages.

Updated on Dec 23, 2013 08:59 AM PST
79. # ProgramDifferential Geometry

Organizers: Tobias Colding (Massachusetts Institute of Technology), Simon Donaldson (Imperial College, London), John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin)

Differential geometry is a subject with both deep roots and recent advances. Many old problems in the field have recently been solved, such as the Poincaré and geometrization conjectures by Perelman, the quarter pinching conjecture by Brendle-Schoen, the Lawson Conjecture by Brendle, and the Willmore Conjecture by Marques-Neves. The solutions of these problems have introduced a wealth of new techniques into the field. This semester-long program will focus on the following main themes:
(1) Einstein metrics and generalizations,
(2) Complex differential geometry,
(3) Spaces with curvature bounded from below,
(4) Geometric flows,
and particularly on the deep connections between these areas.

Updated on Jan 03, 2014 04:22 PM PST
80. # WorkshopConnections for Women: Differential Geometry

Organizers: Christine Breiner (Fordham University), LEAD Natasa Sesum (Rutgers University)

The purpose of this meeting is to help junior female researchers to become familiar with the focus topics of the main MSRI program, and also for the junior researchers to have an opportunity to get acquainted with more senior women researchers in differential geometry.

Updated on Mar 10, 2014 08:35 AM PDT
81. # WorkshopIntroductory Workshop: Modern Riemannian Geometry

Organizers: LEAD Tobias Colding (Massachusetts Institute of Technology), John Lott (University of California, Berkeley), Jeff Viaclovsky (University of Wisconsin)

The week will be devoted to an introduction to modern techniques in Riemannian geometry. This is intended to help graduate students and younger researchers get a headstart, in order to increase their participation during the main semester programs and research lectures. To increase outreach, the week will focus on Riemannian geometry and should be largely accessible. Some minicourses on topics of recent interest will be included. The workshop will also have semi-expository lectures dealing with aspects of spaces with curvature bounded from below, since such spaces will occur throughout the semester. We expect that many Berkeley mathematicians and students will participate in the introductory workshop.

Updated on Jun 07, 2013 02:05 PM PDT
82. # WorkshopKähler Geometry, Einstein Metrics, and Generalizations

Organizers: Simon Donaldson (Imperial College, London), Gang Tian (Princeton University), Jeff Viaclovsky (University of Wisconsin)

The workshop will integrate elements from complex differential geometry with Einstein metrics and their generalizations. The topics will include

- Existence of Kähler-Einstein metrics and extremal Kähler metrics. Notions of stability in algebraic geometry such as Chow stability, K-stability, b-stability, and polytope stability. Kähler-Einstein metrics with conical singularities along a divisor.

- Calabi-Yau metrics and collapsed limit spaces. Connections with physics and mirror symmetry.

- Einstein metrics and their moduli spaces, ε-regularity, noncompact examples such as ALE, ALF, and Poincaré-Einstein metrics. Generalizations of the Einstein condition, such as Bach-flat metrics and Ricci solitons.

- Sasaki-Einstein metrics and metrics with special holonomy. New examples and classification problems.

Updated on Aug 03, 2013 09:30 AM PDT
83. # WorkshopGeometric Flows in Riemannian and Complex Geometry

Organizers: Tobias Colding (Massachusetts Institute of Technology), LEAD John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University)

The workshop will concentrate on parabolic methods in both Riemannian and complex geometry. The topics will include

- Ricci flow. Analytic questions about Ricci flow in three dimensions. Possible applications of Ricci flow to 4-manifold topology. Ricci flow in higher dimensions under curvature assumptions.

- Kähler-Ricci Flow. Applications to the Kähler-Einstein problem. Connections to the minimal model program. Study of Kähler-Ricci solitons and limits of Kähler-Ricci flow.

- Mean curvature flow. Singularity analysis. Generic mean curvature flow.

- Other geometric flows such as Calabi flow and pluriclosed flow.

Updated on Jun 07, 2013 10:39 AM PDT
84. # ProgramGeometric Group Theory

Organizers: Ian Agol (University of California, Berkeley), Mladen Bestvina (University of Utah), Cornelia Drutu (University of Oxford), Mark Feighn (Rutgers University), Michah Sageev (Technion---Israel Institute of Technology), LEAD Karen Vogtmann (Cornell University)

The field of geometric group theory emerged from Gromov’s insight that even mathematical objects such as groups, which are defined completely in algebraic terms, can be profitably viewed as geometric objects and studied with geometric techniques Contemporary geometric group theory has broadened its scope considerably, but retains this basic philosophy of reformulating in geometric terms problems from diverse areas of mathematics and then solving them with a variety of tools. The growing list of areas where this general approach has been successful includes
low-dimensional topology, the theory of manifolds, algebraic topology, complex dynamics, combinatorial group theory, algebra, logic, the study of various classical families of groups, Riemannian geometry and representation theory.

The goals of this MSRI program are to bring together people from the various branches of the field in order to consolidate recent progress, chart new directions, and train the next generation of geometric group theorists.

Updated on Oct 11, 2013 02:11 PM PDT