# Mathematical Sciences Research Institute

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1. # SeminarGeometry and Analysis of Surface Group Representations: Introduction to Spectral Networks (II)

Updated on Mar 26, 2015 04:16 PM PDT
2. # SeminarLorentzian geometric structures seminar: Margulis spacetimes and contracting deformations of hyperbolic surfaces II

Updated on Mar 26, 2015 03:39 PM PDT
3. # SeminarDMS Research Seminar: Renormalized volume, Weil-Petersson geometry and volumes of hyperbolic 3-manifolds that fiber over the circle

Updated on Mar 27, 2015 03:36 PM PDT
4. # SeminarGAAHD Postdoc Seminar: The stable type of the mapping class group and some relatively hyperbolic groups and applications to pointwise ergodic averages

Updated on Mar 26, 2015 03:44 PM PDT
5. # SeminarDMS Postdoc Seminar: Coupled Hitchin Equations

Updated on Mar 26, 2015 04:14 PM PDT
6. # SeminarMSRI Evans Talk: Dynamics on moduli spaces of flat surfaces - questions and new directions

Updated on Mar 30, 2015 12:00 PM PDT
7. # SeminarLorentzian geometric structures seminar

Created on Feb 23, 2015 11:02 AM PST
8. # SeminarGAAHD Research Seminar

Updated on Feb 20, 2015 09:47 AM PST
9. # Seminar3-Manifold Seminar

Created on Jan 29, 2015 09:26 AM PST
10. # SeminarOpen ended seminar

Updated on Mar 06, 2015 09:52 AM PST
11. # SeminarGeometry and Analysis of Surface Group Representations

Created on Jan 22, 2015 04:35 PM PST
12. # SeminarDMS Research Seminar

Updated on Jan 28, 2015 02:17 PM PST
13. # SeminarGAAHD Postdoc Seminar

Created on Jan 28, 2015 01:55 PM PST
14. # SeminarDMS Postdoc Seminar

Created on Jan 28, 2015 01:54 PM PST
15. # WorkshopDynamics on Moduli Spaces

Organizers: Marc Burger (Eidgenössische TH Zürich-Hönggerberg), LEAD David Dumas (University of Illinois at Chicago), Olivier Guichard (Université de Strasbourg I (Louis Pasteur)), François Labourie (Université de Nice Sophia Antipolis), 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 Mar 18, 2015 10:54 AM PDT
16. # SeminarLorentzian geometric structures seminar

Created on Feb 23, 2015 11:04 AM PST
17. # Seminar3-Manifold Seminar

Created on Jan 29, 2015 09:28 AM PST
18. # SeminarOpen ended seminar

Updated on Mar 06, 2015 09:52 AM PST
19. # SeminarGAAHD Research Seminar

Updated on Feb 20, 2015 09:49 AM PST
20. # SeminarGeometry and Analysis of Surface Group Representations

Created on Jan 22, 2015 04:36 PM PST
21. # SeminarDMS Research Seminar

Updated on Jan 28, 2015 02:16 PM PST
22. # SeminarGAAHD Postdoc Seminar

Created on Jan 28, 2015 02:02 PM PST
23. # SeminarDMS Postdoc Seminar

Created on Jan 28, 2015 01:57 PM PST
24. # SeminarLorentzian geometric structures seminar

Created on Feb 23, 2015 11:06 AM PST
25. # SeminarMSRI Evans Talk

Updated on Jan 15, 2015 09:42 AM PST
26. # SeminarOpen ended seminar

Updated on Mar 06, 2015 09:51 AM PST
27. # Seminar3-Manifold Seminar

Created on Jan 29, 2015 09:29 AM PST
28. # SeminarGAAHD Research Seminar

Updated on Feb 20, 2015 09:49 AM PST
29. # SeminarGeometry and Analysis of Surface Group Representations

Created on Jan 22, 2015 04:38 PM PST
30. # SeminarDMS Research Seminar

Updated on Jan 28, 2015 02:15 PM PST
31. # SeminarGAAHD Postdoc Seminar

Created on Jan 28, 2015 02:05 PM PST
32. # SeminarDMS Postdoc Seminar

Created on Jan 28, 2015 02:04 PM PST
33. # SeminarLorentzian geometric structures seminar

Created on Feb 23, 2015 11:07 AM PST
34. # SeminarOpen ended seminar

Updated on Mar 06, 2015 09:51 AM PST
35. # SeminarGAAHD Research Seminar

Updated on Feb 20, 2015 09:50 AM PST
36. # SeminarGeometry and Analysis of Surface Group Representations

Created on Jan 22, 2015 04:39 PM PST
37. # SeminarDMS Research Seminar

Updated on Jan 28, 2015 02:15 PM PST
38. # SeminarGAAHD Postdoc Seminar

Created on Jan 28, 2015 02:07 PM PST
39. # SeminarDMS Postdoc Seminar

Created on Jan 28, 2015 02:06 PM PST
40. # 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 field. 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 Mar 26, 2015 12:01 PM PDT
41. # SeminarLorentzian geometric structures seminar

Created on Feb 23, 2015 11:08 AM PST
42. # SeminarGAAHD Research Seminar

Updated on Feb 20, 2015 09:52 AM PST
43. # SeminarOpen ended seminar

Updated on Mar 06, 2015 09:50 AM PST
44. # SeminarGeometry and Analysis of Surface Group Representations

Created on Jan 22, 2015 04:40 PM PST
45. # SeminarDMS Research Seminar

Updated on Jan 28, 2015 02:14 PM PST
46. # WorkshopPartnerships: a workshop on collaborations between the NSF and private foundations

Organizers: Cynthia Atherton (Heising-Simons Foundation), Paulette Clancy (Cornell University), LEAD David Eisenbud (MSRI - Mathematical Sciences Research Institute), Thomas Everhart (California Institute of Technology), Caty Pilachowski (Indiana University, Bloomington), Robert Shelton (Research Corporation for Science Advancement), Yuri Tschinkel (New York University, Courant Institute)

The National Science Foundation (NSF) and non-profit organizations each provide critical support to the U.S. basic research enterprise in the mathematical and physical sciences. While the missions of these funders differ, many of their goals align and the grantee communities have significant overlap. With the ultimate aim of helping to advance the scientific frontier in the most effective way, we propose to hold a workshop to examine partnerships between the Directorate of Mathematical and Physical Sciences (MPS) at NSF and non-profit funders in MPS-related disciplines to

•       understand different models of collaboration (the “how”);
•       understand different motivations for collaboration (the “why”); and
•       develop opportunities for future communication and/or collaboration.

Updated on Feb 23, 2015 11:34 AM PST
47. # MSRI-UPMSRI-UP 2015: Geometric Combinatorics Motivated by Social Sciences

Organizers: Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), 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 2015 program will be led by Prof. Francis Su from Harvey Mudd College.

Updated on Dec 01, 2014 04:17 PM PST
48. # ProgramSummer Research

Created on Feb 23, 2015 04:41 PM PST
49. # Summer Graduate SchoolSeminaire de Mathematiques Superieures 2015: Geometric and Computational Spectral Theory

Organizers: Alexandre Girouard (Laval University), Dmitry Jakobson (McGill University), Michael Levitin (University of Reading), Nilima Nigam (Simon Fraser University), Iosif Polterovich (Université de Montréal), Frederic Rochon (Université du Québec à Montréal)

The lectures will focus on the following four topics: geometry of eigenvalues, geometry of eigenfunctions, spectral theory on manifolds with singularities and computational spectral theory. There has been a number of remarkable recent developments in these closely related fields. The goal of the school is to shed light on different facets of modern spectral theory and to provide a unique opportunity for graduate students and young researchers to get a “big picture” of this rapidly evolving area of mathematics. A particularly novel aspect of the school is the emphasis on the interactions between spectral geometry and computational spectral theory.

Updated on Jan 28, 2015 10:59 AM PST
50. # Summer Graduate SchoolCRM-PIMS Summer School in Probability

Organizers: LEAD Louigi Addario-Berry (McGill University), Omer Angel, Louis-Pierre Arguin, Martin Barlow, Edwin Perkins, Lea Popovic (Concordia University)

The 2015 CRM-PIMS Summer School in Probability will take place in Montreal, Canada, from June 15-July 11, 2015. The school is built around two principal 24-hour lecture courses, which will be delivered by Alice Guionnet (random matrices, free probability and the enumeration of maps) and Remco van der Hofstad (high-dimensional percolation and random graphs). There will additionally be mini-courses by Louigi Addario-Berry (random minimum spanning trees), Shankar Bhamidi (dynamic random network models) and Jonathan Mattingly (stabilization by noise). Some time is reserved for participants to present their own work.

Updated on Nov 03, 2014 09:28 AM PST
51. # Summer Graduate SchoolGeometric Group Theory

Organizers: LEAD John Mackay (University of Bristol), Anne Thomas (University of Glasgow), Kevin Wortman (University of Utah)

The aim of this workshop is to introduce graduate students to some specific core topics which will be under study at the upcoming MSRI program on Geometric Group Theory (GGT) in 2016.  GGT encompasses a wide range of topics. The four minicourse topics have been chosen because they are central themes in GGT and in the upcoming MSRI program. Moreover, each topic is accessible to students with a range of backgrounds: the basic definitions are straightforward, with many simple and illuminating examples to work through, yet lead through to important questions in current research.

Updated on Aug 28, 2014 01:51 PM PDT
52. # Summer Graduate SchoolNIMS Summer School on Random Matrix Theory

Organizers: LEAD Jinho Baik (University of Michigan)

This summer graduate school will take place at the National Institute for Mathematical Sciences in Daejeon, South Korea.  The purpose of this summer school is to introduce some of the basic ideas and methods of random matrix theory to graduate students.  In particular there will be three lecture series on random matrix theory from three different perspectives: from the view points of the integrable structures, the moment method, and the Stieltjes transorm technique.  In addition to the lectures, there will be discussion sessions, and the students will also have plenty of time to interact with the lecturers and with other students.

Please note that accepted students will be provided up to $1700 in travel reimbursement, in addition to meals and accommodation. Updated on Nov 20, 2014 12:02 PM PST 53. # Summer Graduate SchoolMathematical Topics in Systems Biology Organizers: LEAD Steven Altschuler (University of California, San Francisco), Lani Wu (UCSF) This Summer Graduate School will introduce mathematics graduate students to the rapidly emerging area of systems biology. In particular, we will focus on the design and emergent behaviors of molecular networks used by cells to interpret their environments and create robust temporal-spatial behaviors. This will be a very hands-on workshop with students working alone and in teams to program and present key ideas. Updated on Aug 28, 2014 12:08 PM PDT 54. # Summer Graduate SchoolBerkeley summer course in mining and modeling of neuroscience data Organizers: Ingrid Daubechies (Duke University), Bruno Olshausen (UC Berkeley), Christos Papadimitriou (University of California, Berkeley), Fritz Sommer, LEAD Jeff Teeters (University of California, Berkeley) This course is for students and researchers with backgrounds in mathematics and computational sciences who are interested in applying their skills toward problems in neuroscience. It will introduce the major open questions of neuroscience and teach state-of–the-art techniques for analyzing and modeling neuroscience data sets. The course is designed for students at the graduate level and researchers with background in a quantitative field such as engineering, mathematics, physics or computer science who may or may not have a specific neuroscience background. The goal of this summer course is to help researchers find new exciting research areas and at the same time to strengthen quantitative expertise in the field of neuroscience. The course is sponsored by the National Science Foundation from a grant supporting activities at the data sharing repository CRCNS.org, the Helen Wills Neuroscience Institute, the Simons Institute for the Theory of Computing and the Mathematical Science Research Institute. Updated on Feb 23, 2015 03:59 PM PST 55. # Summer Graduate SchoolGaps between Primes and Analytic Number Theory Organizers: Dimitris Koukoulopoulos (Université de Montréal), LEAD Emmanuel Kowalski (Eidgenössische TH Zürich-Hönggerberg), James Maynard (University of Oxford), Kannan Soundararajan (Stanford University) These courses will give students a full overview of the results of Zhang and Maynard on gaps between primes, and will provide them will a clear understanding of the tools involved. This will make accessible a significant part of modern analytic number theory. The lecturers will also make sure to include, within their course, examples and discussions going further than is strictly required to understand the proofs of Zhang and Maynard, e.g., in the direction of automorphic forms and the Riemann Hypothesis over finite fields. Updated on Dec 09, 2014 12:23 PM PST 56. # Summer Graduate SchoolIncompressible Fluid Flows at High Reynolds Number Organizers: Jacob Bedrossian (University of Maryland), LEAD Vlad Vicol (Princeton University) The purpose of this two week workshop is to introduce graduate students to state-of-the-art methods and results in mathematical fluid dynamics. In the first week, we will discuss the mathematical foundations and modern analysis aspects of the Navier-Stokes and Euler equations. In the second week, we will run two courses concurrently on the topics of inviscid limits and hydrodynamic stability. Specifically, one course will focus on boundary layers in high Reynolds number flows and the Prandtl equations while the other will focus on mixing and connections to turbulence. Through the lectures and associated problem sessions, the students will learn about a number of new analysis tools and principles of fluid mechanics that are not always taught in a graduate school curriculum. Updated on Aug 28, 2014 08:47 AM PDT 57. # 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 (École Polytechnique), 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 58. # ProgramComplementary Program Updated on Jan 26, 2015 04:20 PM PST 59. # WorkshopConnections for Women: Dispersive and Stochastic PDE Organizers: LEAD Kay Kirkpatrick (University of Illinois at Urbana-Champaign), Andrea Nahmod (University of Massachusetts, Amherst) This workshop will consist of various talks given by prominent female mathematicians whose research lies in and interfaces with the fields of nonlinear evolution dispersive PDE, wave phenomena and stochastic processes. These talks will be appropriate for graduate students, post-docs, and researchers in areas above mentioned. The workshop will allocate ample time for group discussions and will include a professional development session. This workshop is open to all mathematicians. Updated on Mar 31, 2015 09:00 AM PDT 60. # WorkshopIntroductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations Organizers: Kay Kirkpatrick (University of Illinois at Urbana-Champaign), LEAD Yvan Martel (École Polytechnique), LEAD Luc Rey-Bellet (University of Massachusetts, Amherst), Gigliola Staffilani (Massachusetts Institute of Technology) The purpose of the program New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems is to bring together a core group of mathematicians from the dispersive PDE and the SPDE communities whose research contains an underlying and unifying problem: analyzing high or infinite dimensional dynamics, where dynamics is understood in a broad sense and arising from the flows generated by either deterministic or stochastic partial differential equations, or from dynamical evolution of large physical systems. The introductory workshop will serve as an overview to the program. It aims at familiarizing graduate students, postdocs, and other researchers to the major topics of the program through short courses and discussions. Updated on Mar 20, 2015 09:22 AM PDT 61. # WorkshopNew challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems Organizers: Jonathan Mattingly (Duke University), LEAD Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice Sophia-Antipolis), Luc Rey-Bellet (University of Massachusetts, Amherst), Daniel Tataru (University of California, Berkeley) This workshop serves to bring into focus the fundamental aim of the jumbo program by both a) showcasing the spectacular progress in recent years in the study of both nonlinear dispersive as well as stochastic partial differential equations and b) bringing to the fore the key challenges for the future in 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. During the two weeks long workshop, we intertwine talks on a wide array of topics by some of the key researchers in both communities and aim at highlighting the most salient ideas, proofs and questions which are important and fertile for cross-pollination’ between PDE and SPDE. Topics include: Global dynamics and singularity formation for geometric and physical nonlinear wave and dispersive models (critical and supercritical regimes); dynamics of infinite dimensional systems (critical phenomena, multi scale dynamics and metastability); symplectic structures of infinite dimensional dynamical systems; randomization and long time dynamics, invariant Gibbs and weighted Wiener measures; derivation of effective dynamics in quantum systems; weak turbulence phenomena; optimization and learning algorithms: distributed, stochastic and parallel. Updated on Jan 28, 2015 11:18 AM PST 62. # 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 Mar 11, 2015 11:45 AM PDT 63. # 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. This workshop is open to all mathematicians. Updated on Nov 08, 2014 11:44 AM PST 64. # 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 Aug 14, 2014 08:49 AM PDT 65. # WorkshopKähler Geometry, Einstein Metrics, and Generalizations Organizers: Olivier Biquard (École Normale Supérieure), Simon Donaldson (Imperial College, London), Gang Tian (Princeton University), LEAD 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 Mar 05, 2015 10:53 AM PST 66. # 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 67. # Summer Graduate SchoolSeminaire de Mathematiques Superieures 2016: Dynamics of Biological Systems Organizers: Thomas Hillen (University of Alberta), Mark Lewis (University of Alberta), Yingfei Yi (University of Alberta) Updated on Feb 18, 2015 02:45 PM PST 68. # Summer Graduate SchoolHarmonic Analysis and EllipticEquations on real Euclidean Spaces and on Rough Sets Organizers: LEAD Steven Hofmann (University of Missouri), Jose Maria Martell (Instituto de Ciencias Matematicas) The goal of the workshop is to present harmonic analysis techniques in$R^n\$ (the `flat" setting), and then to show how those techniques extend to much rougher settings, with application to the theory of elliptic equations. Thus, the subject matter of the workshop will introduce the students to an active, current research area:  the interface between harmonic analysis, elliptic PDE, and geometric measure theory.

Updated on Mar 10, 2015 04:09 PM PDT
69. # Summer Graduate SchoolMixed Integer Nonlinear Programming: Theory, algorithms and applications

Organizers: Franscisco Castro (Universidad de Sevilla), Elena Fernandez (Polytechnical University of Cataluña (Barcelona)), Justo Puerto (Universidad de Sevilla)

Updated on Feb 18, 2015 02:48 PM PST
70. # Summer Graduate SchoolAn Introduction to Character Theory and the McKay Conjecture

Organizers: Robert Guralnick (University of Southern California), Pham Tiep (University of Arizona)

Character Theory of Finite Groups provides one of the most powerful tools to study groups. In this course we will give a gentle introduction to basic results in the Character Theory, as well as some of the main conjectures in Group Representation Theory, with particular emphasis on the McKay Conjecture.

Updated on Jan 13, 2015 12:51 PM PST
71. # Summer Graduate SchoolElectronic Structure Theory

Organizers: LEAD Lin Lin (University of California, Berkeley), Jianfeng Lu (Duke University), James Sethian (University of California, Berkeley)

Updated on Mar 10, 2015 03:55 PM PDT
72. # Summer Graduate SchoolChip Firing and Tropical Curves

Organizers: LEAD Matthew Baker (Georgia Institute of Technology), Melody Chan (Harvard University), Sam Payne (Yale University)

Tropical geometry uses a combination of techniques from algebraic geometry, combinatorics, and convex polyhedral geometry to study degenerations of algebraic varieties; the simplest tropical objects are tropical curves, which one can think of as "shadows" of algebraic curves.  Linear equivalence of divisors on an abstract tropical curve is determined by a simple but rich combinatorial process called "chip firing", which was discovered independently in the discrete setting by physicists and graph theorists.  From a pedagogical point of view, one can view tropical curves as a combinatorial model for the highly analogous but more abstract theory of algebraic curves, but there is in fact much more to the story than this: one can use tropical curves and chip firing to prove theorems in algebraic geometry and number theory.  This field is relatively new, so participants will have the opportunity to start from scratch and still get a glimpse of the cutting edge in this active research area.

Updated on Jan 13, 2015 12:40 PM PST
73. # ProgramGeometric Group Theory

Organizers: Ian Agol (University of California, Berkeley), Mladen Bestvina (University of Utah), Cornelia Drutu (University of Oxford), LEAD Mark Feighn (Rutgers University), Michah Sageev (Technion---Israel Institute of Technology), 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
74. # WorkshopConnections for Women: Geometric Group Theory

Organizers: LEAD Ruth Charney (Brandeis University), Indira Chatterji (Université de Nice Sophia Antipolis), Mark Feighn (Rutgers University), Talia Fernos (University of North Carolina)

This three-day workshop will feature talks by six prominent female mathematicians on a wide range of topics in geometric group theory.  Each speaker will give two lectures, separated by a break-out session during which participants will meet in small groups to discuss ideas presented in the first lecture.   The workshop is open to all mathematicians.

Updated on Nov 08, 2014 10:27 AM PST
75. # WorkshopIntroductory Workshop: Geometric Group Theory

Organizers: Martin Bridson (University of Oxford), Benson Farb (University of Illinois), Zlil Sela (Hebrew University), Karen Vogtmann (Cornell University)

Updated on Oct 30, 2014 08:39 AM PDT