
Hot Topics: KadisonSinger, Interlacing Polynomials, and Beyond
Organizers: Sorin Popa (University of California), LEAD Daniel Spielman (Yale University), Nikhil Srivastava (University of California, Berkeley), Cynthia Vinzant (North Carolina State University)In a recent paper, Marcus, Spielman and Srivastava solve the KadisonSinger Problem by proving Weaver's KS2 conjecture and the Paving Conjecture. Their proof involved a technique they called the “method of interlacing families of polynomials” and a “barrier function” approach to proving bounds on the locations of the zeros of real stable polynomials. Using these techniques, they have also proved that there are infinite families of Ramanujan graphs of every degree, and they have developed a very simple proof of Bourgain and Tzafriri's Restricted Invertibility Theorem. The goal of this workshop is to help build upon this recent development by bringing together researchers from the disparate areas related to these techniques, including Functional Analysis, Spectral Graph Theory, Free Probability, Convex Optimization, Discrepancy Theory, and Real Algebraic Geometry.
Updated on Mar 03, 2015 11:40 AM PST 
Critical Issues in Mathematics Education 2015: Developmental Mathematics: For whom? Toward what ends?
Organizers: Duane Cooper (Morehouse College), Mark Hoover (University of Michigan), LEAD Robert Megginson (University of Michigan), Richard Sgarlotti (Bay College), Katherine Stevenson (California State University, Northridge)This workshop will address the critical issue of developmental mathematics at two and fouryear colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels. It will engage mathematicians, K12 teachers, mathematics educators, and administrators in a conversation about the goals of developmental mathematics and the contributions that our different professional communities make to this work. Key questions that will be addressed are:
1. How do we teach content in ways that acknowledge and leverage each student's prior learning experiences? In particular, how do we take advantage of a student's maturity while refining his or her learning habits where necessary?
2. How can developmental mathematics instruction move students through mathematics which must be relearned while simultaneously gaining momentum on more advanced mathematics (including the development of mathematical practices needed for meaningful mathematical work)?
3. What are strategies for supporting the needs of the wide range of students in developmental mathematics programsthose developing mathematical skills for life in general as well as those developing the foundation necessary to proceed towards a STEM major? How can we successfully address equity issues raised for students from groups underrepresented in STEM fields? How can developmental mathematics instruction blend synchronous and asynchronous instruction to achieve maximal efficiency and impact?
4. What is the proper balance between addressing the needs of the wide range of students mentioned in the preceding point and keeping instruction and course offerings concise?
5. What are the characteristics, training, and practices of a successful developmental mathematics teacher?
6. What support services enhance the success of a developmental mathematics program?
Updated on Mar 02, 2015 04:44 PM PST 
Dynamics on Moduli Spaces
Organizers: Marc Burger (ETH Zurich), 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 (RuprechtKarlsUniversität 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 WeilPetersoon metric, the pressure metric, the Teichmüller metric and its geodesic flow, FenchelNielsen coordinates, FockGoncharov ThursonPenner 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, CullerMorganShalen 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 nondiscrete 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 laminationtype invariants to higher rank structures, rigidity and flexibility for thin subgroups, arithmeticity conditions, and geometric transitions
Updated on Mar 02, 2015 09:33 AM PST 
Advances 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 earlycareer researchers
Updated on Feb 23, 2015 12:13 PM PST 
Partnerships: a workshop on collaborations between the NSF and private foundations
Organizers: Cynthia Atherton (HeisingSimons 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 nonprofit 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 nonprofit funders in MPSrelated 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 
Connections for Women: Dispersive and Stochastic PDE
Organizers: LEAD Kay Kirkpatrick (University of Illinois at UrbanaChampaign), 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, postdocs, 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 Jan 28, 2015 10:48 AM PST 
Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations
Organizers: Kay Kirkpatrick (University of Illinois at UrbanaChampaign), LEAD Yvan Martel (École Polytechnique), LEAD Luc ReyBellet (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 Feb 18, 2015 08:50 AM PST 
New 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 SophiaAntipolis), Luc ReyBellet (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 nondeterministic 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 `crosspollination’ 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 
Connections 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 
Introductory 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 semiexpository 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 
Kähler Geometry, Einstein Metrics, and Generalizations
Organizers: 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 KählerEinstein metrics and extremal Kähler metrics. Notions of stability in algebraic geometry such as Chow stability, Kstability, bstability, and polytope stability. KählerEinstein metrics with conical singularities along a divisor.
 CalabiYau metrics and collapsed limit spaces. Connections with physics and mirror symmetry.
 Einstein metrics and their moduli spaces, εregularity, noncompact examples such as ALE, ALF, and PoincaréEinstein metrics. Generalizations of the Einstein condition, such as Bachflat metrics and Ricci solitons.
 SasakiEinstein metrics and metrics with special holonomy. New examples and classification problems.
Updated on Feb 23, 2015 09:07 AM PST 
Geometric 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 4manifold topology. Ricci flow in higher dimensions under curvature assumptions.
 KählerRicci Flow. Applications to the KählerEinstein problem. Connections to the minimal model program. Study of KählerRicci solitons and limits of KählerRicci 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 
Connections 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 threeday 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 breakout 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 
Introductory 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

All upcoming workshops 