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1. # MSRI-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
2. # Seminaire 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
3. # Geometric 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 Apr 07, 2015 02:15 PM PDT
4. # CRM-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
5. # Mathematical 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 May 15, 2015 10:49 AM PDT
6. # NIMS 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 7. # Berkeley summer course in mining and modeling of neuroscience data Organizers: Ingrid Daubechies (Duke University), Bruno Olshausen (University of California ), 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 8. # Gaps 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 9. # Incompressible 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 10. # Connections 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 11. # Introductory 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 12. # 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 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 May 01, 2015 01:32 PM PDT 13. # Modern Math Workshop 2015 Organizers: LEAD Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Gordon Campbell (SAMSI - Statistical and Applied Mathematical Sciences Institute), Helen Chamberlin (MBI - Mathematical Biosciences Institute), Ricardo Cortez (Tulane University), Sujit Ghosh (SAMSI - Statistical and Applied Mathematical Sciences Institute), Dagan Karp (Harvey Mudd College), Anne Pfister (MSRI - Mathematical Sciences Research Institute), Christian Ratsch (IPAM - Institute for Pure and Applied Mathematics), Ivelisse M. Rubio (University of Puerto Rico), Mariel Vazquez (University of California, Davis), Talitha Williams (Harvey Mudd College) As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to host their annual pre-conference event, the 2015 Modern Math Workshop (MMW). The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhD’s in building their research networks. Updated on May 29, 2015 10:53 AM PDT 14. # 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 Apr 17, 2015 12:32 PM PDT 15. # 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 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 16. # Kähler 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 17. # Hot Topics: Cluster algebras and wall-crossing Organizers: LEAD Mark Gross (University of California, San Diego), Paul Hacking, Sean Keel, Lauren Williams (University of California, Berkeley) Updated on Apr 22, 2015 02:53 PM PDT 18. # 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 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 19. # Seminaire 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 20. # Harmonic 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 21. # Mixed 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 22. # An 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 23. # Electronic Structure Theory Organizers: LEAD Lin Lin (University of California, Berkeley), Jianfeng Lu (Duke University), James Sethian (University of California, Berkeley) Ab initio or first principle electronic structure theories, particularly represented by Kohn-Sham density functional theory (KS-DFT), have been developed into workhorse tools with a wide range of scientific applications in chemistry, physics, materials science, biology etc. What is needed are new techniques that greatly extend the applicability and versatility of these approaches. At the core, many of the challenges that need to be addressed are essentially mathematical. The purpose of the workshop is to provide graduate students a self-contained introduction to electronic structure theory, with particular emphasis on frontier topics in aspects of applied analysis and numerical methods. Updated on Apr 03, 2015 04:46 PM PDT 24. # Chip 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 25. # 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 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 26. # 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 # Past all workshops workshop 1. # WorkshopPartnerships: a Workshop on Collaborations between the NSF/MPS 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 May 20, 2015 01:38 PM PDT 2. # 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 Apr 23, 2015 10:45 AM PDT 3. # WorkshopBay Area Differential Geometry Seminar (BADGS) Spring 2015 Organizers: David Bao (San Francisco State University), Joel Hass (University of California, Davis), LEAD David Hoffman (Stanford University), Rafe Mazzeo (Stanford University), Richard Montgomery (University of California, Santa Cruz) The Bay Area Differential Geometry Seminar meets 3 times each year and is a 1-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon, with 3-4 speakers. Lunch will be available and the final talk will be followed by dinner. Created on Apr 06, 2015 03:13 PM PDT 4. # 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 May 01, 2015 09:18 AM PDT 5. # WorkshopCritical 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 four-year colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels. It will engage mathematicians, K-12 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 programs--those 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 Apr 01, 2015 03:27 PM PDT 6. # WorkshopHot Topics: Kadison-Singer, 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 Kadison-Singer 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 30, 2015 12:51 PM PDT 7. # WorkshopBay Area Differential Geometry Seminar (BADGS) Spring 2015 Organizers: David Bao (San Francisco State University), Joel Hass (University of California, Davis), LEAD David Hoffman (Stanford University), Rafe Mazzeo (Stanford University), Richard Montgomery (University of California, Santa Cruz) The Bay Area Differential Geometry Seminar meets 3 times each year and is a 1-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon, with 3-4 speakers. Lunch will be available and the final talk will be followed by dinner. Updated on Feb 12, 2015 01:23 PM PST 8. # WorkshopIntroductory Workshop: Geometric and Arithmetic Aspects of Homogeneous Dynamics Organizers: Manfred Einsiedler (Eidgenössische TH Zürich-Hönggerberg), Dmitry Kleinbock (Brandeis University), LEAD Jean-François Quint (Université de Bordeaux I), Barbara Schapira (Université de Picardie (Jules Verne)) This Introductory Workshop will consist of several introductory lectures and series of lectures on the recent trends in the field, given by experts in the domain. In addition, there will be several shorter talks by young researchers. Please note that immediately preceding this workshop there is a Connections for Women workshop which will also be introductory in nature. Updated on Feb 09, 2015 10:00 AM PST 9. # WorkshopConnections for Women: Geometric and Arithmetic Aspects of Homogeneous Dynamics Organizers: Elon Lindenstrauss (Hebrew University), LEAD Hee Oh (Yale University) This workshop will consist of several mini-courses given by prominent female mathematicians in the field, intended for graduate students, post-docs, and researchers in areas related to the program. The workshop will also include an informal panel discussion session among female researchers on career issues. This workshop is open to all mathematicians. Updated on Feb 09, 2015 10:05 AM PST 10. # WorkshopIntroductory Workshop: Dynamics on Moduli Spaces of Geometric Structures Organizers: Richard Canary (University of Michigan), LEAD William Goldman (University of Maryland), Ursula Hamenstädt (Universität Bonn), Alessandra Iozzi (Eidgenössische TH Zürich-Hönggerberg) 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 26, 2015 01:25 PM PST 11. # WorkshopConnections for Women: Dynamics on Moduli Spaces of Geometric Structures Organizers: Virginie Charette (University of Sherbrooke), LEAD 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 various talks given by prominent female mathematicians in the field. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program. The workshop will also include a professional development session. This workshop is open to all mathematicians. Updated on Jan 21, 2015 12:34 PM PST 12. # WorkshopAutomorphic forms, Shimura varieties, Galois representations and L-functions Organizers: LEAD Pierre Colmez (Institut de Mathématiques de Jussieu), Stephen Kudla (University of Toronto), Elena Mantovan (California Institute of Technology), Ariane Mézard (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 Dec 08, 2014 09:34 AM PST 13. # 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 Nov 19, 2014 12:12 PM PST 14. # WorkshopBay Area Differential Geometry Seminar (BADGS) Fall 2014 Organizers: David Bao (San Francisco State University), Joel Hass (University of California, Davis), LEAD David Hoffman (Stanford University), Rafe Mazzeo (Stanford University), Richard Montgomery (University of California, Santa Cruz) The Bay Area Differential Geometry Seminar meets 3 times each year and is a 1-day seminar on recent developments in differential geometry and geometric analysis, broadly interpreted. Typically, it runs from mid-morning until late afternoon, with 3-4 speakers. Lunch will be available and the final talk will be followed by dinner. Location: Mathematical Sciences Research Institute, Berkeley CA Updated on Sep 24, 2014 01:43 PM PDT 15. # WorkshopBreaking the Neural Code Organizers: Larry Abbott (Columbia University), Ingrid Daubechies (Duke University), Michael Jordan (University of California), LEAD Liam Paninski (Columbia University) For decades, neuroscientists have dreamed about the possibility of recording from all the neurons in a brain, or of having access to a complete large brain wiring diagram, or ideally to obtain both of these datasets simultaneously, in the same brain. Recent technical advances have brought this dream close to reality in some cases. Now the challenge will be to understand these massive datasets. A few domains will be particularly relevant: • Inferring network structure from noisy and incomplete data • Inferring computational input-output function from structure • Optimal experimental design (incl. compressive sensing methods) for observation of networks • Modeling structured stochastic network dynamics • Optimal control of network dynamics • Inferring low-dimensional dynamics from high-dimensional observations There’s a strong need in neuroscience for deep new ideas from mathematics and statistics, and our hope is that this small, focused workshop without many formal talks will spark collaborations that will lead to breakthroughs in the areas described above. This workshop is by invitation only. This workshop is supported by a generous donation from Sanford Grossman. Updated on Oct 29, 2014 12:22 PM PDT 16. # 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 Oct 28, 2014 01:29 PM PDT 17. # 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. All are welcome to participate in the scientific portions of the workshop and the panel discussion, regardless of gender. Updated on Sep 16, 2014 03:12 PM PDT 18. # WorkshopIntroductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms Organizers: Laurent Berger (École Normale Supérieure de Lyon), Ariane Mézard (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 Aug 29, 2014 09:33 AM PDT 19. # WorkshopConnections for Women: New Geometric Methods in Number Theory and Automorphic Forms Organizers: Wenching 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 Aug 27, 2014 04:44 PM PDT 20. # 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 Aug 11, 2014 12:16 PM PDT 21. # 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 Jun 24, 2014 02:31 PM PDT 22. # Summer Graduate SchoolAlgebraic Topology Organizers: LEAD Jose Cantarero-Lopez (Centro de Investigación en Matemáticas), LEAD Michael Hill (University of Virginia) 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. Videos of selected lectures may be found here. Updated on Jan 15, 2015 11:27 AM PST 23. # 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 24. # Summer Graduate SchoolSeminaire de Mathematiques Superieures 2014: Counting Arithmetic Objects Organizers: Henri Darmon (McGill University), Andrew Granville (Université de Montréal), Benedict Gross (Harvard University) Updated on Jan 16, 2014 08:48 AM PST 25. # 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 Apr 02, 2015 01:15 PM PDT 26. # 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 differential 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 Jun 16, 2014 10:14 AM PDT 27. # 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 May 27, 2014 01:57 PM PDT 28. # WorkshopReimagining the Foundations of Algebraic Topology Organizers: Vigleik Angeltveit (Australian National University), Mark Behrens (Massachusetts Institute of Technology), Julie Bergner (University of California), LEAD Andrew Blumberg (University of Texas) Recent innovations in higher category theory have unlocked the potential to reimagine the basic tools and constructions in algebraic topology. This workshop will explore the interplay between these higher and\infty\$-categorical techniques with classical algebraic topology, playing each off of the other and returning the field to conceptual, geometrical intuition.

Updated on Apr 15, 2014 11:30 AM PDT
29. # WorkshopCritical Issues in Mathematics Education 2014: The role of the mathematics department in the mathematical preparation of teachers

Organizers: Deborah Ball (University of Michigan), Solomon Friedberg (Boston College), LEAD Jim Lewis (University of Nebraska), Despina Stylianou (City College, CUNY), Peter Trapa (University of Utah), Hung-Hsi Wu (University of California, Berkeley), Darryl Yong (Harvey Mudd College)

The 2014 CIME workshop will focus on the role played by mathematics departments in preparing future teachers.  As part of this focus, the workshop will consider two broad questions: What mathematics should teachers know, and how should they come to know this mathematics?

The Conference Board of the Mathematical Sciences publication, The Mathematical Education of Teachers II, recommends that, at institutions that prepare teachers, teacher education should be “an important part of a mathematics department’s mission” (p.19). Certainly, at some universities, mathematicians are significantly involved in the mathematical experiences of students who are planning become teachers. But there are many other departments where this is not true. Future mathematics teachers are enrolled in the department’s mathematics classes, but no one is attending to the fact that this is where they are developing mathematical knowledge and (from watching their instructors) ideas about how teach mathematics.  This role – whether deliberate or latent –– is vitally important for the mathematical preparation of beginning teachers.

The CIME workshop has three core aims: (A) to acquaint mathematicians with basic facts about teacher education and how teacher education intersects with the math department even when no one is taking special note of the department’s role; (B) to explore a set of key questions and best practices central to taking advantage of the role that mathematics departments do – or could – play in the mathematical preparation of teachers:

1. What is known about effective mathematical preparation of teachers, including curriculum, instructional approaches, and assessments?
2. What supports do mathematicians and mathematics departments need to carry out this important role effectively?  What are examples of successful models and what evidence exists about their effects?
3. What are some of the persistent problems or challenges and what are promising examples of addressing these?

and (C) to identify possible action steps to provide more collective capacity for math departments to contribute to teachers’ mathematical education.

Updated on Apr 04, 2014 09:25 AM PDT
30. # WorkshopHot Topics: Perfectoid Spaces and their Applications

Organizers: Sophie Morel (Princeton University), Peter Scholze (Universität Bonn), LEAD Richard Taylor (Institute for Advanced Study), Jared Weinstein (Boston University)

Since their introduction just two years ago, perfectoid spaces have played a crucial role in a number of striking advances in arithmetic algebraic geometry: the proof of Deligne's weight-monodromy conjecture for complete intersections in toric varieties; the development of p-adic Hodge theory for rigid analytic spaces;  a p-adic analogue of Riemann's classification of abelian varieties over the complex numbers; and the construction of Galois representations for torsion classes in the cohomology of many locally symmetric spaces (for instance arithmetic hyperbolic 3-manifolds). We will start the week with an exposition of the foundations of the theory of perfectoid spaces, with the aim of teaching novices to work with them. Then we will discuss their current and potential applications.

Updated on Oct 10, 2014 12:49 PM PDT
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