# Mathematical Sciences Research Institute

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1. # 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
2. # 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 Aug 28, 2014 01:51 PM PDT
3. # 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
4. # 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 Aug 28, 2014 12:08 PM PDT
5. # 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 6. # Berkeley 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 7. # 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 8. # 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 9. # 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 10. # 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
11. # 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
12. # 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
13. # Electronic 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
14. # 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