Programs & Events
Mathematical Aspects of P versus NP and its Variants
Aug 1 - 5, 2011
This workshop will bring together computer scientists and mathematicians to examine the P v. NP problem and its variants from the perspectives of algebra, geometry, and number theory, and to introduce the mathematical aspects of these questions to a larger audience. Diverse researchers working on different aspects of these problems will clarify connections between different approaches.
There will be two main topics: Analogues of P v. NP (e.g., Valiant's conjectures, the Mulmuley-Sohoni Conjecture, the BSS model, and other computational models); and Algebraic, Number Theoretic, and Geometric Aspects of P v. NP (e.g., Holographic algorithms, characterizations of NP in terms of sheaf cohomology, sparse polynomials, and other arithmetic approaches).
The workshop will emphasize the "work" aspect, so there will be few scheduled lectures, with extensive discussion periods, and follow-up lectures scheduled impromptu as needed.
Organizing Committee
- Saugata Basu
- Joseph Landsberg
- Joseph Maurice Rojas
Cluster Algebras and Statistical Physics
Aug 15 - 19, 2011
Cluster algebras are commutative algebras with a distinguished set of generators grouped into overlapping subsets of fixed cardinality; the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. These algebras were developed to explain the "Laurent phenomenon", in which certain a priori rational functions defined by these mutations turn out to always be Laurent polynomials. Cluster algebras encode a surprisingly widespread range of phenomena in settings as diverse as quiver representations, Teichmüller theory, invariant theory, tropical calculus, Poisson geometry, and polyhedral combinatorics. This workshop will explore the connection between cluster algebras and various topics in statistical physics, including the dimer model on surfaces, integrable systems such as the KP equation, and certain dynamical systems (Y- and Q-systems) which play an important role in the theory of the thermodynamic Bethe... (more)
Organizing Committee
- Lauren Williams
- David Wilson
Research Experiences for Undergraduate Faculty (REUF)
Jun 4 - 8, 2012
This workshop, sponsored by AIM, ICERM, and the NSF, will introduce undergraduate faculty to research opportunities in several fields of mathematics that will equip them with the tools to mentor students in undergraduate research in mathematics. Lectures at the workshop will provide background information and introduce open problems. The majority of the workshop will be spent working on problems, reporting on progress, and formulating plans for future work.
The workshop will be hosted at ICERM.
Preference will be given to faculty who teach and advise substantial numbers of minority students.
Mathematical topics at the workshop will include algebra, graph theory, and number theory.
For more information email workshops@aimath.org or go to http://aimath.org/ARCC/workshops/reuf4.html.
Organizing Committee
- Leslie Hogben
- Roselyn Williams
- Ulrica Wilson
NSF/CBMS Conference: Finite Element Exterior Calculus (FEEC)
Jun 11 - 15, 2012
FEEC is a recent advance in the mathematics of finite element methods that employs differential complexes to construct stable numerical schemes for several important types of application problems. It has aroused great interest because it both presents interesting mathematical problems and shows great potential for application in computational science and engineering. The concentrated sequence of lectures in this program will provide participants with an understanding of the mathematical tools required to fully grasp the concepts in FEEC. ICERM is pleased to host this NSF-CBMS Regional Research Conference.
Douglas Arnold will deliver 10 lectures, one in the morning and one in the afternoon of each day of the workshop. Richard Falk and Anil Hirani will both give one presentation.
Limited funding is available to support participants.
Organizing Committee
- Alan Demlow
- Johnny Guzman
- Dmitriy Leykekhman
Summer@ICERM 2012: Geometry and Dynamics
Jun 18 - Aug 10, 2012
Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.
Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.
Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.
Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.
The Summer@ICERM 2012 program is designed for a select group of 10-12 undergraduate scholars. Students in the 2012 program worked in small groups of two or three, supervised by a faculty advisor and aided by a teaching... (more)
Organizing Committee
- Pat Hooper
- Sergei Tabachnikov
Bridging Scales in Computational Polymer Chemistry
Aug 6 - 10, 2012
Many important advances in material and biomedical science will come from controlling the chemical properties and nanoscale morphology of polymer mixtures. Predicting the longtime continuum-level properties of such complex systems poses a canonical computational challenge due to the disparate length and time scales separating the molecular description from the macroscopic behavior, particularly the evolution of morphology. This workshop focuses on four overlapping approaches to bridging this gap: Accelerated Molecular Methods, Coarse-Graining of Molecular Dynamics, Computational Approaches to Self-Consistent Mean Field, and Coupled Molecular and Continuum-Variational models. The goal is to spur the development of hybrid computational methods with the capacity to identify and characterize the rare events and the driving forces which steer the systems towards equilibrium, and connect the burgeoning growth in parallel-computation techniques for particle-based systems with recently... (more)
Organizing Committee
- Andrew Christlieb
- Cecilia Clementi
- Keith Promislow
- Mark Tuckerman
- Zhengfu Xu
Issues in Solving the Boltzmann Equation for Aerospace Applications
Jun 3 - 7, 2013
Being central to gas dynamics, the Boltzmann equation describes gas flows at the microscopic level in regimes from free molecular to continuum. Its descriptive power makes it indispensable for predicting non-continuum phenomena in gases when experimental data is limited or not available. The Boltzmann equation is used in a wide range of applications, from external aerodynamics and thruster plume flows to vacuum facilities and microscale devices. Accurate solution of the Boltzmann equation for modeling gas flows arising in aerospace applications continues to be a challenge. Existing numerical capabilities fall short of capturing the complexities of engineering design. Reasons for this range from the absence of mathematical models that capture the physics properly to higher dimensionality of kinetic models and the resulting high cost of computations to the failure of mathematical theories to handle complex geometries of real life applications.
The goal of this workshop is to facilitate... (more)
Organizing Committee
- Alexander Alekseenko
- Jose Camberos
- Irene Gamba
- Sergey Gimelshein
- Prakash Vedula
- Ingrid Wysong
Summer@ICERM 2013: Geometry and Dynamics
Jun 17 - Aug 9, 2013
Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.
Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.
Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.
Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.
The Summer@ICERM 2013 program is designed for a select group of 10-12 undergraduate scholars. Students will work in small groups of two or three, supervised by faculty advisors and aided by teaching assistants.
The faculty... (more)
Organizing Committee
- Chaim Goodman-Strauss
- Sergei Tabachnikov
IdeaLab 2013: Program for Early Career Researchers
Jul 15 - 19, 2013
Interested in discussing cutting edge research ideas with both peers and leaders in their field?
Interested in broadening your professional network across the mathematical sciences?
Interested in the opportunity to present your ideas and hear about funding opportunities from program officers?
The Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles,... (more)
Organizing Committee
- Henry Cohn
- Jeffrey Hoffstein
- Christopher Jones
- Pamela Martin
- Bjorn Sandstede
- Joseph Silverman
Research Experiences for Undergraduate Faculty (REUF)
Jul 22 - 26, 2013
This workshop, sponsored by AIM, ICERM, and the NSF, will introduce undergraduate faculty to research opportunities in several fields of mathematics that will equip them with the tools to mentor students in undergraduate research in mathematics. Lectures at the workshop will provide background information and introduce open problems. The majority of the workshop will be spent working on problems, reporting on progress, and formulating plans for future work.
The workshop will be hosted at ICERM.
Preference will be given to faculty who teach and advise substantial numbers of minority students.
If you would like to participate, please apply by filling out the on-line form no later than March 22, 2013. Applications are open to all, and we especially encourage women, underrepresented minorities, junior mathematicians, and researchers from primarily undergraduate institutions to... (more)
Organizing Committee
- Leslie Hogben
- Roselyn Williams
- Ulrica Wilson
Computational Nonlinear Algebra
Jun 2 - 6, 2014
Over the last two decades, algebraic and numerical techniques for nonlinear problems have begun a steady and relentless transition from mostly academic constructions, to widely used tools across the mathematical sciences, engineering and industrial applications. The workshop will bring together participants from many diverse fields including computer vision, cryptography, optimization and control, partial differential equations, robotics, and quantum computation, with the common interest in nonlinear algebraic computations. The main goal is to assess the state of the art, to stimulate further progress, and to accelerate developments by bringing together these diverse communities and have them share computational challenges and successes.
Organizing Committee
- Greg Blekherman
- Lek-Heng Lim
- Pablo Parrilo
- Andrew Sommese
- Rekha Thomas
Summer@ICERM 2014: Polygons and Polynomials
Jun 16 - Aug 8, 2014
Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.
Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.
Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.
Now, imagine having this experience with support for travel within the U.S., room and board paid, plus a $3,000 stipend*.
The Summer@ICERM 2014 program is designed for a select group of 12-14 undergraduate scholars. Students work in groups of two or three, supervised by faculty advisors and aided by teaching assistants. The faculty advisors... (more)
Organizing Committee
- Michael Mossinghoff
- Sinai Robins