The Virtual Institute for Mathematical and Statistical Sciences (VIMSS)
DescriptionICERM's Virtual Institute of Mathematical and Statistical Sciences (VIMSS) began with a partnership connecting two US mathematical sciences institutes with several mathematics and statistics institutes in India. VIMSS has sponsored joint workshops, research visits and graduate educational activities with support from the US National Science Foundation, the IndoUS Science and Technology Forum, and the Indian Department of Science and Technology.
VIMSS at ICERM presently includes jointly funded international collaborations with institutes and institutions in Brazil, China, Israel, Japan, and South Africa. These collaborations create a thriving "virtual" institute in the mathematical and statistical sciences.
Programs
 Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, RI
 Statistical and Applied Mathematical Sciences Institute (SAMSI), Research Triangle Park, NC
In Brazil:
 Instituto Nacional de Matemática Pura e Aplicada (IMPA)
China/Hong Kong:
 Hong Kong University of Science and Technology (HKUST)
In India:
 Chennai Mathematical Institute (CMI),
 Chennai Indian Institute of Science (IISc),
 Bangalore Indian Institute of Science Education and Research (IISER),
 Pune Institute of Mathematical Sciences (IMSc),
 Chennai Indian Statistical Institute (ISI), Kolkata, Delhi, Bangalore
 Tata Institute of Fundamental Research (TIFR),
 Mumbai University of Delhi (DU), Delhi
 ICERM is also collaborating with ICTS.
In Israel:
 School of Mathematical Sciences at the Tel Aviv University
In Japan:
In South Africa:
The Hong Kong University of Science and TechnologyICERM VIMSS Program:
Integral Equation Methods, Fast Algorithms and Their Applications to Fluid Dynamics and Materials Science
(HKUST: Dec. 29 2016 Jan. 12, 2017, ICERM: May 30June 9, 2017)
This program will focus on integral equation methods, fast algorithms and their applications to fluid dynamics and materials science. Integral equation methods have been used for more than a century to establish existence and uniqueness results for a variety of elliptic, parabolic and hyperbolic partial differential equations (PDEs). From a computational perspective, they have been used most extensively in the elliptic (steady state or time harmonic) case, because of their ability to handle complex geometry, unbounded domains and radiation conditions and because of the availability of fast algorithms to reduce the cost of handling the dense matrices that arise from their discretization. These algorithms include fast multipole methods (FMM), methods based on the Fast Fourier Transform (FFT) or the nonuniform FFT (“NUFFT”), and hierarchical compressionbased methods (wavelet and SVDbased schemes, Hmatrices, HSSmatrices, etc.). The fundamental issue is that discretization of an elliptic boundary integral equation yields a dense N × N matrix, where N denotes the number of degrees of freedom used to describe the unknown. The straightforward application of a dense matrix to a vector requires O(N2) work, while classical Gaussian elimination techniques require O(N3) work to solve the system. The various fast algorithms listed above provide the ability to apply the discretized integral operator to a vector in O(N) or O(N log N) operations. When combined with modern iterative methods (such as GMRES), wellconditioned integral equation formulations such as second kind integral equations (SKIEs) have reduced the total work required to near optimal complexity, bringing large scale simulations within practical reach.
The program will bring a group of researchers from the US and HKUST with common interests and complementary expertise to work intensively on constructing wellconditioned integral equation formulations, developing highorder, fast, and robust algorithms with scalable implementation, and applying them to solve complex, largescale real physical applications in multiphase flows and dislocation dynamics and to propose positive conditions on the Hadamard conjecture.
Organizing Committee
From HKUST
 XiaoPing Wang
(Department of Mathematics, HKUST)  Yang Xiang
(Department of Mathematics, HKUST)
From the US
 Shidong Jiang
(New Jersey Institute of Technology)  Andreas Kloeckner
(Department of Computer Science,
University of Illinois at UrbanaChampaign)
Target Applications and Algorithm Developments
Interfacial phenomena play a vital role in technological applications in such diverse areas as fluids, biology and material science. Numerical simulation of interface dynamics is a difficult task. The MBO scheme is an efficient numerical method for simulating interface dynamics driven by surface energy minimization. The scheme is also generalized to wetting dynamics and droplet spreading on rough solid surfaces (X. Xu, D. Wang and X.P. Wang, 2015).
In this program, we will develop integral equation formulations and design NUFFTbased fast algorithms for these problems. As compared with existing numerical schemes, the proposed method restricts the computation to a small neighborhood of the material interfaces, provides highorder discretization for smooth or piecewise smooth cases, and achieves near optimal complexity. We will also pay particular attention to scalable implementation to take advantage of modern heterogeneous parallel computers so that real physical 3D problems can be simulated and studied within minutes and hours instead of days and weeks.
Possible Projects:
 Develop integral equation formulations and design NUFFTbased fast algorithms for problems with complex and rough boundaries.
 Generalize the MBOtype schemes to multiphase fluid flow (i.e. couple with the NavierStokes equations).
 Develop parallel algorithms for 3D interface dynamic problems.
Dislocations are line defects in crystals. The climb motion of dislocations is assisted by diffusion and emission and/or absorption of vacancies or interstitials, and plays crucial roles in the plastic deformation of crystalline materials at high temperature. Numerical simulation of the dynamics of dislocation lines, or discrete dislocation dynamics (DDD), is an important tool for the study of plasticity. However, in early DDD simulations, the formulations of dislocation climb were based only on several special cases (single, straight dislocations) for which analytical solutions are available.
Recently, Prof. Yang Xiang and collaborators derived a Green's function formulation for the climb of curved, multiple dislocations in threedimensions (Threedimensional formulation of dislocation climb, Y.J. Gu, Y. Xiang, S.S. Quek, and D.J. Srolovitz, J. Mech. Phys. Solids, 83, 319337, 2015). This new formulation is able to capture the longrange contribution to the dislocation climb velocity associated with vacancy diffusion, which was missing in the previous DDD simulation models.
In this proposed collaborative research workshop, robust numerical methods will be discussed and implemented to calculate the dislocation climb velocity accurately and efficiently, including boundary integral equation methods, NUFFT method, accurate dislocation discretization method, etc. Parallelization and other high performing methods will also be discussed for dislocation climb simulations in large systems.
Possible Projects:
 Construct second kind integral equation formulation for the dislocation climb in the equilibrium state of vacancy diffusion.
 Develop and implementing FMM/NUFFT based fast algorithms for solving the integral equation formulation for the vacancy diffusion equation in dislocation climb.
 Apply the above algorithm to study largescale dislocation climb problems.
In 1908, Hadamard conjectured that the Green's function for the clamped plate problem, or mathematically, the first Dirichlet problem of the biharmonic equation on a convex domain is nonnegative. However, after 1949 numerous counterexamples disproved the positivity conjecture of Hadamard. The first result in this direction came by Duffin (1949), who showed that the Green function changes sign on a long rectangle. Garabedian then showed change of sign of the Green function in ellipses with ratio of half axes ≈ 1.6 (1951). Hedenmalm, Jakobsson and Shimorin (2002) mention that sign change occurs already in ellipses with ratio of half axes ≈ 1.2. Sign change is also proven by CoffmanDuffin (1980) in any bounded domain containing a corner, the angle of which is not too large. Their arguments are based on previous results by Osher and Seif (1973) and cover, in particular, squares. This means that neither in arbitrarily smooth uniformly convex nor in rather symmetric domains the Green function needs to be positive. In fact, convexity is neither sufficient nor necessary for a positive Green function. And the question of under what geometry the Green function will be nonnegative remains open.
In this program, we will study this problem numerically, and we will aim for our numerical results to provide new insights and lead to some positive conjectures on the geometry of the domain for which the Green function for the clamped plate problem is nonnegative. Our numerical study is based on a second kind integral equation formulation for the clamped plate problem. As the negative value of the Green function often first appears on the points close to the boundary, one needs highorder quadrature scheme in order to be able to compute the involved nearly singular integrals accurately. Finally, since one needs to scan many different geometries, fast algorithms are also in urgent need. We plan to develop and apply the FMMaccelerated QBX (quadrature by expansion) scheme for the discretization and evaluation of associated integral operators.
Possible Projects:
 Implement parallel FMMaccelerated QBX scheme with arbitrary precision.
 Study the Hadamard conjecture in the case of ellipses and identifying the ellipse with smallest ratio of half axes where the Green function becomes negative.
 Study the Hadamard conjecture in the case of an arbitrary convex smooth curve to provide some conjecture and insight about this case.
Metamaterials are materials whose properties at the scale of a propagating wave with which they are interacting (that is, above the atomic scale, but well below the macroscopic bulk scale) determine key properties of the interaction. Metamaterials often consist of periodic arrays of structures, with purposefully placed ‘defects’ in the periodic lattice to achieve desired properties. For example, photonic crystals typically consist of a unit cell designed such that the bulk materials has one or multiple band gaps, that is, a range of wavelengths at which EM waves will not propagate in the bulk material. Defects then allow the creation of carefully designed propagation pathways within the nonpropagating bulk materials. Because of the mismatch in scale between the wavelength of light and the scale of the bulk structure, simulation of metamaterials is a formidable task that could stand to benefit tremendously from better computational tools. Material interfaces in metamaterials are typically sharp, leading to PDE BVPs with piecewise constant coefficients, which makes these problems very amenable to being studied with the help of boundary integral equation methods. Highorder accuracy, as provided by the QBX quadrature scheme, is a key ingredient, since the propagation properties of EM waves are sensitive to small perturbations, making simulation at low orders of accuracy unaffordable. The quasiperiodization method of Barnett and Greengard (2010) is another recent advance that has the (thus far unexploited) potential to aid in the study of metamaterials. In this program, we propose to create a computational toolkit for the study of metamaterials. Envisioned contributions extending beyond the creation of the toolkit include enabling the study of materials with bulkscale defects as well as efficient and accurate numerical methods for the truncation of such calculations in the integral equation setting.
Possible Projects:
 Design and implement a scheme to couple the QBX quadrature scheme embedded in a highfrequency FMM in three dimensions with a variant of the Barnett/Greengard periodization method.
 Investigate truncation and acceleration schemes for bulk calculations.
 Develop distributedmemory parallel algorithms for approaching largescale metamaterial simulations.
Mathematical and Statistical Aspects of Cryptography
(January 1214, 2012) (in Kolkata, India)
This workshop focuses on mathematical and statistical aspects of public key cryptography. The main ingredients from mathematics so far include discrete logarithms and factoring over the integers, generalizations of the discrete logarithm to elliptic curves, hyperelliptic curves and further generalizations, aspects of infinite nonabelian groups, and closest vector problems (CVP) in integer lattices. Cryptanalysis in all of these areas can involve analyses of patterns in vast amounts of data, hence the need for statistical methods. One goal of this workshop, though not the only one, is to focus attention on the problem of quantifying the complexity of latticebased problems, for example extrapolating the difficulty of solving a CVP in an integer lattice as a function of its dimension and other parameters.
A copy of the presentations given at this workshop is available as a PDF document.
Organizing Committee
 Jeff Hoffstein
(ICERM, Brown University)  Jill Pipher
(ICERM, Brown University)  Bimal Roy
(Indian Statistical Institute)
Winter School and Conference on Computational Aspects of Neural Engineering
(December 1021, 2012) (in Bangalore, India)
We are pleased to announce the first joint IMIICERM Winter School on Computational Aspects of Neural Engineering. The course is directed at graduate students, postdoctoral fellows, and other researchers from the physical sciences (e.g. physics, mathematics, computer science, engineering) and the life sciences (e.g. neuroscience, biology, physiology). The course will offer participants the opportunity to learn about the foundations of neural engineering and braincomputer interfacing, and develop their skills in computational analysis of neural data for the control of external devices. The topics will range from primers on neuroscience, signal processing, and machine learning to braincomputer interfacing based on multi neuronal activity, electrocorticography (ECoG), and electroencephalography (EEG).
The course will consist of 3 hours of lectures each morning, followed by a 3hour MATLABbased computer laboratory in the afternoon. Participants will pair up for these laboratories, and an effort will be made to pair someone from the life sciences with someone from the physical sciences. All classes and laboratories will be held on the campus of the Indian Institute of Science (IISc).
This program is part of the IISc Mathematics Initiative (IMI) at the Indian Institute of Science and the VIMSS program at ICERM.
Organizing Committee
 G. Rangarajan
(IISc, Bangalore)  Rajesh Rao
(University of Washington, Seattle)
Workshop and Conference on Limit Theorems in Probability
(January 211, 2013) (in Bangalore, India)
Ever since Jakob Bernoulli proved the law of large numbers for Bernoulli random variables in 1713, the subject of limit theorems has been a driving force for the development of probability theory as a whole.
The elucidation of different flavours of laws of large number, central limit theorems and laws of iterated logarithm, their extensions to Markov chains or sums of weakly dependent or stationary processes, limit theorems for
Banach space valued random variables, etc., have given rise to a rich theory as well as the basic tools for tackling any problem involving randomness.
Today, 300 years after the landmark result of Bernoulli, it is fruitful to look back at the way in which search for limit theorems has shaped the subject. It is also fruitful to consider how the emphasis has evolved over
time from simple limit theorems to getting bounds on the rates of convergence or obtaining inequalities, which are of more immediate relevance in applications to nite samples. The current workshop and conference will focus
on some of these topics, and also more broadly on issues of current interest in probability theory.
The workshop (January 28, 2013) will consist of five short courses on a variety of topics, aimed at the level of graduate students but also of potential interest to researchers in probability and related fields.
After the workshop the conference (January 911, 2013) will have lectures on recent developments in various relevant fields of probability.
Organizing Committee
 Manjunath Krishnapur
(Indian Institute of Science, Bangalore)  Kavita Ramanan
(Brown University, Providence)
Computational Topology and Data Analysis Workshop
(November 1721 2014)
The review of Mathematical Sciences research at South African universities commissioned by the National Research Foundation highlighted the isolation of South African mathematics from its applications and related disciplines and not being fully distributed across different areas of mathematics. In particular it noted that there are contemporary mainstream subfields that are not represented and some research is disconnected from areas of contemporary interest. The newly established Centre for Mathematical and Computational Sciences and the African Institute for Mathematical Sciences are collaborating to address some of these gaps by coorganising workshops that will introduce new areas of study to the South African Mathematical Sciences Research landscape.
There is heightened awareness and renewed interest in (Big) Data Analysis since the announcement that South Africa together with Australia would be hosting the Square Kilometre Array project. One of the programmes to be pursued by the Centre for Mathematical and Computational Sciences is the Mathematical and Statistical underpinnings of Big Data.
Computational Topology or Applied Algebraic Topology is a fairly new line of study that combines topological results with efficient computational tools to analyse data and solve problems in many fields, including sensor networks, clustering, robotics, protein biochemistry, computer graphics and image analysis etc. The main objectives of the workshop are to (a) is to introduce the relatively new area of Computational Topology to the attendees and to ‘seed’ this area in the mathematical research landscape in South Africa; (b) give an overview of some of the most important developments and results; (c) discuss some of the contemporary issues, promising directions and open problems and questions. It is hoped that at the end of the workshop researchers in the mathematical sciences and related disciplines will have acquired the basic knowledge prerequisite to undertake research in Topological Data Analysis. The target audience will be researchers from the mathematical, statistical and computational sciences who may want to incorporate into their research aspects or computational topology; postgraduate students who might want to undertake a doctoral project in this area and practitioners from public or private sector.
A typical day will consist of two lectures in the morning and one lecture in the afternoon, each of one hour duration followed by thirty minutes of discussion, brainstorming or handsone activities. There will be a 90minute session in the afternoon which will vary from short presentations by young mathematicians; case study presentations by practitioners; panel discussion by experts from academia, private and public sectors.
Graduate Student TeamBased Research: Computational Symplectic Topology
(May 17 – May 26, 2015 in TelAviv, and July 27 – August, 5, 2015 at ICERM)
Symplectic and contact geometry and topology, which provide a natural setting for Hamiltonian dynamics, comprise a broad spectrum of interrelated disciplines in the mainstream of modern mathematics. The past two decades gave rise to several exciting developments in these fields: on one hand, powerful new mathematical tools and concepts were introduced, solving longstanding problems that were previously unattainable; and on the other hand, challenging and exciting new questions arose for future research. Presently, symplectic and contact geometry have connections with an amazingly wide range of areas in mathematics and physics: differential and algebraic geometry, complex analysis, dynamical systems, lowdimensional topology, quantum mechanics, and string theory.
The research program will address a number of cuttingedge research topics within symplectic and Hamiltonian dynamics, with a special focus on computational and experimental aspects.
Program StructureSeveral projects will be developed by the faculty organizers. Graduate students will be collaborating in teams formed around each project. All graduate students will participate in both sessions of the program: 05/17/2015  05/26/2015 in TelAviv, and 07/27/2015  08/05/2015 at ICERM. Between the site visits, the teams will continue collaborating remotely via email and videoconferencing.
Selection and financial arrangementsWe plan to have 14 graduate students participate in the program (7 from US universities and 7 Israeli students). Review of applications will begin on January 2, 2015 and close when the positions are filled. Accepted USbased graduate students will be reimbursed for travel (to ICERM and to TelAviv) and for local accommodations (shared housing). A meal allowance is included.
Organizing Committee
 Richard Hind
(Department of Mathematics, University of Notre Dame)  Yaron Ostrover
(School of Mathematical Sciences at Tel Aviv University)  Leonid Polterovich
(School of Mathematical Sciences at Tel Aviv University)  Michael Usher
(Department of Mathematics, University of Georgia)



Monday  July 27, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  10:00  Welcome and Breakfast  11th Floor Lecture Hall  
10:00  11:00  Progress report: Project 1 (capacities)  11th floor lecture hall  
11:30  12:30  Progress Report: Project 2 (eggbeaters)  
12:30  2:30  Lunch  
2:30  3:30  Khanevsky  1  11th floor lecture hall  
4:00  5:00  Borman  1  11th floor lecture hall 
Tuesday  July 28, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  11:00  Khanevsky  2  10th floor classroom  
11:30  12:30  Borman  2  10th floor classroom  
12:30  2:30  Lunch  
2:30  5:00  Work in Groups  Group #1: 11th floor conference room Group #2: 10th floor collaborative space  
5:00  6:30  Welcome Reception  11th Floor Collaborative Space 
Wednesday  July 29, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  5:00  Work in Groups  Group #1: 11th floor conference room Group #2: 10th floor collaborative space 
Thursday  July 30, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  12:30  Work in Groups  Group #1: 11th floor conference room Group #2: 10th floor collaborative space  
12:30  2:30  Lunch  
2:30  3:30  Progress Report: Project 1 (capacities)  10th Floor Classroom  
4:00  5:00  Progress Report: Project 2 (eggbeaters)  10th Floor Classroom 
Friday  July 31, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  5:00  Work in Groups  Group #1: 11th floor conference room Group #2: 10th floor collaborative space 
Monday  August 3, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  5:00  Work in Groups  Group #1: 11th floor conference room Group #2: 10th floor collaborative space 
Tuesday  August 4, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  12:00  Concluding Report: Project 1 (capacities)  11th floor lecture hall  
12:00  12:05  Computational Symplectic Topology Group Picture  11th Floor Lecture Hall  
12:00  2:00  Lunch  
2:00  4:00  Concluding Report: Project 2 (eggbeaters)  11th floor lecture hall 
Wednesday  August 5, 2015  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  12:00  Work in Groups  
12:00  2:00  Lunch  
2:00  4:30  Conclusion 
D. AlvarezGavela, V. Kaminker, A. Kislev, K. Kliakhandler, A. Pavlichenko, L. Rigolli, D. Rosen, O. Shabtai, B. Stevenson, J. Zhang. Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms. Posted on arXiv.
BrownICERMKobe Simulation Summer School
(August 17  31, 2015 split between Providence, RI, USA and Kobe, Japan)
This program has three objectives. First, it provides graduate students with opportunities to acquire fundamental knowledge and skills in high performance computing, including parallel computing and visualization in 3D caves, and to expose them to the research carried out in these areas at Brown and Kobe Universities. Second, graduate students will learn how to work collaboratively in teams, thus preparing them for the changing nature of research. Finally, the program will provide students with opportunities to develop a global perspective and mindset through participation in a culturally rich and diverse program.
FormatThe summer school will take place during 1731 August 2015 (not counting travel before and after the program). During the first week in Providence, students will attend minicourses that provide an introduction to numerical algorithms, parallel computing, training on the FX10 supercomputer in Kobe, and application areas. Simultaneously, student teams, led by advanced graduate students, postdocs, and faculty, will begin to work on their projects. During the second week in Kobe, the student teams will continue to work on their projects, run simulation on Kobe’s FX10 (which has the same architecture as RIKEN’s K computer), and visualize results and data on Kobe’s 3D visualization system. Teams present their results on the last day to an audience of administrators and research faculty at Kobe University.
Distinctive FeaturesThe program is distinguished by (i) the small number of participants and their teams, which allows for individual instruction, mentoring, and support, (ii) a twoweek intensive research summer school which enhances multicultural competencies among students, and (iii) the participation of distinctive researchers from Brown, Kobe, and the RIKEN Advanced Institute for Computational Science as guest lecturers.
PrerequisitesThis program is open to MSc and first to secondyear graduate students. Prior exposure to scientific computing and programming is useful but not required. Online resources and lectures will be offered during July 2015 prior to the program.
Organizing Committee
 Jill Pipher
(ICERM, Brown University)  Nobuyuki Kaya
(Kobe University)  Bjorn Sandstede
(ICERM, Brown University)
The first two BrownICERMKobe Simulation Schools ran in August 2013 and 2014, each time with 3 research teams, consisting of one team leader and 45 team members. In 2014, the projects were
 Peridynamic Theory of Solid Mechanics
 Dissipative Particle Dynamics Simulation
 Direct Numerical Simulation of Turbulent Channel Flow
Location  Date 

Providence, RI, USA  1721 August 2015 
Travel  2224 August 2015 
Excursion  25 August 2015 
Kobe, Japan  2630 August 2015 
Kobe, Japan  31 August 2015 (Final Presentations) 