### The Virtual Institute for Mathematical and Statistical Sciences *(VI-MSS)*

**Description**

ICERM's Virtual Institute of Mathematical and Statistical Sciences (VI-MSS) began with a partnership connecting two US mathematical sciences institutes with several mathematics and statistics institutes in India. VI-MSS has sponsored joint workshops, research visits and graduate educational activities with support from the US National Science Foundation, the Indo-US Science and Technology Forum, and the Indian Department of Science and Technology. It is part of a broader NSF initiative known as SAVI (Science Across Virtual Institutes).

VI-MSS at ICERM presently includes jointly funded international collaborations with institutes and institutions in Brazil, Israel, Japan, and South Africa. These collaborations create a thriving "virtual" institute in the mathematical and statistical sciences.

### Programs

**In United States:**

- 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)

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:

Nothing scheduled at this time.

Nothing scheduled at this time.

### Graduate Student Team-Based Research: Computational Symplectic Topology

*(May 17 – May 26, 2015 in Tel-Aviv, and July 27 – August, 5, 2015 at ICERM)*

**Description**

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 long-standing 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, low-dimensional topology, quantum mechanics, and string theory.

The research program will address a number of cutting-edge research topics within symplectic and Hamiltonian dynamics, with a special focus on computational and experimental aspects.

**Program Structure**

Several 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 Tel-Aviv, and 07/27/2015 - 08/05/2015 at ICERM. Between the site visits, the teams will continue collaborating remotely via email and video-conferencing.

**Selection and financial arrangements**

We 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 US-based graduate students will be reimbursed for travel (to ICERM and to Tel-Aviv) 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)

### Brown-ICERM-Kobe Simulation Summer School

*(August 17 - 31, 2015 split between Providence, RI, USA and Kobe, Japan)*

**Description**

**Goals**

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.

**Format**

The summer school will take place during 17-31 August 2015 (not counting travel before and after the program). During the first week in Providence, students will attend mini-courses that provide an introduction to numerical algorithms, parallel computing, training on the FX-10 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 FX-10 (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 Features**

The program is distinguished by (i) the small number of participants and their teams, which allows for individual instruction, mentoring, and support, (ii) a two-week intensive research summer school which enhances multi-cultural competencies among students, and (iii) the participation of distinctive researchers from Brown, Kobe, and the RIKEN Advanced Institute for Computational Science as guest lecturers.

**Prerequisites**

This program is open to MSc and first- to second-year 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)

**Group Projects**

**Group Project 1:**Fracture mechanics of brittle materials using peridynamics

**Group Project 2:**Self-assembly of micelles using dissipative particle dynamics

**Group Project 3:**Vortex dynamics of turbulent channel flow using pseudospectral methods

**History**

The first two Brown-ICERM-Kobe Simulation Schools ran in August 2013 and 2014, each time with 3 research teams, consisting of one team leader and 4-5 team members. In 2014, the projects were

- Peridynamic Theory of Solid Mechanics
- Dissipative Particle Dynamics Simulation
- Direct Numerical Simulation of Turbulent Channel Flow

**Schedule**

Location | Date |
---|---|

Providence, RI, USA | 17-21 August 2015 |

Travel | 22-24 August 2015 |

Excursion | 25 August 2015 |

Kobe, Japan | 26-30 August 2015 |

Kobe, Japan | 31 August 2015 (Final Presentations) |

Nothing scheduled at this time.

### Mathematical and Statistical Aspects of Cryptography

*(January 12-14, 2012) (in Kolkata, India)*

**Description**

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 non-abelian 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 lattice-based 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 10-21, 2012) (in Bangalore, India)*

**Description**

We are pleased to announce the first joint IMI-ICERM 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 brain-computer 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 brain-computer 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 3-hour MATLAB-based 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 2-11, 2013) (in Bangalore, India)*

**Description**

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 2-8, 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 9-11, 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 17-21 2014)*

**Description**

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 co-organising 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 hands-one activities. There will be a 90-minute 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.