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, Japan, and South Africa. These collaborations create a thriving "virtual" institute in the mathematical and statistical sciences.

- 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 Africa:

The VI-MSS program includes joint conferences, workshops, and minicourses hosted both abroad and in the United States at these institutions. In addition, VI-MSS supports exchange visits for faculty, postdocs, and students between these institutions.

**Applications for U.S. based researchers to attend VI-MSS programs should apply here. **

**All applicants for VI-MSS visits to ICERM from our partner institutes in India are first processed at IISc, Bangalore.
Applicants from India should apply here.**

**Visitors from India whose visit has been approved should submit their ICERM applications here.**

(in Kolkata, India)

- Jeff Hoffstein

(ICERM, Brown University) - Jill Pipher

(ICERM, Brown University) - Bimal Roy

(Indian Statistical Institute)

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.
*

(in Bangalore, India)

- G. Rangarajan

(IISc, Bangalore) - Rajesh Rao

(University of Washington, Seattle)

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.

(in Bangalore, India)

- Manjunath Krishnapur

(Indian Institute of Science, Bangalore) - Kavita Ramanan

(Brown University, Providence)

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.