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by Sharon Guynup
Again this winter and spring, some of the world’s most creative and original mathematical minds will gather weekly to share ideas and brainstorm over concepts and equations. It’s an elite group that speaks a language incomprehensible to nearly anyone outside their field.
In recent years, mathematicians like Stevens’ Alexei Miasnikov have been increasingly active in attempts to solve complex computational problems in groups.
As a consultant to Stevens, Miasnikov made a novel suggestion to mathematics professor Bob Gilman some years back: form a center to bring interested mathematicians together around new mathematical techniques for practical problems in cryptography. His idea sparked the creation of the Algebraic Cryptography Center (ACC) four years ago – where Miasnikov came on board as the newest staff member and Distinguished Professor of Mathematics in October.
But these weekly lectures and discussions are not convened at the Center, or even in Hoboken: They are convened virtually, in cyberspace. This online seminar, like the ACC, is the brainchild of Miasnikov and his young colleagues Alex Myasnikov and Alexander Ushakov, and is a kind of synaptical networking for a growing, international cadre of mathematicians.
Although the Center has formal collaborations with Moscow State University, Passau University, and a handful of others to exchange grad students and bring in a stream of collaborators from other institutions, Miasnikov wanted to further link top mathematical minds—across oceans and continents. He envisioned a series of weekly lectures on the web, creating a forum for the global community of mathematicians to share ideas and communicate on a regular basis.
The seminar launched on an experimental basis last April, with three lectures given live on the Internet. These first presenters hailed from three continents, with lectures by mathematician Murray Elder from Queensland University, Andrew Duncan, a “reader in algebra” at Newcastle University, and Alexander Ushakov, a member of the Algebraic Cryptography Center.
Participants huddle over computers, logging in alone or in groups from their offices, classrooms, or living rooms. Stevens’ Wimba web technology, an advanced e-learning system, allows viewers to physically participate in a number of ways. Most important among them is the ability to inject comments and ask questions. The software also has an eBoard function that allows viewers to add to or alter equations posted by the week’s lecturer.
“It’s like a musical jam,” says Gilman. But it seems that this “jam” has grown into an orchestra. Audiences of up to 60 people gather online for each lecture from across the globe, hailing from four continents, Europeans, Australians, Russians, Americans and Canadians. In some cases, groups of professors gather in groups or convene a group of students or an entire class across rolling time zones from Australia and Russia to Europe, the U.S. and Canada. It’s toughest on the Australians who tune in; sometimes the seminar kicks off at 11:00 p.m. or even midnight their time.
Over the fall, the series continued with 10 lectures by some of the world’s preeminent math scholars, representing the University of Geneva, Vanderbilt University, the University of Bordeaux, Stevens, McGill University, Russia’s Steklov Institute of Mathematics, and more. Some are theoretical mathematical talks. Others deal with practical problems. For example the schedule for this spring includes a series of talks on postquantum cryptography. Cryptography has historically dealt with written communications but now is used to safeguard data transmission. Encrypted systems, for example, protect your ATM card so someone can’t empty your bank account, protect e-commerce and allow classified government or military information to be transmitted safely. These encryption systems are based on computational problems thousands of digits long.
The problem is that lightning-fast, powerful quantum computers will be able to crack encryption codes that are currently in use. While the quantum computing field is still in its infancy, both government and military agencies are funding its research. With quantum computers on the horizon, there is a pressing need for deeply complex mathematical problems that could be used to build new cryptographic systems to protect them. This abstract mathematic approach is new to the field of cryptography, and trying to find a new mathematical basis for safe encryption is the focus of the Algebraic Cryptography Center’s research. Miasnikov notes that no single mathematical discipline can do this alone – it requires experts proficient in algebra, statistics , number theory, computer science, and more – a lot of deep math to play with. He’s also shown that determining the complexity and therefore, the reliability of the so-called “crypto primitives” that might form the basis for a new, ironclad data encryption system is best done as a group.
But the online series steps beyond cryptography to include lectures in many areas of theoretical mathematics. This spring, the Center will work to fine-tune the interactive visual potential, possibly adding video conferencing – and will move towards building a more focused series of talks. The e-learning system also offers the potential for small groups to convene in breakout rooms, a possibility that is under consideration.
Gilman notes that mathematics inquiry used to be a solitary endeavor, working alone with pencil and paper, with very few individuals working in specific areas of the field. But, he says, “The world has changed a lot since then.”
This lecture series is another step towards building a network of mathematicians with diverse interests, a group that ACC faculty hope will build new, global collaborations over joint projects, solving nearly unsolvable problems.