Embracing complexity

Jul 30, 2010

Mathematicians from more than a dozen countries will gather at Case Western Reserve University next week to discuss the theoretical world of high dimensions.

While we live in a three-dimensional world, in this discipline, mathematicians work with thousands, millions, billions of dimensions - even dimensions approaching infinity.

The conference, Aug. 2-6, is the culminating event of a three-year National Science Foundation Focused Research Group grant, led by Stanislaw Szarek and Elisabeth Werner, CWRU mathematics professors. Other institutions participating in the project are Kent State University, the University of Michigan and the University of Missouri. The funding, in the amount of $1.4 million, is being used primarily to facilitate interaction among the researchers at the participating institutions and to support graduate students in this subfield of mathematics.

For Werner, mathematics provides the basis for expressing abstract contents: mathematicians develop a language that allows them to express the thinking process in a precise form.

The title of the conference "Perspectives in High Dimensions" refers to a relatively new area in mathematics, "Asymptotic Geometric Analysis." In applications, if dimension represents a parameter of a system or phenomenon; high dimensionality appears because "real world" phenomena are and cannot be fully described by just a few numbers.

In general, as dimension increases, the difficulty of sampling and computation go up rapidly, a phenomenon scientists and mathematicians sometimes call "the curse of dimensionality." However, there are also patterns that emerge as dimension increases, and this is exactly what Asymptotic Geometric Analysis investigates.

For example, as dimension increases, a geometrical structure does not necessarily become more chaotic, but often regularity emerges, explain Elizabeth Meckes and Mark Meckes, CWRU math professors and members of the local conference organizing committee. One might even talk about the "blessing of dimensionality."

Over the last several years, this area of has grown rapidly and the methods developed there have found many applications: from facial recognition computer programs to quantum computing, statistics to probability.

Next week, researchers and students will hear speakers from around the world present their findings on the geometry of high-dimensional spaces, properties of large matrices, modeling complex sensor networks, methods of reducing the high dimensionality of data and analyzing the information, and much more.

Explore further: 'Moral victories' might spare you from losing again

add to favorites email to friend print save as pdf

Related Stories

Math institute gets largest NSF grant ever

Jul 20, 2005

The Institute for Mathematics and its Applications in Minnesota has received the largest math research grant ever made by the National Science Foundation.

Spacetime May Have Fractal Properties on a Quantum Scale

Mar 25, 2009

(PhysOrg.com) -- Usually, we think of spacetime as being four-dimensional, with three dimensions of space and one dimension of time. However, this Euclidean perspective is just one of many possible multi-dimensional ...

Who cares about the fourth dimension?

Feb 03, 2009

Austrian scientists are trying to understand the mysteries of the holographic principle: How many dimensions are there in our universe?

Recommended for you

Narcissistic CEOs and financial performance

5 hours ago

Narcissism, considered by some as the "dark side of the executive personality," may actually be a good thing when it comes to certain financial measures, with companies led by narcissistic CEOs outperforming those helmed ...

Election surprises tend to erode trust in government

6 hours ago

When asked who is going to win an election, people tend to predict their own candidate will come out on top. When that doesn't happen, according to a new study from the University of Georgia, these "surprised losers" often ...

User comments : 2

Adjust slider to filter visible comments by rank

Display comments: newest first

BloodSpill
not rated yet Jul 31, 2010
Blessings and curses of working in really high numbers (in this case, dimensions).

Mathematicians sure are boring!
frajo
1 / 5 (1) Jul 31, 2010
Mathematicians sure are boring!
Then why do you pay attention?