## Areas of Expertise (7)

## Biography

Income inequality in the United States continually fluctuates, but the large gap between rich and poor remains. Dr. Volpert has done extensive research on the variation in income inequality and the mathematical causes behind its rise and fall. An expert source on applied mathematics at the intersection of ﬁnance and economics, he is also an authoritative voice on the ways in which teachers can help students understand and use mathematics.

## Education (4)

#### University of Oregon: PhD

#### University of Oregon: MS

#### University of Oregon: MS

#### Universität Konstanz: Vordiplom

## Select Accomplishments (5)

#### Mathematical Association of America's 2013 Halmos-Ford Writing Award (professional)

2013-08-02

Awarded for article, "On the Mathematics of Income Inequality: Splitting the Gini Index in Two," co-authored with Robert T. Jantzen.

#### Crawford Award for Excellence in the Teaching of Mathematics (professional)

Regional section of the Mathematical Association of America, 2011.

#### Christian R. and Mary F. Lindback Award for Outstanding Teaching (professional)

2009

Villanova University's prestigious award annually recognizes a faculty member who excels in undergraduate teaching.

#### Founders Award for Service to the Graduate School of Arts and Sciences (professional)

Villanova University, 2006.

#### Bridgebuilder’s Award from the Learning Support Services at Villanova University (professional)

Awarded in recognition of support of students with learning differences, 2005.

## Links (1)

## Affiliations (1)

- Mathematics Association of America

## Select Media Appearances (1)

#### Just how big is 7 billion?

**CNN.com** online

2011-10-31

The global population is expected to reach 7 billion Monday -- just 12 years after hitting 6 billion -- and the milestone has many pondering the complex challenges associated with billions more people on Earth in the coming years.

Some are also pondering something else: Just how big is 7 billion really?

"The number is just outside of our usual everyday scale of thinking," said Klaus Volpert, an associate professor of mathematics at Villanova University. "We count to 10 on our fingers and that's our scale, you know? Even counting to a million is already kind of outside of the everyday experience. And then once you go past a million, it becomes a blur."

## Select Academic Articles (4)

**How Well Do Long-Term Bond Interest Rates Predict Stock Market Returns?**

*Journal of Investing*

Klaus Volpert

2013

We observe that over the last 50 years, long-term interest rates in the U.S. have had a remarkable record of predicting stock-market returns, specifically in the 16- to 17-year range. We quantify this phenomenon and test via standard models and Monte Carlo simulations whether such a phenomenon is likely to arise by chance. We show that the probability for that is small, but not negligible.

**On the Mathematics of Income Inequality: Splitting the Gini Index in Two**

*The American Mathematical Monthly*

Robert T. Jantzen and Klaus Volpert

December 2012 issue. Vol. 119, 2012, pp. 824-837

Income distribution is described by a two-parameter model for the Lorenz curve.

This model interpolates between self-similar behavior at the low and high ends of the income

spectrum, and naturally leads to two separate indices describing both ends individually. These

new indices accurately capture realistic data on income distribution, and give a better picture

of how income data is shifting over time.

**Finite spectral sequences and Massey powers in the deformation theory of graded Lie algebras and associative algebras**

*Journal of Pure and Applied Algebra*

Klaus Volpert

87, p. 281-300, 1993

**A Spectral Sequence Connecting the Spencer Cohomology of a Transitive Lie Algebra with is Deformation Cohomology**

*Algebras, Groups and Geometries*

Klaus Volpert

Vol 7, p. 313-344, 1990.