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Math Professor Awarded Fellowship At German University

Math Professor Awarded Fellowship At German University

Dr. Ivan Avramidi Will Spend Sabbatical At University of Bonn

SOCORRO, N.M. -- Tech professor Dr. Ivan Avramidi has been selected for a prestigious fellowship by the Alexander von Humboldt Foundation in Germany. The math professor will spend three months working with colleagues at the University of Bonn during the fall 2016 semester.

Avramidi will be collaborating with Professor Dr. Werner Mueller, with whom he has many common research interests in global analysis. Avramidi has a wide range of research interests in differential and spectral geometry, partial differential equations, mathematical physics, quantum field theory, quantum gravity and financial mathematics that overlap with many faculty of the University of Bonn.

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Dr. Ivan Avramidi

 

Avramidi works on the so-called “heat kernel” which is among the most important tools of global analysis, spectral geometry, differential geometry, mathematical physics and financial mathematics. It enables one to study the asymptotic properties of the spectrum of elliptic partial differential operators and their relation to the geometry of the underlying manifold.

“This is a central theme in geometric analysis and differential geometry,” he said. “In particular, the basic question of spectral geometry is: ‘To what extent does the spectrum of an elliptic partial differential operator determine the geometry of the underlying manifold?’, or, simply put: ‘Can one hear the shape of a drum?’ ”

Avramidi published a new book in late 2015 that delves into “heat kernel methods,” relating mathematics to the world of high finance. Heat Kernel Methods and Its Applications is intended for advanced undergraduate or beginning graduate students in physics and mathematics. The book also provides a useful reference for professional physicists and applied mathematicians, as well as for quantitative analysts and financial industry practitioners.

“I have been working in the field of mathematics pretty long, including publishing 60 papers on the subject,” he said. “But it was always tied to physics and math. As it turns out, in finance, they are using very similar techniques mathematically to solve certain equations that I am an expert in.”

Avramidi is an alumnus of the Humboldt Foundation. He was supported by the Foundation from 1994 to 1996, and is returning to initiate a new research collaboration with colleagues at the Mathematical Institute of the University of Bonn. The German institution is an internationally renowned center for mathematical research; it hosts the Hausdorff Center for Mathematics and the Max Planck Institute for Mathematics. The Humboldt Foundation has supported more than 27,000 scholars in its existence. Every year about 1,000 academicians earn fellowships – either foreigners to conduct research in Germany or Germans to conduct research abroad.

“Humboldt is a pretty major player in supporting science,” Avramidi said. “I speak German fluently, so I’m excited to go. This fellowship is only for alumni of Humboldt. They like these collaborations to continue so they sponsor this type of activities.”

Avramidi joined the New Mexico Tech faculty in 1999, achieving full professorship in 2005. He earned his Ph.D. at Moscow State University in 1987.

– NMT –