Math at CMU Welcomes Two New Faculty Members

David Offner

David Offner joined the Department of Mathematical Sciences as an associate teaching professor in fall 2019. He received his Ph.D. from Carnegie Mellon and was most recently an associate professor at Westminster College in New Wilmington, Pennsylvania. Offner also previously served as a Shelly Visiting Associate Professor at Carnegie Mellon.

“I am interested in the structural properties of graphs,” Offner said about his research in the field of combinatorics. Graphs can be thought of as informal “networks” with nodes and connections, he notes, and
his research looks at questions such as how the large version of these networks can be decomposed into copies of smaller sub-networks, or how many of those connections in a network must be severed to remove all the copies of
a sub-network within it.

“Much of my work is related to questions in theoretical computer science and optimization that are also beautiful and challenging pure mathematics problems in their own right,” Offner said. “There are a number of easy to state conjectures in this field that nonetheless have proven hard to understand and will require new insights to solve.”

Several years ago, Offner organized a research collaboration to study the topic of polychromatic colorings of graphs.
In a paper published last year in the Journal of Combinatorics, Offner and his collaborators specifically looked at these colorings on hypercubes, geometric figures in four or more dimensions that are analogous to regular cubes in the three- dimensional world.

Offner has an impressive record as a mentor of undergraduate research projects. He has advised over 30 students who completed projects in the last few years, and many of these students went on to present their work at professional meetings or publish them in mathematics journals.

Outside of his research, Offner enjoys spending time with his wife and two children and coaching and watching sports of all kinds.

“I am excited to work with the talented and hard-working students at Carnegie Mellon and to interact and collaborate with brilliant colleagues,” Offner said.

Martin Larsson

Martin Larsson joined the Department of Mathematical Sciences as an associate professor in fall 2019. A native of Sweden, Larsson received his Ph.D. from Cornell University and was most recently an assistant professor at the Swiss Federal Institute of Technology in Zürich.

“My research is in mathematical finance,” Larsson said. “It’s about developing the mathematics needed to model phenomena that we see in financial markets and economic systems more broadly.”

Larsson said he found himself attracted to this area of mathematics because it blends theory with applications. “I get to talk to all kinds of people, from pure mathematicians to finance academics to bankers and regulators,” Larsson said, noting that his research touches on everything from interest rates to energy prices to models for volatility.

“Lots of interesting things pop up when you start to think about individuals that interact, often in a highly strategic manner, in an environment with lots of noise and randomness,” Larsson said. “And for the record: it’s not about predicting the stock market!”

An example of Larsson’s work is a study published in October 2019 in The Annals of Applied Probability titled “affine Volterra processes.” In it, Larsson and his collaborators developed a theory for a class of models that have become increasingly important for describing volatility, thus making them more practical to work with.

“These models are tricky to analyze because they lack various nice features that people are used to working with,” Larsson said. “We show that despite this, concrete computations are still possible in these more challenging models.”

“Carnegie Mellon exerts a strong pull on anyone doing research in mathematical finance,” Larsson said of what drew him to join the faculty here. Besides its research, Larsson also described Carnegie Mellon’s bachelor’s and master’s programs in computational finance as “trailblazers” in his field. “Being part of that is very exciting.”

Outside of his work, Larsson enjoys being outdoors with his wife and is looking forward to exploring the hiking opportunities around Pittsburgh, as well as its breweries, coffee shops and restaurants. “So far we’ve only begun to scratch the surface!” he said.