# Mathematics doctoral student receives Heberlein Teaching Award

The mathematics department is proud to announce that WSU mathematics doctoral student, Mohammad Behzad Kang, has been awarded the 2022 Heberlein Teaching Award.

The Heberlein award honors graduate students for excellence in teaching. The Heberlein award is given quite selectively: Each year, between one and three graduate students across all of Wayne State University, are given the Heberlein award. Since the Heberlein award was first awarded in 1998, a mathematics student has received the Heberlein award three times: Tony Crachiola in 2001, Araz Hashemi in 2014, and Mohammad in 2022.

Mohammad graduated magna cum laude with his bachelor's degree in mathematics at WSU in 2018, and he graduated with an M.S. in Mathematics from WSU in 2019. Mohammad has been a graduate teaching assistant (GTA) since 2018 and has taught eight full classes at WSU, but Mohammad was already an experienced teacher before beginning as a GTA: Mohammad was an instructor in Math Corps during 2017 and 2018, an undergraduate teaching assistant in the Center for Excellence and Equity in Mathematics in 2014-2016, and during 2015-2017 he was a tutor in the Math Resource Center.

Mohammad's research is focused on algebraic topology. His doctoral thesis project focuses on proving a difficult conjecture which has been open since the 1970s. This conjecture is about a question that arises primarily in computations in algebraic topology, and which has some deep connections to number theory. Specifically, the conjecture is that the cohomology of the group of unitary n-by-n matrices agrees with the cohomology of the Morava stabilizer group with coefficients in the residue field of the ring of components of the Morava E-theory of a formal group law of height n.

In Mohammad's master's thesis, he made progress on proving this conjecture by translating it into a problem in Lie theory and approaching the problem using tools from the theory of Lie groups and Lie algebras. This approach hadn't been taken before, and it led to some insights and some progress on the conjecture. Mohammad's doctoral thesis, in progress, continues this approach using more novel ideas, particularly by adapting some methods of Deligne for solving problems in geometry, using those ideas to make certain calculations in the theory of Lie algebras rather than in geometry.

This is exciting work even with the progress on the conjecture Mohammad has already made, but it is also exciting because Mohammad's methods may be able to prove the conjecture completely by the time his doctoral thesis is finished. Alongside Mohammad's research in pure mathematics, Mohammad also has a continuing side project in applied topology: he is a co-author on a recently-submitted paper on statistical methods in topological data analysis of fMRI data.

Before the Heberlein award, Mohammad has been recognized with awards for excellence in scholarship: in 2019 Mohammad received the Janowitz award from the WSU mathematics department, in 2018 the first-place award in the WSU College of Liberal Arts and Sciences Undergraduate Research Fair, in 2018 the Robert and Nancy Irvan Endowed Scholarship in Mathematics, an AGRADE scholarship in 2018, and in 2017 and in 2018 (both years) Mohammad received the Outstanding Undergraduate Award. In 2018, Mohammad was the commencement speaker at WSU's graduation ceremonies.

Congratulations Mohammad, and thanks for your excellent teaching!