We are pleased to inform you that Mr. Mikhail Karpukhin, a PhD student in mathematics at McGill University, is the 2018 recipient of the Carl Herz Prize.
Mikhail Karpukhin is completing his Ph.D. studies under the supervision of Dmitry Jakobson and Iosif Polterovich. Previously, he was a student of Alexei Penskoi at Moscow State University and the Independent University of Moscow.
Mikhail works in spectral geometry and has authored six journal publications as well as two preprints. His Ph.D. thesis is concerned with the eigenvalue bounds for Laplace and Dirichlet-to-Neumann operators on Riemannian manifolds. His most important result up-to-date is probably an isoperimetric inequality for the first Laplace eigenvalue on non-orientable surfaces, which extends the celebrated bounds obtained by Yang-Yau and Li-Yau in the early 1980s. Mikhail has also established the best currently known explicit isoperimetric inequalities for Steklov eigenvalues on surfaces. His other contributions include the study of Dirichlet-to-Neumann operators on differential forms, multiplicity estimates for Steklov eigenvalues on surfaces and results on extremal metrics for Laplace eigenvalues on spheres, tori and Klein bottles.
Throughout his studies at McGill University, Mikhail was supported by Tomlinson and Schulich graduate scholarships. In a few months, Mikhail is expected to start a three-year Visiting Assistant Professorship at the University of California at Irvine.
The Carl Herz Prize recognizes a research contribution made by a doctoral student registered at one of the ISM universities whose supervisor is a member of an ISM scientific group. The $4,000 cash prize is accompanied by a $1,000 travel grant, allowing the recipient to present his or her research at a conference. This year’s Selection Committee consisted of Virginie Charette (Université de Sherbrooke), Damir Kinzebulatov (Laval), Giovanni Rosso (Concordia), Yvan Saint-Aubin (Université de Montréal) and Russell Steele (McGill).