### Fall 2020 update

I have very specific supervision plans for the next two academic years. I am currently **not** accepting any applications for undergraduate/graduate/postdoctoral research.

### Undergraduate students

If you are currently an undergrad student at UofM and would like to do some research project under my supervision, feel free to get in touch with me by email and include the following: list of math courses you completed with grades, any other relevant experience, ideas/preferences regarding the project. You are strongly encouraged to consider applying for an undergraduate summer research award.

### Potential graduate students (M.Sc. or Ph.D.)

If you are interested in pursuing a M.Sc. or Ph.D. degree under my supervision on a thesis topic related to my research interests (for M.Sc. this relation can be quite distant; for Ph.D. note that my research is of rather theoretical character, so if you have M.Sc. in applied mathematics, then you have to be ready for theoretical work and have excellent background), contact me by email and include the following: a brief descriptions of topics or specific research problems that interest you, an overview of any research experience you have, your curriculum vitae, your grade point average and a copy of your transcripts (in English). You might not get a reply if you do not follow the above guidelines.

You are encouraged to contact me as early as 12-24 months before your intended arrival to the UofM. Then, in case of mutual interest and agreement, we can work on a small research project which would be supervised remotely (for 3-12 months). If we are both satisfied with the outcome/workflow of that project, you would be able to apply formally in timely manner for graduate studies at the UofM.

Please visit the Graduate Studies section of the Department of Mathematics website for more information on application procedures and funding opportunities.

### Potential postdocs

PIMS postdoctorall fellowship is described here. It is rather mandatory that your research experience is close to my published work. Ideally we should complete a joint project before you apply.

### Some (hard) problems/directions that are of interest to me

#### Optimal meshes for convex domains

#### $L_1$ Bernstein inequality for hyperbolic cross

#### Mutually unbiased bases

#### Simplex conjecture

#### Whitney-type inequality for cubes

### Current trainees

- Mingyang Diao (MSc program) is working on a question in combinatorial geometry

### Former trainees

- Jiyoung Kim "Some properties of hyperbolic cross polynomials" (undergraduate research project, May - August 2020)
- Aseespal Singh Sehgal "Discretization of integral norms of hyperbolic cross polynomials in two dimensions" (undergraduate research project, May - August 2020)
- Olena Usoltseva Estimates of Christoffel function on multivariate domains (PhD thesis, 2019)
- Serhii Brodiuk and Nazar Palko [S. Brodiuk, N. Palko, A. Prymak,
*On Banach-Mazur distance between planar convex bodies*, Aequationes Mathematicae,**92**(2018) 993-1000 download (arXiv) view Springer's version through ReadCube] (undergraduate research project, February 2017 - March 2018) - Justin Roznik "Algorithmic construction of 3-monotone quadratic spline with fixed knots" (undergraduate research project, August 2017)
- Yuxiang Hu "On uniqueness of (175,72,20,36)-strongly regular graph" (undergraduate research project, May - August 2017)
- Patrick Naylor "Whitney constants for approximation by linear functions" (undergraduate research project, May 2014)
- Oleksandr Maizlish [O. Maizlish, A. Prymak,
*Convex polynomial approximation in R^d with Freud weights*, Journal of Approximation Theory,**192**(2015) 60--68 download (arXiv)] (postdoc, May - August 2014) - Danylo Radchenko Orientation preserving approximation (MSc thesis, 2012)
- Ivan Iurchenko Properties of extremal convex bodies (MSc thesis, 2012)