Dr.Dmitry Berdinsky

berdinsky

Lecturer

PhD in Computer Science: The University of Auckland, Auckland, New Zealand

Office :  B 207/2

Tel : 02-2201-5541

Fax : 0-2201-5343

Email : berdinsky@gmail.com

Links : HOMEPAGE

Research Activities

Areas of Expertise

Group theory; Differential Geometry

Current Interests and Activities

My research interests include, but not limited to, studying structures in low-dimensional spaces and their representations. The meaning of the term structure varies from minimal surfaces and metric structures to fundamental groups of three-manifolds and three-dimensional meshes. More specifically, my recent activities focus on: 

  1. Finite automata presentations of nonautomatic fundamental groups of three-manifolds and their qualitative and quantitative properties.
  2. Minimal and constant mean curvature surfaces in three-dimensional Thurston geometries.
  3. Splines over two-dimensional and three-dimensional box-meshes.

Depending on a particular problem, the study involves elements of group theory and automata theory, differential geometry and integrable systems, combinatorics and algebraic topology.  

EDUCATION

  • PhD in Computer Science: The University of Auckland, Auckland, New Zealand (2013 – 2016)
  • PhD in Mathematics: Sobolev Institute of Mathematics, Novosibirsk, Russian Federation (2006-2009)
  • Master of Science in Mathematics: Novosibirsk State University, Novosibirsk, Russian Federation (2004-2006)
  • Bachelor of Science in Mathematics: Novosibirsk State University, Novosibirsk, Russian Federation (2000-2004)

Publication

1.Berdinsky D., Taimanov I., “Surfaces in three-dimensional Lie groups” // Siberian Math. Journal 2005, V. 46. pp. 1005-1019

2. Berdinsky D., Taimanov I., “Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional” // Siberian Math. Journal 2007, V. 48. pp. 395-407

3. Berdinsky D. and Taimanov I. // Oberwolfach reports. 2007, V.4, N 2, pp. 1353–1358

4. Berdinsky D., “On some generalization of the Willmore functional for surfaces in SL2” // Siberian Electronic Mathematical Reports 2010, V. 7. pp. 140-149

5. Berdinsky D., “On constant mean curvature surfaces in the Heisenberg group” // Siberian Advances in Mathematics 2012, V. 22 N 2. pp. 75-79

6. Berdinsky D., Rybnikov I., “On orthogonal curvilinear coordinate systems in constant curvature spaces” // Siberian Math. Journal 2011, V. 52. pp. 394-401

7. Berdinsky D., “On minimal surfaces in the Heisenberg group” // Bulletin of Kemerovo State University 2011, V. 3/1 (47). pp. 34–38

8. Berdinsky D., Oh M., Kim T., Mourrain B., “On the problem of instability in the dimension of a spline space over a T-mesh” // Computers&Graphics 2012, V. 36 N. 5. pp. 507–513

9. Berdinsky D., Kim T., Bracco C., Cho D., Mourrain B., Oh M., Kiatpanichgij S., “Dimensions and bases of hierarchical tensor-product splines” // Journal of Computational and Applied Mathematics 2014, V. 257. pp. 86–104

10. Berdinsky D., Kim T., Bracco C., Cho D., Oh. M, Seo Y., Kiatpanichgij S., “Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness” // Computer-Aided Design 2014, V. 47. pp. 96-107

11. Bracco C., Berdinsky D., Cho D., Oh M., Kim T., “Trigonometric Generalized T-splines” // Computer Methods in Applied Mechanics and Engineering 2014, V. 268. pp. 540–556

12. Berdinsky D., Kim T., Cho D., Bracco C., Kiatpanichgij S., “Bases of T-meshes and the refinement of hierarchical B-splines” // Computer Methods in Applied Mechanics and Engineering 2015, V. 283. pp. 841-855

13. Berdinsky D., Khoussainov B., “On automatic transitive graphs” // A.M. Shur and M.V. Volkov (Eds.): Developments in Language Theory 2014 // Lecture Notes in Computer Science, V. 8633, p. 1-12

14. Berdinsky D., Khoussainov B., “Cayley automatic representations of wreath products” // International Journal of Foundations of Computer Science 2016, V. 27 N. 2. pp. 147-159

15. Berdinsky D., “Cayley automatic groups and numerical characteristics of Turing transducers” // S. Brlek and C. Reutenauer (Eds.): Developments in Language Theory 2016 // Lecture Notes in Computer Science, V. 9840, p. 26-37

16. Berdinsky D., Vyatkin Y.,”Willmore-like functionals for surfaces in 3-dimensional Thurston geometries”// to appear in Osaka Journal of Mathematics

17. Berdinsky D., Vyatkin Y.,”Willmore-like functionals for surfaces in 3-dimensional Thurston geometries” Osaka Journal of Mathematics 2017, V. 54 N. 1. pp. 75-83 

18.Berdinsky D., Trakuldit P. “Measuring Closeness Between Cayley Automatic Groups and Automatic Groups” In: Klein S., Martín-Vide C., Shapira D. (Eds.): Language and Automata Theory and Applications 2018. Lecture Notes in Computer Science, Springer, Cham // V. 10792, p. 245-257 

PROFESSIONAL EXPERIENCE

  • Lecturer, Mahidol University, Thailand, 2016 – present
  • Teaching Assistant, The University of Auckland, New Zealand, 2014 – 2015
  • Postdoctoral Fellow, Seoul National University, South Korea, 2011 – 2013
  • Research Fellow, Sobolev Institute of Mathematics, Russian Federation, 2009 – 2010
  • Teaching Assistant, Novosibirsk State University, Russian Federation, 2004 – 2011