Krener Assistant Professor
Department of Mathematics
University of California, Davis
One Shield Avenue, Davis, CA, 95616
Office: MSB 2149
My research interests span between Low-dimensional Topology, Hyperbolic Geometry and Comutational Geometry. My mentor at UCD is Prof. Joel Hass. Here is my CV. I mainly work on problems related to hyperbolic 2- and 3-manifolds: their triangulations and lengths spectra. I am also interested in mesh generation algorithms for 2D surfaces which are theoretically rigorous and practical for implementations. In my research I use computer programs Mathematica, Snap, SnapPea, SnapPy, Regina, Sage, Python and MeshLab.
University of California, Davis, USA, Krener Assistant Professor, 2016 - now
California Institute of Technology, USA, Instructor, 2014
Palacky University, Czech Republic, PhD in mathematics, 2012
Princeton University, USA, Visiting Student Researcher, 2008-2011
Kazan State University, Russia, MS in Mathematics, 2007
Glazov State Pedagogical Institute, Russia, B.C. in Pedagogy of Mathematics, 2003
(Summa Cum Laude)
Publications and Preprints
1. Spun triangulations of closed hyperbolic 3-manifolds, (with M.Goerner, F.Luo), to appear.
2. Verified computations of Length spectrum for hyperbolic 3-manifolds (with R.Haraway, N.Hoffman, M.Goerner), to appear.
3. Approximate surfaces in R^3 by meshes of guaranteed regularity (with J.Hass), preprint (2019).
4. Hyperbolic Flowers, submitted, arxiv:1910.05900.
5. Rigorous computations with an approximate Dirichlet domain, Topology and its Applications, Vol. 268 (2019), 106900.
6. Quadratic differentials, measured foliations and metric graphs on the punctured plane, (with K.Diaz, S.Gupta), submitted, arxiv: 1803.09198.
7. Exceptional hyperbolic three-manifolds, (with D.Gabai), Commentarii Mathematici Helvitici, Vol. 90, 3 (2015), 703-730.
8. Two Models of Non-Euclidean Spaces Generated by Algebras, Acta Univ. Carolina, Vol. 51, 2 (2010), 37-48.
9. The projectivisation of conformal model of non-Euclidean sphere fiber bundle by double numbers, Proceedings of Laptev geometry conference, Penza (2007), 37-43.
10. The projectivisation of conformal model of noneuclidian sphere fiber bundle Proceedings of Lobachevsky conference, Kazan (2006), 84-86
Package MidNormal for Python (with Joel Hass)
Package Ortholines for Mathematica (with David Gabai)
Jinyi Zhou, undergraduate student at UC Davis, 2018-2019
Alex Henny, undergraduate student at Caltech, 2014
Grants, Honors & Awards
Robert Bartnik Visiting Fellowship, Monash University, Australia, 2016
GEAR Network award for short-term visit to Institut Fourier, Grenoble, France, 2016
GEAR Network award for short-term visit to IAS, Princeton, 2015
AWM Mathematics Mentoring Travel Grant, 2015
Visiting Research fellowship, Princeton University, USA, 2009
Student Scholarship from the President of Udmurt Republic, Russia, 2002
- UC Davis
Fall 2019: MAT 21B Integral Calculus
Spring 2019: MAT 21B Integral Calculus
Winter 2019: MAT 111 History of Mathematics
Fall 2018: MAT 17B Calculus for Bio Science
Spring 2018: MAT 125B Real Analysis
Winter 2018: MAT 111 History of Mathematics
Winter 2016: MAT 21B Integral Calculus
Fall 2014: Riemannian Geometry
Spring 2014: Topics in Low Dimensional Topology
Winter 2014: Differential Geometry and Topology
David Gabai, Princeton University
Joel Hass, University of California, Davis
Feng Luo, Rutgers University
Nina Amenta, University of California, Davis
Monica Vazirani, University of California, Davis (teaching)