Maria Trnkova


Krener Assistant Professor

Department of Mathematics

University of California, Davis

One Shield Avenue, Davis, CA, 95616

Email: mtrnkova(at)math(dot)ucdavis(dot)edu

Office: MSB 2149


Research

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. 


Academic Positions

University of California, Davis, USA, Krener Assistant Professor, 2016 - now 

California Institute of Technology, USA, Instructor, 2014


Education

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 


Computer codes

Package MidNormal for Python (with Joel Hass) 

Package Ortholines for Mathematica (with David Gabai) 


Mentoring

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 


Teaching

- 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

- Caltech

Fall 2014: Riemannian Geometry

Spring 2014: Topics in Low Dimensional Topology

Winter 2014: Differential Geometry and Topology


References

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)