**Thesis Information**

**Title:** Intersection Patterns of Edges in Topological Graphs

**Adviser:** János Pach

**Institution:** École Polytechnique Fédérale de Lausanne

**Graduation Date:** May 2012

**Contact Information**

Email Candidate

Candidate Website

**Candidate Bio:**

I did my B.Sc. in CS at Comenius University, Bratislava, Slovakia, graduating in 2005; M.Sc. in CS at Simon Fraser University, Burnaby, BC, Canada, with Gábor Tardos, graduating in 2008; and PhD in Mathematics with János Pach at EPFL, Lausanne, Switzerland, graduating in 2012. I held postdoctoral research positions at EPFL (2012-13), Charles University, Prague, Czechia (2013), Columbia University, NYC (2013-2015), and IST Austria, Klosterneuburg, Austria (2015-2019). I joined University of Arizona as a postdoctoral research associate in September 2019.

**Research Summary:**

"The general area of my research is studying combinatorial properties of arrangements of basic geometric objects such as points, lines, polygons, polyhedra, discs, convex sets, etc., motivated mainly by computational problems. Closely related to this, I am interested in topological graph theory, which can be regarded as the study of arrangements of curves on a fixed set of endpoints.

I have worked on a variety of problems in combinatorial geometry and the theory of topological graphs.

My scientific achievements include the first algorithm with a polynomial running time for clustered planarity, and the confirmation of a conjecture of M. Skopenkov from 2003 and its weaker variant by A. Skopenkov and Repovs from 1998 extending the classical Hanani-Tutte theorem to the setting of approximating maps of graphs."

**Teaching Aims:**

Teaching and mentoring is one of the most important aspects of academic life and often one of the most rewarding ones. In my past teaching experience, I really enjoyed giving classes related to my research interests and lecturing about material that I wanted to better understand myself.

**Paper 1:**

Hugo A. Akitaya, Radoslav Fulek, Csaba D. Tóth: Recognizing Weak Embeddings of Graphs. SODA 2018: 274-292 (full version to appear in TALG)

Link to PDF**Paper 2:**

Z_2-Genus of Graphs and Minimum Rank of Partial Symmetric Matrices. SoCG 2019: 39:1-39:16

Link to PDF**Paper 3:**

Martin Balko, Radoslav Fulek, Jan Kynčl: Crossing Numbers and Combinatorial Characterization of Monotone Drawings of K_n . Discrete & Computational Geometry 53(1): 107-143 (2015)

Link to PDF**Keywords:** computational geometry, combinatorics, algorithms, algorithmic graph theory, optimization