Currently I work as a Lecturer at UC San Diego.
I did my PhD at EPFL in Discrete and Combinatorial Geometry under the supervision of Janos Pach.
My general research interests are mostly in the area of discrete and combinatorial geometry. In particular, I am interested in topological graphs and combinatorial properties of arrangements of basic geometric objects such as points, lines, polygons, polyhedra, discs, convex sets etc.
July 2020 - Present
I joined UCSD as a lecturer at the department of mathematics.
September 2019 - September 2020
I joined University of Arizona as a postdoctoral researcher hosted by Stephen Kobourov.
July 2017 - June 2019
I was working in the group of Uli Wagner on eliminating intersections in drawings of graphs.
March 2015 - June 2017
I joined IST Austria as an IST Fellow affiliated with the group of Uli Wagner.
September 2013 - February 2015
During my research stay at Columbia I was hosted by Maria Chudnovsky. The stay was funded by Early Postdoc.Mobility Grant of Swiss National Science Foundation with the project on Arrangements of Geometric Objects and Topological Graphs.
February 2013 - August 2013
During this research stay I was hosted by Jan Kratochvil.
May 2012 - January 2013
During this research stay I was hosted by Janos Pach.
Atomic Embeddability, Clustered Planarity, and Thickenability (with C. Toth)
Counterexample to an Extension of the Hanani–Tutte Theorem on the Surface of Genus 4 (with J. Kyncl)
Recognizing Weak Embeddings of Graphs (with H. Akitaya and C. Toth)
Crossing Numbers and Combinatorial Characterization of Monotone Drawings of K_n (with M. Balko and J. Kyncl)
Intersecting Convex Sets by Rays (with A. Holmsen and J. Pach)
Joint work with Csaba TothJournal of Combinatorial Optimization 2020
Joint work with Hugo Akitaya and Csaba TothACM Transactions on Algorithms 2019
Joint work with Jan KynclCombinatorica 2019
Joint work with Steven Chaplick and Pavel KlavikJournal of Graph Theory 2019
Joint work with Marcus Schaefer and Michael PelsmajerJ. Graph Algorithms Appl. 2017
Joint work with Jan Kyncl, Igor Malinovic and Domotor PalvolgyiElectr. J. Comb. 2015
Joint work with many peopleDiscrete and Computational Geometry 2015
Joint work with Martin Balko and Jan KynclDiscrete and Computational Geometry 2015
Joint work with Balazs Keszegh, Filip Moric and Igor UljarevicGraphs and Combinatorics 2013
Joint work with Fabrizio Frati and Andres Ruiz-VargasJ. Graph Algorithms Appl. 2013
Joint work with Emilio Di Giacomo, Fabrizio Frati, Luca Grilli and Marcus KrugComputational Geometry 2013
Joint work with Eyal Ackerman and Csaba TothSIAM J. Discrete Math. 2012
Joint work with Karin Arikushi, Balazs Keszegh, Filip Moric, and Csaba TothComputational Geometry 2012
Joint work with Andrew SukThirty Essays on Geometric Graph Theory, J. Pach ed., 2012
Joint work with Marcus Schaefer, Michael Pelsmajer and Daniel StefankovicThirty Essays on Geometric Graph Theory, J. Pach ed., 2012
Joint work with Noushin Saeedi and Deniz SariozThirty Essays on Geometric Graph Theory, J. Pach ed., 2012
Joint work with Michael Pelsmajer, Marcus Schaefer and Daniel StefankovicJ. Graph Algorithms Appl. 2012
Joint work with Janos PachComputational Geometry 2011
Joint work with many peopleElectr. J. Comb. 2010
Joint work with Filip Moric and David PritchardDiscrete Mathematics 2010
Joint work with Andreas Holmsen and Janos PachDiscrete and Computational Geometry 2009
Joint work with Alon Efrat, Stephen Kobourov and Csaba TothGD 2020
Joint work with Bernd Gaertner, Andrey Kupavskii, Pavel Valtr and Uli WagnerSOCG 2019
Joint work with Jan KynclSOCG 2019
Joint work with Rados RadoicicGD 2015
Joint work with Andres Ruiz-VargasSoCG 2013
Joint work with Hongmei He, Ondrej Sykora and Imrich VrtoSOFSEM 2005
The purpose of the proposed project is two-fold. On the one hand, we aim to develop mathematical tools helpful in the design of fast graph drawing algorithms that minimize the number of edge crossings, under additional constraints. Our approach is based crucially on the Hanani-Tutte paradigm which reduces the detection of the existence of the desired crossing-free drawing of a graph to the algebraic problem of solving a system of linear equations. For this problem provably fast algorithms exist. On the other hand, along the way we intend to address several fundamental open problems about higher dimensional analogs of graphs, and graphs drawn in the plane and on more complicated surfaces, whose resolution would likely have a large impact on the area of graph/network visualization, as well as on the area of combinatorial and computational geometry.