János Pach
Encyclopedia
János Pach is a mathematician
and computer scientist
working in the fields of combinatorics
and discrete and computational geometry
. He is a Distinguished Professor of Mathematics at CUNY, a Research Professor at the Courant Institute of Mathematics
at NYU, a Research Fellow of the Alfréd Rényi Institute of Mathematics
in the Hungarian Academy of Sciences
, and Professor of Mathematics at the École Polytechnique Fédérale de Lausanne
.
Pach was born and grew up in Hungary
. He comes from a distinguished family: his father, Zsigmond Pál Pach was a well known historian
, his uncle, Pál Turán
was one of the best known Hungarian mathematicians.
Pach received his Candidate degree from the Hungarian Academy of Sciences
, in 1983, where his advisor was Miklós Simonovits
. He received Grünwald Medal of the János Bolyai Mathematical Society
(1982), Ford Award from the Mathematical Association of America
(1990), and the Alfréd Rényi Prize
from the Hungarian Academy of Sciences
(1992). He authored several books and over 200 research papers, and was the program chair for the International Symposium on Graph Drawing
in 2004. Pach is editor-in-chief of the journal Discrete and Computational Geometry
. Pach was one of the most frequent collaborators of Paul Erdős
, authoring over 20 papers with him and thus has an Erdős number
of one.
Pach's research is focused in the areas of discrete geometry
and geometric graph theory
.
Some of Pach's most-cited research work concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning
problems, the maximum number of k-sets and halving lines
that a planar point set may have, crossing numbers of graphs
, and embedding of planar graph
s onto fixed sets of points.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and computer scientist
Computer scientist
A computer scientist is a scientist who has acquired knowledge of computer science, the study of the theoretical foundations of information and computation and their application in computer systems....
working in the fields of combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and discrete and computational geometry
Computational geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...
. He is a Distinguished Professor of Mathematics at CUNY, a Research Professor at the Courant Institute of Mathematics
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences is an independent division of New York University under the Faculty of Arts & Science that serves as a center for research and advanced training in computer science and mathematics...
at NYU, a Research Fellow of the Alfréd Rényi Institute of Mathematics
Alfréd Rényi Institute of Mathematics
The Alfréd Rényi Institute of Mathematics is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. Since its creation, the institute has been the center of mathematical research in Hungary. It received...
in the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
, and Professor of Mathematics at the École Polytechnique Fédérale de Lausanne
École polytechnique fédérale de Lausanne
The École polytechnique fédérale de Lausanne is one of the two Swiss Federal Institutes of Technology and is located in Lausanne, Switzerland.The school was founded by the Swiss Federal Government with the stated mission to:...
.
Pach was born and grew up in Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
. He comes from a distinguished family: his father, Zsigmond Pál Pach was a well known historian
Historian
A historian is a person who studies and writes about the past and is regarded as an authority on it. Historians are concerned with the continuous, methodical narrative and research of past events as relating to the human race; as well as the study of all history in time. If the individual is...
, his uncle, Pál Turán
Pál Turán
Paul Turán was a Hungarian mathematician who worked primarily in number theory. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting 46 years and resulting in 28 joint papers.- Life and education :...
was one of the best known Hungarian mathematicians.
Pach received his Candidate degree from the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
, in 1983, where his advisor was Miklós Simonovits
Miklós Simonovits
Miklós Simonovits is a Hungarian mathematician who currently works at the Rényi Institute of Mathematics in Budapest and is a member of the Hungarian Academy of Sciences. He is on the advisory board of the journal Combinatorica. He is best known for his work in extremal graph theory...
. He received Grünwald Medal of the János Bolyai Mathematical Society
János Bolyai Mathematical Society
The János Bolyai Mathematical Society is the Hungarian mathematical society, named after János Bolyai, a 19th century Hungarian mathematician, a co-discoverer of non-Euclidean geometry. It is the professional society of the Hungarian mathematicians, applied mathematicians, and mathematics teachers...
(1982), Ford Award from the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
(1990), and the Alfréd Rényi Prize
Alfréd Rényi Prize
The Alfréd Rényi Prize is awarded biannually by the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science in honor of founder Alfréd Rényi. By the current rules it is given to one or two fellows of the Institute in recognition of their outstanding performance in mathematics...
from the Hungarian Academy of Sciences
Hungarian Academy of Sciences
The Hungarian Academy of Sciences is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest.-History:...
(1992). He authored several books and over 200 research papers, and was the program chair for the International Symposium on Graph Drawing
International Symposium on Graph Drawing
The International Symposium on Graph Drawing is an annual academic conference in which researchers present peer reviewed papers on graph drawing, information visualization of network information, geometric graph theory, and related topics.-Significance:...
in 2004. Pach is editor-in-chief of the journal Discrete and Computational Geometry
Discrete and Computational Geometry
Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986, the journal publishes articles on in discrete geometry and computational geometry....
. Pach was one of the most frequent collaborators of Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, authoring over 20 papers with him and thus has an Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
of one.
Pach's research is focused in the areas of discrete geometry
Discrete geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles,...
and geometric graph theory
Geometric graph theory
In mathematics, a geometric graph is a graph in which the vertices or edges are associated with geometric objects or configurations. Geometric graph theory is a specialization of graph theory that studies geometric graphs...
.
Some of Pach's most-cited research work concerns the combinatorial complexity of families of curves in the plane and their applications to motion planning
Motion planning
Motion planning is a term used in robotics for the process of detailing a task into discrete motions....
problems, the maximum number of k-sets and halving lines
K-set (geometry)
In discrete geometry, a k-set of a finite point set S in the Euclidean plane is a subset of k elements of S that can be strictly separated from the remaining points by a line. More generally, in Euclidean space of higher dimensions, a k-set of a finite point set is a subset of k elements that can...
that a planar point set may have, crossing numbers of graphs
Crossing number (graph theory)
In graph theory, the crossing number cr of a graph G is the lowest number of edge crossings of a planar drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero.The concept originated in...
, and embedding of planar graph
Planar graph
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints...
s onto fixed sets of points.