Daniela Kühn (born 1973) is a German mathematician and the Mason Professor in Mathematics at the

University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...

in Birmingham, England.Staff profile
University of Birmingham School of Mathematics, accessed 2012-09-12. She is known for her research in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, and particularly in extremal combinatorics and

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

Biography

Kühn earned the Certificate of Advanced Studies in Mathematics (

Cambridge Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. Origin In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate s ...

) from

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

in 1997 and a Diploma in Mathematics from the

Chemnitz University of Technology Chemnitz University of Technology () is a public university in Chemnitz, Germany. With around 8,300 students, it is the third largest university in Saxony. It was founded in 1836 as ''Königliche Gewerbschule'' (Royal Mercantile College) and ...

in 1999, followed by her doctorate from the

University of Hamburg The University of Hamburg (, also referred to as UHH) is a public university, public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('':de:Allgemeines Vorlesungswesen, ...

in 2001, under the supervision of Reinhard Diestel. After working as a postdoctoral researcher at Hamburg and the

Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...

, she moved to the

as a lecturer in 2004, and was awarded the

Mason Professorship Mason may refer to: Occupations * Mason, brick mason, or bricklayer, a worker who lays bricks to assist in brickwork, or who lays any combination of stones, bricks, cinder blocks, or similar pieces * Stone mason, a craftsman in the stone-cutti ...

of Mathematics in 2010.

Research

In 2004 Kühn published a pair of papers in ''

Combinatorica ''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science Computer science is the study of computation, information, and automation. Computer science spans Theore ...

'' with her thesis advisor, Reinhard Diestel, concerning the

cycle space In graph theory, a branch of mathematics, the (binary) cycle space of an undirected graph is the set of its even-degree subgraphs. This set of subgraphs can be described algebraically as a vector space over the two-element finite field. The dime ...

s of infinite graphs. In these graphs the appropriate generalizations of

cycles Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in ...

and

spanning tree In the mathematical field of graph theory, a spanning tree ''T'' of an undirected graph ''G'' is a subgraph that is a tree which includes all of the vertices of ''G''. In general, a graph may have several spanning trees, but a graph that is no ...

s hinge on a proper treatment of the

ends End, END, Ending, or ENDS may refer to: End Mathematics *End (category theory) *End (topology) *End (graph theory) *End (graph_theory)#Cayley_graphs, End (group theory) (a subcase of the previous) *End (endomorphism) Sports and games *End (gridir ...

of the graph. Reviewer

R. Bruce Richter R. or r. may refer to: * ''Reign'', the period of time during which an Emperor, king, queen, etc., is ruler * ''Rex (title), Rex'', abbreviated as R., the Latin word meaning King * ''Regina'', abbreviated as R., the Latin word meaning Queen regnan ...

writes that "the results are extremely satisfactory, in the sense that standard theorems for finite graphs have perfect analogues" but that "there is nothing simple about any aspect of this work. It is a nice mix of graph-theoretic and topological ideas." In 2011, Kühn and her co-authors published a proof of

Sumner's conjecture Sumner's conjecture (also called Sumner's universal tournament conjecture) is a conjecture in extremal graph theory on oriented trees in tournaments. It states that every orientation of every n-vertex tree is a subgraph of every (2n-2)-vertex tou ...

, that "every ''n''-vertex

polytree In mathematics, and more specifically in graph theory, a polytree (also called directed tree, oriented tree; . or singly connected network.) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, a polytree is form ...

forms a subgraph of every (2''n'' − 2)-vertex

tournament A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses: # One or more competitions held at a single venue and concen ...

", for all but finitely many values of ''n''.

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

reviewer K. B. Reid wrote that their proof "is an important and welcome development in tournament theory".

Awards and honours

In 2002, Kühn won the Richard Rado Prize, a biennial best dissertation award given by the Section for Discrete Mathematics of the

German Mathematical Society The German Mathematical Society (, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in ...

. Together with Deryk Osthus and Alain Plagne, she was one of the first winners of the

European Prize in Combinatorics The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarde ...

in 2003. Together with Osthus, she was a recipient of the 2014

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehe ...

of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

for "their many results in extremal graph theory and related areas. Several of their papers resolve long-standing open problems in the area." She was an Invited Speaker at the 2014

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

, in

Seoul Seoul, officially Seoul Special Metropolitan City, is the capital city, capital and largest city of South Korea. The broader Seoul Metropolitan Area, encompassing Seoul, Gyeonggi Province and Incheon, emerged as the world's List of cities b ...

. and appointed as a

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

Wolfson Research Merit Award The Royal Society Wolfson Fellowship, known as the Royal Society Wolfson Research Merit Award until 2020, is a 5 years fellowship awarded by the Royal Society since 2000. The scheme is described by the Royal Society as providing ''long-term flexib ...

holder in 2015. She was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 2024.

References

{{DEFAULTSORT:Kuhn, Daniela Living people 21st-century German mathematicians Graph theorists University of Hamburg alumni Academics of the University of Birmingham Whitehead Prize winners 1973 births Royal Society Wolfson Research Merit Award holders 21st-century German women mathematicians Fellows of the Royal Society