Jennifer Carol Schultens (born 1965) is an American mathematician specializing in

low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot th ...

and

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

. She is a professor of mathematics at the

University of California, Davis The University of California, Davis (UC Davis, UCD, or Davis) is a public land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the University of California system. The institut ...

Education

Schultens earned her Ph.D. in 1993 at the

University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, Santa Barbara, California with 23,196 undergraduate ...

. Her dissertation, ''Classification of Heegaard Splittings for Some Seifert Manifolds'', was supervised by Martin Scharlemann.

Research

Schultens is the author of the book '' Introduction to 3-Manifolds'' (

Graduate Studies in Mathematics Graduate Studies in Mathematics (GSM) is a series of graduate-level textbooks in mathematics published by the American Mathematical Society (AMS). The books in this series are published ihardcoverane-bookformats. List of books *1 ''The General To ...

, 2014). With Martin Scharlemann and Toshio Saito, she is a co-author of ''Lecture Notes On Generalized Heegaard Splittings'' (World Scientific, 2016). Her dissertation research involved the classification of

Heegaard splitting In the mathematical field of geometric topology, a Heegaard splitting () is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Definitions Let ''V'' and ''W'' be handlebodies of genus ''g'', and ...

s of three-dimensional manifolds into handlebodies, which she also published in the

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

. Other topics in her research include the behavior of

knot invariant In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some i ...

s like

bridge number In the mathematical field of knot theory, the bridge number is an invariant of a knot defined as the minimal number of bridges required in all the possible bridge representations of a knot. Definition Given a knot or link, draw a diagram of the ...

when knots are combined by the

connected sum In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classifi ...

operation, and the Kakimizu complexes of knot complements and other spaces.

Personal

Schultens is married to mathematician

Michael Kapovich Michael Kapovich (also ''Misha Kapovich'', Михаил Эрикович Капович, transcription Mikhail Erikovich Kapovich, born 1963) is a Russian-American mathematician. Kapovich was awarded a doctorate in 1988 at the Sobolev Institute o ...

References

External links

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* {{DEFAULTSORT:Schultens, Jennifer 1965 births Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Topologists University of California, Santa Barbara alumni University of California, Davis faculty 20th-century American women 21st-century American women