Kathryn Pamela Hess (born 1967) is an American mathematician who has served as professor of mathematics at

École Polytechnique Fédérale de Lausanne École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

(EPFL) since 1999. She is known for her work on

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

, and

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

, both pure and applied. In particular, she applies the methods of algebraic topology to the study of

neurology Neurology (from el, wikt:νεῦρον, νεῦρον (neûron), "string, nerve" and the suffix wikt:-logia, -logia, "study of") is the branch of specialty (medicine), medicine dealing with the diagnosis and treatment of all categories of co ...

, cancer biology, and materials science. She is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Life

Kathryn Hess was born 21 September 1967 in

Bryn Mawr, Pennsylvania Bryn Mawr, pronounced , from Welsh for big hill, is a census-designated place (CDP) located across three townships: Radnor Township and Haverford Township in Delaware County, and Lower Merion Township in Montgomery County, Pennsylvania. It i ...

. She began to accelerate in mathematics in 1979, thanks to the Mathematical Talent Development Project (MTDP) set up in

Eau Claire, Wisconsin Eau Claire (; ) (French for "clear water") is a city mostly located in Eau Claire County, Wisconsin, of which it is the county seat, and with a small portion in Chippewa County, Wisconsin. It had a population of 69,421 in 2020, making it the stat ...

, by her parents, through the Association for High Potential Children, which they also founded. Both programs are currently defunct. Hess earned a BSc with honors in mathematics from the

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

in 1985. She received her doctorate in mathematics from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

in 1989 under the direction of . Her dissertation was entitled ''A Proof of Ganea's Conjecture for Rational Spaces''.

Work

Hess has worked and written extensively on topics in

including

, model categories and

algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense o ...

. She has also used the methods of algebraic topology and

to investigate homotopical generalizations of

descent theory In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology. Since the topologists' glue is the use of equivalence relations on topological spaces, the theory starts with some ideas on identification. Descent of vecto ...

and Hopf–Galois extensions. In particular, she has studied generalizations of these structures for

ring spectra In stable homotopy theory, a ring spectrum is a spectrum ''E'' together with a multiplication map :''μ'': ''E'' ∧ ''E'' → ''E'' and a unit map : ''η'': ''S'' → ''E'', where ''S'' is the sphere spectrum. These maps have to satisfy a ...

and

differential graded algebra In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. __TOC__ Definition A differential graded alg ...

s. She has more recently used algebraic topology to understand structures in

and materials science. As of March 2022, she has been the principal academic advisor for 14 mathematics PhDs at EPFL, including 4 women.

Awards and honors

In addition to her strong publication record, Hess has been widely recognized for her pedagogical abilities. She received the Agepoly prize for best teacher in the Basic Sciences Faculty in 2005, the Credit Suisse prize for best EPFL teacher in 2012, and the "Polysphere d'Or" Agepoly prize for best teacher at EPFL in 2013.https://www.epfl.ch/labs/hessbellwald-lab/wp-content/uploads/2018/10/CV_0416.pdf She was named an individual member of the Swiss Academy of Engineering Sciences in 2016 and a fellow of the

for "contributions to homotopy theory, applications of topology to the analysis of biological data, and service to the mathematical community" in 2017. In 2017, she received an award as a distinguished speaker of the

European Mathematical Society The European Mathematical Society (EMS) is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians. The current ...

. She delivered one of the public lectures during the Eighth European Congress of Mathematics on 21 June 2021.

Selected publications

References

External links

Videos.

Women Inspire Innovation: Kathryn Hess Bellwald, EPFL
{{DEFAULTSORT:Hess, Kathryn Living people Fellows of the American Mathematical Society 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Topologists École Polytechnique Fédérale de Lausanne faculty Massachusetts Institute of Technology School of Science alumni People from Bryn Mawr, Pennsylvania Mathematicians from Pennsylvania 1967 births 20th-century women mathematicians 21st-century women mathematicians University of Wisconsin–Madison College of Letters and Science alumni 20th-century American women 21st-century American women