Kathryn Hess Bellwald
Fields of expertise
Applications of algebraic topology in computer science, neuroscience, cancer research, and chemical engineering.
Her research focuses on algebraic topology and its applications, primarily in the life sciences, but also in materials science. She has published extensively on topics in pure algebraic topology including homotopy theory, operad theory, and algebraic K-theory. On the applied side, she has elaborated methods based on topological data analysis for high-throughput screening of nanoporous crystalline materials, classification and synthesis of neuron morphologies, and classification of neuronal network dynamics. She has also developed and applied innovative topological approaches to network theory, leading to a powerful, parameter-free mathematical framework relating the activity of a neural network to its underlying structure, both locally and globally.
In 2016 she was elected to Swiss Academy of Engineering Sciences and was named a fellow of the American Mathematical Society and a distinguished speaker of the European Mathematical Society in 2017. In 2021 she gave an invited Public Lecture at the European Congress of Mathematicians. She has won several teaching prizes at EPFL, including the Crédit Suisse teaching prize and the Polysphère d’Or.
Publications and theses supervised
giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data ExplorationJournal Of Machine Learning Research. 2021-01-01.
Twisting structures and morphisms up to strong homotopyJournal Of Homotopy And Related Structures. 2020. DOI : 10.1007/s40062-019-00249-w.
Topological classification of microglia topological classification of microglia2019-07-01. 14th European Meeting on Glial Cells in Health and Disease (GLIA), Porto, PORTUGAL, Jul 10-13, 2019. p. E733-E733.
Topological classification of retinal microglia during development2019-07-01. Annual Meeting of the Association-for-Research-in-Vision-and-Ophthalmology (ARVO), Vancouver, CANADA, Apr 28-May 02, 2019.
Topological Analysis Enables Prediction Of Functional And Social Outcomes In Early Psychosis2019-04-01. Congress of the Schizophrenia-International-Research-Society (SRIS), Orlando, FL, Apr 10-14, 2019. p. S137-S137. DOI : 10.1093/schbul/sbz022.119.
Configuration Spaces Of ProductsTransactions Of The American Mathematical Society. 2019-02-15. DOI : 10.1090/tran/7617.
Two-Tier Mapper, an unbiased topology-based clustering method for enhanced global gene expression analysisBioinformatics. 2019-02-07. DOI : 10.1093/bioinformatics/btz052.
Injective And Projective Model Structures On Enriched Diagram CategoriesHomology Homotopy And Applications. 2019-01-01. DOI : 10.4310/HHA.2019.v21.n2.a15.
The Homotopy Theory Of Coalgebras Over Simplicial ComonadsHomology Homotopy And Applications. 2019-01-01. DOI : 10.4310/HHA.2019.v21.n1.a11.
Generating and identifying functional subnetworks within structural networksUS2018197069 . 2018.
A necessary and sufficient condition for induced model structuresJournal Of Topology. 2017. DOI : 10.1112/topo.12011.
Topological Analyses Of Metabolomic Data To Identify Markers Of Early Psychosis And Disease Biotypes2017. 16th International Congress on Schizophrenia Research (ICOSR), San Diego, CA, MAR 24-28, 2017. p. S211-S212.
The Boardman-Vogt tensor product of operadic bimodulesAlgebraic Topology: Applications and New Directions; 2014. p. 71-98.
Cobordism, Cohomology Theories and Formal Group Laws2011
Why H Z-algebra Spectra are Differential Graded Algebras?2010
A homotopy-equivalence between Cacti and Configuration Spaces2010
Twisting structures and strongly homotopy morphismsArXiv. 2010.
A general framework for homotopic descent and codescentArXiv. 2010.
Les groupes d'homotopie supérieurs et la longue suite exacte d'une fibration2009
Topics in Homological Algebra2009
Complex Topological K-theory2009
Algèbres de Hopf2008
Noeuds et invariants de Vassiliev2008
Théories d'homologie et de cohomologie généralisées2008
Rational homotopy theory: a brief introduction2007. University of Chicago, July 26-August 6, 2004. p. 175-202.
A chain coalgebra model for the James mapHomology, Homotopy and Applications. 2007.
Towards a general theory of homotopic Hopf-Galois extensions2006
An alpine anthology of homotopy theory. Proceedings of the 2nd Arolla conference on algebraic topology, Arolla, Switzerland, August 24-29, 2004. (English)2006
An algebraic model for mod 2 topological cyclic homologyString Topology and Cyclic Homology; Birkhäuser, 2006. p. 97-163.
String Topology and Cyclic HomologyBirkhäuser.
Simulations as homotopiesElectronic Notes in Theoretical Computer Science. 2004. DOI : 10.1016/j.entcs.2004.08.016.
Commutative free loop space models at large primesMathematische Zeitschrift. 2003. DOI : 10.1007/s00209-003-0206-y.
Using the topological characterization of synchronous modelsElectronic Notes in Theoretical Computer Science. 2003. DOI : 10.1016/S1571-0661(04)80834-X.
Teaching & PhD
Life Sciences Engineering
Doctoral Program in Mathematics
Doctoral Program in Neuroscience
Doctoral Program in Computational and Quantitative Biology