Kathryn Hess Bellwald
Full Professor
kathryn.hess@epfl.ch +41 21 693 42 45 http://hessbellwald-lab.epfl.ch
Citizenship: Swiss
EPFL SV BMI UPHESS
MA B3 454 (Bâtiment MA)
Station 8
CH-1015 Lausanne
+41 21 693 42 45
+41 21 693 75 75
Office:
MA B3 454
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Web site: Web site: https://hessbellwald-lab.epfl.ch
EPFL AVP-SAO GE
CE 1 631 (Centre Est)
Station 1
CH-1015 Lausanne
+41 21 693 42 45
Office:
CE 1 631
EPFL
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CH-1015 Lausanne
+41 21 693 42 45
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MATH-DIV
Web site: Web site: https://math.epfl.ch/
Fields of expertise
Homotopy theory, category theory.
Applications of algebraic topology in computer science, neuroscience, cancer research, and chemical engineering.
Applications of algebraic topology in computer science, neuroscience, cancer research, and chemical engineering.
Biography
Kathryn Hess Bellwald received her PhD from MIT in 1989 and held positions at the universities of Stockholm, Nice, and Toronto before moving to the EPFL.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
Infoscience publications
Publications and theses supervised
From trees to barcodes and back again II: Combinatorial and probabilistic aspects of a topological inverse problem
Computational Geometry. 2024. DOI : 10.1016/j.comgeo.2023.102031.Dynamics of CLIMP-63 S-acylation control ER morphology
Nature Communications. 2023-01-17. DOI : 10.1038/s41467-023-35921-6.Of mice and men: Increased dendritic complexity gives rise to unique human networks
2023Neuroengineering of hallucinations through fMRI neurofeedback: Understanding and modulating neural dynamics for the control of hallucinations in health and disease
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-9439.Longitudinal evaluation of the mechanisms supporting post-stroke motor recovery using TMS-EEG coupling
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-9626.Preface
Foundations Of Data Science. 2022-12-01. DOI : 10.3934/fods.2022021.A tool for mapping microglial morphology, morphOMICs, reveals brain-region and sex-dependent phenotypes
Nature Neuroscience. 2022-09-30. DOI : 10.1038/s41593-022-01167-6.A Shadow Perspective on Equivariant Hochschild Homologies
International Mathematics Research Notices. 2022-09-21. DOI : 10.1093/imrn/rnac250.Intact Drosophila central nervous system cellular quantitation reveals sexual dimorphism
Elife. 2022-07-08. DOI : 10.7554/eLife.74968.Computational tools for twisted topological Hochschild homology of equivariant spectra
Topology And Its Applications. 2022-07-01. DOI : 10.1016/j.topol.2022.108102.Evaluation of individual and ensemble probabilistic forecasts of COVID-19 mortality in the United States
Proceedings Of The National Academy Of Sciences Of The United States Of America. 2022-04-12. DOI : 10.1073/pnas.2113561119.Computational synthesis of cortical dendritic morphologies
Cell Reports. 2022-04-05. DOI : 10.1016/j.celrep.2022.110586.A Künneth theorem for configuration spaces
Journal of the London Mathematical Society. 2022-02. DOI : 10.1112/jlms.12536.Modeling and simulation of rat non-barrel somatosensory cortex. Part I: Modeling anatomy
bioRxiv. 2022. DOI : 10.1101/2022.08.11.503144.Persistent Homology with Improved Locality Information for more Effective Delineation
IEEE Transactions on Pattern Analysis and Machine Intelligence. 2022. DOI : 10.1109/TPAMI.2023.3246921.Epigenetic plasticity as a signature for memory allocation
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9085.Reduced representations of complexes, signals, and multifiltrations
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9924.A Hopf algebra model for Dwyer's tame spaces
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9066.Determining patterns of post-stroke motor recovery through longitudinal multimodal MRI: A step towards patient stratification
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9725.Collapse-invariant properties of spaces equipped with signals or directions
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9158.Hopf algebras and Hopf-Galois extensions in infinity-categories
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9067.Neuromodulation of neocortical microcircuitry: a multi-scale framework to model the effects of cholinergic release
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-8866.Genetic selection for low glucocorticoid responsiveness recapitulates PTSD-related phenotypes: a behavioral, neuroimaging and sleep-physiology study
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-8427.From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9852.Digital Reconstruction of the Neuro-Glia-Vascular Architecture
Cerebral Cortex. 2021-12-01. DOI : 10.1093/cercor/bhab254.Homotopical relations between 2-dimensional categories and their infinity-analogues
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-8678.giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration
Journal Of Machine Learning Research. 2021-01-01.Surprise-based model estimation in reinforcement learning: algorithms and brain signatures
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-10399.Topology predicts long-term functional outcome in early psychosis
Molecular Psychiatry. 2021. DOI : 10.1038/s41380-020-0826-1.From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives
Algorithms. 2020-12-11. DOI : 10.3390/a13120335.A computational biophysical model of thalamic and reticular nucleus microcircuitry: from neurons to emergent network dynamics
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7472.Numerical methods for structural anomaly detection using model order reduction and data-driven techniques
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7734.New Results in Integer and Lattice Programming
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7727.Computing Cyclic Isogenies between Principally Polarized Abelian Varieties over Finite Fields
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7524.Twisting structures and morphisms up to strong homotopy
Journal Of Homotopy And Related Structures. 2020. DOI : 10.1007/s40062-019-00249-w.Topological classification of microglia topological classification of microglia
2019-07-01. 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 development
2019-07-01. Annual Meeting of the Association-for-Research-in-Vision-and-Ophthalmology (ARVO), Vancouver, CANADA, Apr 28-May 02, 2019.The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness
Consciousness And Cognition. 2019-07-01. DOI : 10.1016/j.concog.2019.04.002.Objective Morphological Classification of Neocortical Pyramidal Cells
Cerebral Cortex. 2019-04-01. DOI : 10.1093/cercor/bhy339.Topological Analysis Enables Prediction Of Functional And Social Outcomes In Early Psychosis
2019-04-01. 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 Products
Transactions 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 analysis
Bioinformatics. 2019-02-07. DOI : 10.1093/bioinformatics/btz052.Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-7245.Topological exploration of artificial neuronal network dynamics
Network Neuroscience. 2019-01-01. DOI : 10.1162/netn_a_00080.Injective And Projective Model Structures On Enriched Diagram Categories
Homology Homotopy And Applications. 2019-01-01. DOI : 10.4310/HHA.2019.v21.n2.a15.Extensive amenability and a Tits alternative for topological full groups
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9407.Large-scale variational inference for Bayesian joint regression modelling of high-dimensional genetic data
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9139.On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9277.The Homotopy Theory Of Coalgebras Over Simplicial Comonads
Homology Homotopy And Applications. 2019-01-01. DOI : 10.4310/HHA.2019.v21.n1.a11.A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9275.Generating and identifying functional subnetworks within structural networks
US2023297808 ; US11615285 ; US2018197069 . 2018.On some problems related to 2-level polytopes
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-9025.Kazhdan's Property (T) and Property (FH) for measured groupoids
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8755.High-Throughput Screening Approach for Nanoporous Materials Genome Using Topological Data Analysis: Application to Zeolites
Journal of Chemical Theory and Computation. 2018. DOI : 10.1021/acs.jctc.8b00253.Development of topological tools for the analysis of biological data
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8835.Model-based reinforcement learning and navigation in animals and machines
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8950.Reductive overgroups of distinguished unipotent elements in simple algebraic groups
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8362.Neuronal morphologies: the shapes of thoughts
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8255.Towards a unified understanding of synaptic plasticity
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8186.On some algebraic and extremal problems in discrete geometry
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-8115.Algebraic and topological methods in combinatorics
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7855.Using the Green's function to simplify and understand dendrites
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7869.Towards an (∞,2)-category of homotopy coherent monads in an ∞-cosmos
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7748.Representing groups against all odds
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7823.Quantifying similarity of pore-geometry in nanoporous materials
Nature Communications. 2017. DOI : 10.1038/ncomms15396.A necessary and sufficient condition for induced model structures
Journal Of Topology. 2017. DOI : 10.1112/topo.12011.Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
Frontiers In Computational Neuroscience. 2017. DOI : 10.3389/fncom.2017.00048.Topological Analyses Of Metabolomic Data To Identify Markers Of Early Psychosis And Disease Biotypes
2017. 16th International Congress on Schizophrenia Research (ICOSR), San Diego, CA, MAR 24-28, 2017. p. S211-S212.Towards new invariants for principal bundles
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7610.Hyper-specificity of perceptual learning
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7311.A posteriori error estimation for partial differential equations with random input data
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7260.Homology of the three flag Hilbert Scheme
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7244.Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7120.Cellular Homotopy Excision
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7127.Simple topological graphs
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6889.Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6958.Cocycle growth for the Steinberg representation
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6599.Waldhausen K-theory of spaces via comodules
Advances in Mathematics. 2016. DOI : 10.1016/j.aim.2015.12.019.The Hochschild complex of a twisting cochain
Journal of Algebra. 2016. DOI : 10.1016/j.jalgebra.2015.11.040.Progesterone and Overlooked Endocrine Pathways in Breast Cancer Pathogenesis
Endocrinology. 2015. DOI : 10.1210/en.2015-1392.Sur quelques foncteurs de bi-ensembles
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6753.Restricting representations of classical algebraic groups to maximal subgroups
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6583.Kan spectra, group spectra and twisting structures
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6466.Left-induced model structures and diagram categories
2015. WIT: Women in Topology Workshop, Banff, Alberta, Canada, August 18–23, 2013. p. 49-81. DOI : 10.1090/conm/641/12859.Homotopic Hopf-Galois extensions of commutative differential graded algebras
Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6150.The Boardman-Vogt tensor product of operadic bimodules
Algebraic Topology: Applications and New Directions; 2014. p. 71-98.The homotopy theory of coalgebras over a comonad
Proceedings of the London Mathematical Society. 2014. DOI : 10.1112/plms/pdt038.Homotopy completion and topological Quillen homology of structured ring spectra
Geometry & Topology. 2013. DOI : 10.2140/gt.2013.17.1325.Complete intersections in rational homotopy theory
Journal of Pure and Applied Algebra. 2013. DOI : 10.1016/j.jpaa.2012.08.009.Normal and conormal maps in homotopy theory
Homology, Homotopy and Applications. 2012. DOI : 10.4310/HHA.2012.v14.n1.a5.Multiplicative structure in equivariant cohomology
Journal Of Pure And Applied Algebra. 2012. DOI : 10.1016/j.jpaa.2011.12.012.Long knots and maps between operads
Geometry and Topology. 2012. DOI : 10.2140/gt.2012.16.919.Homotopic Descent over Monoidal Model Categories
Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-5200.Cobordism, Cohomology Theories and Formal Group Laws
2011Why H Z-algebra Spectra are Differential Graded Algebras?
2010A homotopy-equivalence between Cacti and Configuration Spaces
2010Catégories simpliciales enrichies et K-théorie de Waldhausen
Lausanne, EPFL, 2010. DOI : 10.5075/epfl-thesis-4862.Categorical Foundations for K-theory
Lausanne, EPFL, 2010. DOI : 10.5075/epfl-thesis-4861.Twisting structures and strongly homotopy morphisms
ArXiv. 2010.A general framework for homotopic descent and codescent
ArXiv. 2010.Teaching & PhD
Teaching
Mathematics
Life Sciences Engineering
PhD Students
Hem Bjørnar Gullikstad, Maggs Kelly Spry, Manna Riddha, Youssef Markus Kirolos,Past EPFL PhD Students
Amrani Ilias , Brunner Jan , Ebli Stefania , Ergus Aras , Garin Adélie Eliane , Hacker Celia Camille , Karpova Varvara , Marcone Rachel , Michel Nicolas Mathieu , Moser Lyne , Müller Patrick , Naïto Théophile , Rovelli Martina , Stephan Marc , Werndli Kay Remo , Wu Haoqing , Zaganidis Dimitri ,Courses
Group Theory
After an introduction to category theory, we will apply the general theory to the particular cas of groups, which will allow us to see notions such as quotient groups and group actions from a new and useful perspective.
Homotopical algebra
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in algebra and topology.
Reading group in applied topology II
In this reading group, we will work together through recent important papers in applied topology.
Participants will take turns presenting articles, then leading a discussion of the contents.
Reading group in applied topology I
The subject of this reading group is Ginerstra Bianconi's book "Higher-order networks - an introduction to simplicial complexes". Participants will take turns presenting chapters, then leading a discussion of the contents. In the last session, the author will give a guest lecture.
Working group in Topology I
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, and topological algebraic geometry.
Working group in Topology II
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, topological algebraic geometry and twisted K-theory