Kathryn Hess Bellwald
EPFL SV BMI UPHESS
MA B3 454 (Bâtiment MA)
Station 8
CH-1015 Lausanne
+41 21 69 34245
+41 21 69 37922
Web site: http://hessbellwald-lab.epfl.ch
Unit: UPHESS
Office: MA B3 454
+41 21 69 37922
Web site: http://hessbellwald-lab.epfl.ch
Unit: UPHESS
Office: MA B3 454
Unit: EDMA-ENS
Unit: MATH-DIV
Unit: SMA-ENS
Fields of expertise
Homotopy theory, category theory.
Applications of algebraic topology in computer science, neuroscience, cancer research, and chemical engineering.
Publications
Publications and theses supervised
W. Dwyer; K. Hess; B. Knudsen : Configuration Spaces Of Products; Transactions Of The American Mathematical Society. 2019-02-15. DOI : 10.1090/tran/7617.
H. Ruffieux / A. C. Davison; J. Hager (Dir.) : Large-scale variational inference for Bayesian joint regression modelling of high-dimensional genetic data. Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9139.
I. Malinovic / F. Eisenbrand; Y. Faenza (Dir.) : On approximation algorithms and polyhedral relaxations for knapsack problems, and clustered planarity testing. Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9277.
K. Hess; M. Kedziorek : The Homotopy Theory Of Coalgebras Over Simplicial Comonads; Homology Homotopy And Applications. 2019-01-01. DOI : 10.4310/HHA.2019.v21.n1.a11.
A. G. Marcone / M. Troyanov (Dir.) : A Gauss-Bonnet Theorem for Asymptotically Conical Manifolds and Manifolds with Conical Singularities. Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-9275.
R. Flores; J. Scherer : Cellular Covers of Local Groups; Mediterranean Journal Of Mathematics. 2018-12-01. DOI : 10.1007/s00009-018-1273-y.
M. F. Aprile / F. Eisenbrand; Y. Faenza (Dir.) : On some problems related to 2-level polytopes. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-9025.
C. M. Gippa / N. Monod (Dir.) : Kazhdan's Property (T) and Property (FH) for measured groupoids. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8755.
Y. Lee; S. D. Barthel; P. Dłotko; S. M. Moosavi; K. Hess et al. : 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.
R. Jeitziner / C. Brisken; K. Hess Bellwald (Dir.) : Development of topological tools for the analysis of biological data. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8835.
D. S. Corneil / W. Gerstner (Dir.) : Model-based reinforcement learning and navigation in animals and machines. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8950.
M. T. Korhonen / D. Testerman (Dir.) : Reductive overgroups of distinguished unipotent elements in simple algebraic groups. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8362.
L. Kanari / H. Markram; J. C. Shillcock (Dir.) : Neuronal morphologies: the shapes of thoughts. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8255.
G. Chindemi / H. Markram; E. B. Muller (Dir.) : Towards a unified understanding of synaptic plasticity. Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8186.
S. H. Nassajianmojarrad / J. Pach (Dir.) : On some algebraic and extremal problems in discrete geometry. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-8115.
A. C. Vâlculescu / J. Pach (Dir.) : Algebraic and topological methods in combinatorics. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7855.
W. A. M. Wybo / H. Markram; M.-O. Gewaltig (Dir.) : Using the Green's function to simplify and understand dendrites. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7869.
D. Zaganidis / K. Hess Bellwald (Dir.) : Towards an (∞,2)-category of homotopy coherent monads in an ∞-cosmos. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7748.
M. Gheysens / N. Monod (Dir.) : Representing groups against all odds. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7823.
Y. Lee; S. D. Barthel; P. Dlotko; S. M. Moosavi; K. Hess et al. : Quantifying similarity of pore-geometry in nanoporous materials; Nature Communications. 2017. DOI : 10.1038/ncomms15396.
K. Hess; M. Kedziorek; E. Riehl; B. Shipley : A necessary and sufficient condition for induced model structures; Journal Of Topology. 2017. DOI : 10.1112/topo.12011.
M. W. Reimann; M. Nolte; M. Scolamiero; K. Turner; R. Perin et al. : 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.
M. Fournier; M. Scolamiero; M. Gholam-Rezaee; H. Moser; C. Ferrari et al. : 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.
M. Rovelli / K. Hess Bellwald (Dir.) : Towards new invariants for principal bundles. Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7610.
L. Grzeczkowski / M. Herzog; F. Mast (Dir.) : Hyper-specificity of perceptual learning. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7311.
D. S. Guignard / F. Nobile; M. Picasso (Dir.) : A posteriori error estimation for partial differential equations with random input data. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7260.
D. Boccalini / T. Hausel (Dir.) : Homology of the three flag Hilbert Scheme. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7244.
R. Grandi / T. Hausel (Dir.) : Motivic invariants of moduli spaces of rank 2 Bradlow-Higgs triples. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7120.
K. R. Werndli / K. Hess Bellwald; J. Scherer (Dir.) : Cellular Homotopy Excision. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7127.
A. J. Ruiz Vargas / J. Pach (Dir.) : Simple topological graphs. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6889.
M. M. Steinlechner / D. Kressner (Dir.) : Riemannian Optimization for Solving High-Dimensional Problems with Low-Rank Tensor Structure. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6958.
T. Dumont / N. Monod (Dir.) : Cocycle growth for the Steinberg representation. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-6599.
K. Hess; B. Shipley : Waldhausen K-theory of spaces via comodules; Advances in Mathematics. 2016. DOI : 10.1016/j.aim.2015.12.019.
K. Hess : The Hochschild complex of a twisting cochain; Journal of Algebra. 2016. DOI : 10.1016/j.jalgebra.2015.11.040.
M. Bayeh; K. Hess; V. Karpova; M. Kedziorek; E. Riehl et al. : Left-Induced Model Structures and Diagram Categories. 2015. WIT: Women in Topology Workshop, Banff Int Res Stn, Banff, CANADA, AUG 18-23, 2013. p. 49-81. DOI : 10.1090/conm/641/12859.
C. Brisken; K. Hess Bellwald; R. Jeitziner : Progesterone and Overlooked Endocrine Pathways in Breast Cancer Pathogenesis; Endocrinology. 2015. DOI : 10.1210/en.2015-1392.
R. F. Chevalley / J. Thévenaz (Dir.) : Sur quelques foncteurs de bi-ensembles. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6753.
M. Cavallin / D. Testerman (Dir.) : Restricting representations of classical algebraic groups to maximal subgroups. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6583.
M. Stephan / K. Hess Bellwald (Dir.) : Kan spectra, group spectra and twisting structures. Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6466.
M. Bayeh; K. Hess; V. Karpova; M. Kedziorek; E. Riehl et al. : Left-induced model structures and diagram categories; Contemporary Mathematics. 2015. DOI : 10.1090/conm/641/12859.
V. Karpova / K. Hess Bellwald (Dir.) : Homotopic Hopf-Galois extensions of commutative differential graded algebras. Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6150.
W. Dwyer; K. Hess : The Boardman-Vogt tensor product of operadic bimodules; Contemporary Mathematics. 2014. DOI : 10.1090/conm/620/12352.
K. Hess; B. Shipley : The homotopy theory of coalgebras over a comonad; Proceedings of the London Mathematical Society. 2014. DOI : 10.1112/plms/pdt038.
J. E. Harper; K. Hess : Homotopy completion and topological Quillen homology of structured ring spectra; Geometry & Topology. 2013. DOI : 10.2140/gt.2013.17.1325.
E. D. Farjoun; K. Hess : Normal and conormal maps in homotopy theory; Homology, Homotopy and Applications. 2012. DOI : 10.4310/HHA.2012.v14.n1.a5.
K. Hess : Multiplicative structure in equivariant cohomology; Journal Of Pure And Applied Algebra. 2012. DOI : 10.1016/j.jpaa.2011.12.012.
W. Dwyer; K. Hess : Long knots and maps between operads; Geometry and Topology. 2012. DOI : 10.2140/gt.2012.16.919.
P. Müller / K. Hess-Bellwald (Dir.) : Homotopic Descent over Monoidal Model Categories. Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-5200.
L. Kiwi : Cobordism, Cohomology Theories and Formal Group Laws ; 2011.
V. Karpova : Why H Z-algebra Spectra are Differential Graded Algebras? ; 2010.
P. Egger : A homotopy-equivalence between Cacti and Configuration Spaces ; 2010.
I. Amrani / K. Hess-Bellwald (Dir.) : Catégories simpliciales enrichies et K-théorie de Waldhausen. Lausanne, EPFL, 2010. DOI : 10.5075/epfl-thesis-4862.
N. Michel / K. Hess-Bellwald (Dir.) : Categorical Foundations for K-theory. Lausanne, EPFL, 2010. DOI : 10.5075/epfl-thesis-4861.
K. Hess; J. Scott : Twisting structures and strongly homotopy morphisms; preprint. 2010.
K. Hess; A. Tonks : The loop group and the cobar construction; Proceedings of the American Mathematical Society. 2010.
L. Antonioli : Les groupes d'homotopie supérieurs et la longue suite exacte d'une fibration ; 2009.
L. Kiwi : Topics in Homological Algebra ; 2009.
V. Karpova : Complex Topological K-theory ; 2009.
T. Naïto / K. Hess-Bellwald (Dir.) : Coalgèbres d'Alexander-Whitney. Lausanne, EPFL, 2009. DOI : 10.5075/epfl-thesis-4381.
K. Hess : Homotopic Hopf-Galois extensions: foundations and examples; Geometry and Topology Monographs. 2009.
K. Hess; P.-E. Parent; J. A. Scott : CoHochschild homology of chain coalgebras; Journal of Pure and Applied Algebra. 2009. DOI : 10.1016/j.jpaa.2008.08.001.
L. Kiwi : Algèbres de Hopf ; 2008.
F. Mayencourt : Noeuds et invariants de Vassiliev ; 2008.
V. Karpova : Théories d'homologie et de cohomologie généralisées ; 2008.
J. Brunner / K. Hess-Bellwald (Dir.) : The link between the infinite mapping class group of the disk and the braid group on infinitely many strands. Lausanne, EPFL, 2008. DOI : 10.5075/epfl-thesis-4132.
K. Hess : Rational homotopy theory: a brief introduction. 2007. University of Chicago, July 26-August 6, 2004. p. 175-202.
K. Hess; P.-E. Parent; A. Tonks; K. Worytkiewicz : A model structure à la Thomason on 2 - CAT; Journal of Pure and Applied Algebra. 2007. DOI : 10.1016/j.jpaa.2005.12.010.
K. Hess; P.-E. Parent; J. Scott : A chain coalgebra model for the James map; Homology, Homotopy and Applications. 2007.
K. Hess; R. Levi : An algebraic model for the loop space homology of a homotopy fiber; Algebr. Geom. Topol.. 2007. DOI : 10.2140/agt.2007.7.1699.
C. Bujard : Towards a general theory of homotopic Hopf-Galois extensions ; 2006.
D. Arlettaz; K. Hess : An alpine anthology of homotopy theory. Proceedings of the 2nd Arolla conference on algebraic topology, Arolla, Switzerland, August 24-29, 2004. (English). 2006.
K. Hess : An algebraic model for mod 2 topological cyclic homology; String Topology and Cyclic Homology; Birkhäuser, 2006. p. 97-163.
R. L. Cohen; K. Hess; A. A. Voronov : String Topology and Cyclic Homology ; Birkhäuser.
K. Hess; P.-E. Parent; J. Scott; A. Tonks : A canonical enriched Adams-Hilton model for simplicial sets; Adv. Math.. 2006.
B. Pochon / R. Guerraoui (Dir.) : Transformations in distributed computations and applications to set agreement. Lausanne, EPFL, 2006. DOI : 10.5075/epfl-thesis-3587.
K. Hess; P.-E. Parent; A. Tonks; K. Worytkiewicz : Simulations as homotopies; Electronic Notes in Theoretical Computer Science. 2004. DOI : 10.1016/j.entcs.2004.08.016.
S. Blanc / K. Hess-Bellwald (Dir.) : Modèles tordus d'espaces de lacets libres et fonctionnels. Lausanne, EPFL, 2004. DOI : 10.5075/epfl-thesis-3102.
N. Dupont; K. Hess : Commutative free loop space models at large primes; Math. Z.. 2003. DOI : 10.1007/s00209-003-0206-y.
S. Blanc; R. Guerraoui; K. Hess; P. Kouznetsov; P.-E. Parent et al. : Using the topological characterization of synchronous models; Electronic Notes in Theoretical Computer Science. 2003. DOI : 10.1016/S1571-0661(04)80834-X.
O. Sauvageot / K. Hess-Bellwald (Dir.) : Stabilisation des complexes croisés. Lausanne, EPFL, 2003. DOI : 10.5075/epfl-thesis-2692.
K. Hess : Review of "Rational Homotopy Theory" by Félix, Halperin and Thomas; Bulletin of the London Mathematical Society. 2002.
K. Hess; P.-E. Parent : Emergence of the Witt group in the cellular lattice of rational spaces; Transactions of the American Mathematical Society. 2002. DOI : 10.1090/S0002-9947-02-03049-0.
K. Hess : Model categories in algebraic topology; Applied Categorical Structures. 2002. DOI : 10.1023/A:1015218106586.
N. Dupont; K. Hess : An algebraic model for homotopy fibers; Homology, Homotopy and Applications. 2002.
N. Dupont; K. Hess : Hochschild cohomology is topological; J. Pure Appl. Algebra. 2001. DOI : 10.1016/S0022-4049(00)00171-7.
K. Gafaiti / M. Troyanov (Dir.) : Algèbres de Royden et homéomorphismes à p-dilatation bornée entre espaces métriques mesurés. Lausanne, EPFL, 2001. DOI : 10.5075/epfl-thesis-2422.
D. Arlettaz; K. Hess : Une dégustation topologique: homotopy theory in the Swiss Alps : Proceedings of the Arolla conference on algebraic topology, Arolla, Switzerland, August 25-September 1, 1999.. 2000. Une dégustation topologique: homotopy theory in the Swiss Alps.
K. Hess : Perturbation and transfer of generic algebraic structure. 1999. Higher homotopy structures in topology and mathematical physics, Poughkeepsie, NY, USA, June 13-15, 1996. p. 103-143.
K. Hess : A history of rational homotopy theory; History of Topology; Elsevier Science B.V., 1999. p. 757-796.
N. Dupont; K. Hess : How to model the free loop space algebraically; Math. Ann.. 1999. DOI : 10.1007/s002080050303.
N. Dupont; K. Hess : Noncommutative algebraic models for fiber squares; Math. Ann.. 1999. DOI : 10.1007/s002080050302.
C. Oberson / K. Hess-Bellwald (Dir.) : Degré d'entrelacement de chaînes polygonales et application à l'étude des polymères. Lausanne, EPFL, 1999. DOI : 10.5075/epfl-thesis-2009.
F. Simoncini / K. Hess-Bellwald (Dir.) : Autour de quelques invariants d'homotopie rationnelle. Lausanne, EPFL, 1998. DOI : 10.5075/epfl-thesis-1893.
K. Hess; J.-M. Lemaire : Nice and lazy cell attachments; J. Pure Appl. Algebra. 1996. DOI : 10.1016/0022-4049(95)00131-X.
K. Hess; J.-M. Lemaire : Generalizing a definition of Lusternik and Schnirelmann to model categories; Journal of Pure and Applied Algebra. 1994. DOI : 10.1016/0022-4049(94)90140-6.
N. Dupont; K. Hess : Twisted tensor models for fibrations; J. Pure Appl. Algebra. 1994. DOI : 10.1016/0022-4049(94)90136-8.
K. Hess : Mild and tame homotopy theory; Journal of Pure and Applied Algebra. 1993. DOI : 10.1016/0022-4049(93)90003-C.
K. Hess : Twisted tensor products of DGA's and the Adams-Hilton model for the total space of a fibration. 1992. Adams Memorial Symposium on Algebraic Topology, Manchester, 1990. p. 29-51.
K. Hess : A proof of Ganea's conjecture for rational spaces; Topology. 1991. DOI : 10.1016/0040-9383(91)90006-P.
K. Hess : A general framework for homotopic descent and codescent; preprint.
Teaching & PhD
Teaching
- Mathematics,
- Life Sciences Engineering
PhD Programs
- Doctoral Program in Mathematics
- Doctoral Program in Neuroscience
- Doctoral Program in Computational and Quantitative Biology
PhD Students
Ebli Stefania
Ergus Aras
Garin Adélie Eliane
Hacker Celia Camille
Moser Lyne
Wu Haoqing
Blanc Sylvestre ...
Brunner Jan ...
Karpova Varvara ...
Marcone Rachel ...
Michel Nicolas ...
Müller Patrick ...
Naïto Théophile ...
Oberson Chantal ...
Rovelli Martina ...
Sauvageot Orin ...
Simoncini Fabio ...
Stephan Marc ...
Werndli Kay Remo ...
Zaganidis Dimitri ...
Ergus Aras
Garin Adélie Eliane
Hacker Celia Camille
Moser Lyne
Wu Haoqing
Past PhD Students
Amrani Ilias ...Blanc Sylvestre ...
Brunner Jan ...
Karpova Varvara ...
Marcone Rachel ...
Michel Nicolas ...
Müller Patrick ...
Naïto Théophile ...
Oberson Chantal ...
Rovelli Martina ...
Sauvageot Orin ...
Simoncini Fabio ...
Stephan Marc ...
Werndli Kay Remo ...
Zaganidis Dimitri ...
Courses
Linear Algebra
The purpose of the course is to introduce the basic notions of linear algebra and its applications. 
Topology
We begin by recalling the purely axiomatic framework of topology, in particular products of spaces. We then study the notions of separability and connectivity, global and local. Finally we consider constructions of spaces as quotients and the notion of ...
Algebraic topology
We study in depth the notion of homology of a topological space, with emphasis on computational methods, even while carefully treating the theoretical foundations.
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