E-mail: tillmann_at_maths.ox.ac.uk

Phone: 44-1865-273572

- Cohomology Theories in Encyclopaedia of Mathematical Physics , (2006), 545-553
- The homotopy type of the cobordism category (joint S. Galatius, I. Madsen, M.Weiss) Acta Math. 202 (2009), no. 2, 195-239
- Braids, mapping class groups, and categorical delooping (joint Y. Song) Math. Ann. 339 (2007), no. 2, 377-393
- Artin's map in stable homology, Bull. Lond. Math. Soc. 39 (2007), no. 6, 989-992
- Mapping configuration spaces to moduli spaces (joint with G. Segal) Groups of diffeomorphisms, 469-477, Adv. Stud. Pure Math., 52, Math. Soc. Japan, Tokyo, 2008
- On the Farrell cohomolgoy of the mapping class group of non-orientable surfaces (joint G. Hope) Proc. Amer. Math. Soc. 137 (2009), no. 1, 393-400
- The representation of the mapping class group of a surface on its fundamental group in stable homology Q. J. Math. 61 (2010), no. 3, 373-380
- Vanishing of the universal charcteristic classes for handlebody groups and boundary bundles (joint J Giansiracusa) J. Homotopy Relat. Struct. 6 (2011), no. 1, 103-112
- Spaces of graphs and surfaces Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 73-90
- Mumford's conjecture - a topological outlook Handbook of Moduli Spaces 2012
- Embeddings of braid into mapping class groups and their homology (joint C.-F. Boedigheimer) in Configuration Spaces: Geometry, Combinatorics and Topology 2012 Sco. Norm. Sup. Pisa, 173-191
- Localisations of cobordism categories and invertible TFTs in dimension two (joint R. Juer) Homology, Homotopy and Applications, 15(2), 2013, 1-31
- Tubular configurations: equivariant scanning and splitting (joint R. Manthorpe) Journal of the London Mathematical Society,90, 2014, 640-662
- Infinite loop spaces and nilpotent K-theory (joint A. Adem, J.M. Gomez, J. Lund)
- A roadmap for the computation of persistent homology (joint N. Otter, M. Porter, P. Grindrod, H. Harrington)
- Homology stability for symmetric diffeomorphisms and mapping class groups Math. Proc. Cam. Phil. Soc.

- Slides for my talk at the AMS-Current Events Bulletin, New Orleans 2011
- Slides for my talk at the Abel Conference in honor of J. Milnor, IMA 2012
- Slides for my talk at the Stanford Symposium in honor of G. Carlsson, R. Cohen and I. Madsen, 2012
- Slides for my talk at The Legacy of Daniel Quillen, MIT 2012
- Slides for my talk at the Joint BMC/BAMC 150th LMS meeting, Cambridge 2015
- Lecture 1 Lecture 2 2016 V Congreso Latinoamericano de Matematicos
- Slides for my "Fridays at 2" talk at Oxford, 2019

- The Journal of Topology
- Algebraic and Geometric Topology
- The Quarterly Journal of Mathematics
- Geometry & Topology
- Journal of the American Mathematical Society
- London Mathematical Society Lecture Notes

- Topology and geometry of moduli spaces, AIM 2005
- Launch Meeting for the Journal of Topology, Oxford 2007
- Moduli spaces, Bonn 2008 (winter school and conference)
- 25th Nordic and 1st British-Nordic Congress of Mathematicians, Oslo 2009
- ICWM, Hyderabad 2010
- Applied Topology Day, Monday February 28, 2011
- Memorial Meeting for Dan Quillen (1940-2011), Oxford 2011
- Homotopy Algebra and its Applications, Luminy 2012
- Algebraic Topology: applications and new directions, Stanford Symposium 2012
- Segal 70th: Aspects of Topology in Geometry and Physics, Oxford 2012
- Higher Structures in Topology and Number Theory, Oxford 2013
- CAT 2015: Topological Data Analysis, Oxford
- Research School 7-11 September on Computational Algebraic Topology, Oxford 2015
- Alan Turing Institute scoping workshop on TDA, Oxford 2015
- Algebraic Topology: manifolds unlocking higher structures, Clay workshop 2015
- Weiss 60th: Topology of Manifolds, Lisbon 2016
- Topology in Ecuador, Galapagos 2017
- CMI-LMS Research School: Algebraic Topology of Manifolds, Oxford 2017
- Topological data analysis of exclusion zones, Edinburgh 2017
- Spires: from theory to applications and back, Oxford 2019

- Mathematics at Merton College
- Section c: Algebraic Topology; for the unofficial course webpage click here.
- Section c: Lie Groups; for the unofficial course webpage click here
- Part A: Number Theory; for the unofficial course webpage click here
- MSc: Computational Algebraic Topology; for the unofficial course webpage click here
- Topology Advanced Class; for the advanced classes webpage click here

- Paul Higgins, New York
- Tilman Bauer, KTH Stockholm (MSc)
- Paolo Salvatore, Rome
- Paul Mitchener, Sheffield (jointly supervised by J. Roe)
- Nathalie Wahl, Copenhagen
- Chris Douglas, Oxford (MSc)
- Catarina Carvalho, Lisbon (jointly supervised by V. Nistor)
- Graham Hope, Oxford
- Jeff Giansiracusa, Swansea
- Liz Hanbury, Durham
- George Raptis, Regensburg
- Oscar Randal-Williams, Cambridge
- Martin Palmer, Muenster
- Richard Manthorpe, London (MSc)
- Rozy Juer, London (MSc)
- Hongyun Yon, Oxford
- Simon Gritschacher, Oxford
- Nina Otter, Oxford (jointly supervised by Heather Harrington)
- Renee Hoekzema, Oxford
- Tomas Zeman
- Barbara Mahler
- Jan Steinebrunner
- Luciana Bonatto
- Oliver Vipond