My research work is in higher category theory and homotopy theory. I am particularly interested in the interactions between these two areas. I also work on questions in homological algebra. I have maintained an active involvement in my field via collaborations and research stages at some of the main research centres for my area, such as the Centre of Australian Category Theory at Macquarie University.

Publications and Preprints

Research Monograph

Simplicial Methods for Higher Categories

'Simplicial Methods for Higher Categories: Segal-type Models of Weak n-Categories' (344 pages) Algebra and Applications 26, Springer (2019).

University of Leicester press release

Journal Papers and Preprints

L. Moser, V. Ozornova, S. Paoli, M. Sarazola, P. Verdugo, Stable homotopy hypothesis in the Tamsamani model, Topology and its Applications, to appear, arXiv2001.05577v2
D.Blanc, S.Paoli, Comonad cohomology of track categories, Journal of Homotopy and Related Structures, 14 (4) (2019), 881-917 arXiv.1801.05065
D. Blanc, S. Paoli, Segal-type algebraic models of n-types, Algebraic and Geometric Topology, 14 (2015) 3419-3491.
S. Paoli, D. Pronk, The weakly globular double category of fractions of a category, Theory and Application of categories, 29 (2014) 696-774.
S. Paoli, D. Pronk, A double categorical model of weak 2-categories, Theory and Application of categories, 28, (2013), 933-980.
D. Blanc, S. Paoli, Two-track categories, Journal of K-theory, 8(1) (2011), 59-106.
T. M. Fiore, S. Paoli, A Thomason model structure on the category of small n-fold categories, Algebraic and Geometric Topology, 10 (2010), 1933-2008.
S. Paoli, Weakly globular catn-groups and Tamsamani’s model, Advances in Mathematics, 222, (2009) 621-727.
S. Paoli, Internal categorical structures, ‘Towards Higher Categories’, The IMA volumes in Mathematics and its applications, edited J. C. Baez and J. P. May, Springer (2009), 85-103.
T. M. Fiore, S. Paoli, D. A. Pronk, Model structures on the category of small double categories, Algebraic and Geometric Topology, 8 (2008) 1855-1959.
S. Lack, S. Paoli, 2-nerves for bicategories, K-theory, 38 (2), (2008), 153-175.
S. Paoli, Semistrict models of connected 3-types and Tamsamani weak 3-groupoids, Journal of Pure and Appl. Algebra, 211, (2007), 801-820.
S. Lack, S. Paoli, An operadic approach to internal structures, Applied Categorical Structures, 13 (3), (2005), 205-222.
S. Paoli On the non-balanced property of the category of crossed modules in groups, Journal of Pure and Appl. Algebra, 197, (1-3) , (2005), 19-22.
S. Paoli, (Co)homology of crossed modules with coefficients in a $\pi_1$-module, Homology, Homotopy and Applications, 5 (1) (2003), 261-296.

Networks, Seminar and Conference Organization

Research network

YaMCATS is an LMS-funded research network in category theory between the Universities of Birmingham, Leeds, Leicester and Sheffield. I am the grant-holder.

Conferences and workshops (co-organised)

SYCO6, University of Leicester, 16-17 December 2019.
32nd British Topology Meeting, University of Leicester, 6-8 September 2017.
Algebraic Topology Session at the 31st Summer Conference on Topology and its Applications, University of Leicester, 2-5 August 2016
YaMCATS meetings, 2014 - present
TTT93, University of Leicester, 12 November 2014

Steering Committee member

I am a member of the Steering Committee of the conference series 'Symposium of Compositional Structures (SYCO)'.

Programme Committee Member

SYCO 1, University of Birmingham, September 2018, SYCO 2, University of Strathclyde, December 2018, SYCO 3, University of Oxford, March 2019, SYCO 4, Chapman University May 2019, SYCO6 University of Leicester December 2019.
Applied Category Theory Conference ACT2019, University of Oxford, July 2019.

Seminar on Category Theory and its applications

I am organising the Seminar on Category Theory and its applications.

Editorial duties

I am a member of the editorial board of the journal Compositionality. This is an inter-disciplinary journal for research using compositional ideas, notably of category-theoretic origin, in sciences. The journal also accepts submissions in pure category theory.

Grants

LMS Scheme 1 conference grant, 2019.
LMS Scheme 3 grant for YaMCATS network, 2014-present.
LMS Scheme 1 conference grant, 2016.
EU Marie Curie International Reintegration Grant HOMALGHIGH (2011-2015).
Between 2005-2008, I was principal investigator of the Australian Research Council Postdoctoral Fellowship DP0558598 held at Macquarie University.

Women in Mathematics

I am one of the team leaders for the programme Women in Topology, Hausdorff Research Institute for Mathematics, August 2019.

PhD Supervision

Current PhD students:

Peter Guthmann

Past PhD students:

Andrew Smith (completed 2019)

Talks

Invited conference and workshop talks

(upcoming) GeoCat2020, July 2020.
(postponed to 2021) 35th British Topology Meeting, Durham, 2-4 September 2020.
(postponed to 2021) Galway Topology Colloquium 2020, 6-8 July 2020.
Ada Lovelace Day Conference, University of Warwick, 16 October 2019.
International Category Theory Conference CT2019, University of Edinburgh, July 2019.
Categorical Methods in Algebra, University of Palermo (Italy), May 2019.
East Midlands Seminar in Geometry, Loughborough University, December 2018.
2018 CMS Summer Meeting (Canada) June 2018.
GDR Topologie Algebrique (France), October 2017.
Categories for homotopy theory and rewriting, CIRM Luminy (France), September 2017.
Higher Structures Lisbon 2017, July 2017.
British Mathematics Colloquium 2017, Topology Session, April 2017.
9th Meeting of the Yorkshire and Midlands Category Seminar, Nov. 2016
Higher structures: Advances, MATRIX University of Melbourne, June 2016
Opening conference for the program on Higher Structures in Geometry and Physics, Max Planck Institute Bonn, January 2016
AMS 2014 Fall Sectional Meeting, October 2014
Séminaire Itinérant de categories, Louvain La Neuve, May 2013
Satellite thematic session in homotopy theory ECM6, July 2012
Foundational Methods in Computer Science 2012, June 2012
TTT85, University of Manchester, October 2012
The 6th Scottish Category Seminar, University of Strathclyde, May 2012
The 2009 Meeting of the Israel Mathematical Union, Homotopy theory Session, April 2009
NovemberFest, Carnegie Mellon University, November 2009
Fall 2009 AMS Eastern Section Meeting, Homotopy theory session October 2009
2009 Summer Conference of Topology and its Applications, Category theory session, July 2009
Fields Institute Workshop on Higher Categories and their Applications, January 2007
TTT39, March 2003

Invited talk series

Talk series (5 talks), University of Vienna, December 2018. Abstracts and Slides

Topology Proseminar, University of Chicago (USA) series of 3 talks, April 2016.

Australian Category Seminar, Macquarie University (Australia), series of 9 talks between August-December 2015

Selected invited seminar talks

These can be found here

Contributed conference and workshop talks

These can be found here

Teaching

Current teaching: Linear Statistical Models.

Teaching qualification: Fellow of the HEA.

Administration

I am currently Examination Officer for the School of Mathematics and Actuarial Science.

External Examining

I have been external examiner of PhD theses at the following institutions: University of Leeds (UK), Macquarie University (Australia), Universite Paris-Diderot (France), University of Vienna (Austria).

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Contact details

Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 229 7407

Campus Based Courses

Undergraduate: mathsug@le.ac.uk
Postgraduate Taught: mathspg@le.ac.uk

Postgraduate Research: pgrmaths@le.ac.uk

Distance Learning Course

Actuarial Science:

DL Study

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