# Dr Frank Neumann

## Associate Professor of Mathematics

School/Department:
**School of Computing and Mathematical Sciences**

Telephone: +44 (0)116 252 2722

Email: fn8@leicester.ac.uk

### Profile

### Research

My major research areas are in algebra, geometry and topology and their various interactions and applications. My current research activities are in particular in algebraic geometry and algebraic topology and I am very much interested in interactions between these fields. My recent interests focus on the geometry, topology and arithmetic of moduli stacks, homological algebra of differential graded categories and the homotopy theory of classifying spaces and loop spaces. My research has also direct links with arithmetic geometry, invariant theory, representation theory, category theory , differential geometry and mathematical physics. Over the years I obtained substantial research funding for various research projects from national and international funding bodies including the European Union, London Mathematical Society (LMS), Royal Society, Nuffield Foundation, EPSRC and several international research councils and organisations including Italian and Spanish research councils.

I am an organiser of the Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON). The LAGOON global webinar series has a strong focus on Representation Theory and Algebraic Geometry and their many interactions covering topics such as homological mirror symmetry, stability conditions, derived categories, dg-categories, Hochschild cohomology of algebras, moduli spaces and algebraic stacks, derived algebraic geometry and other topics.

I am also an organiser of the Transpennine Topology Triangle (TTT). The Transpennine Topology Triangle is a topology seminar partially supported by the London Mathematical Society. It has nodes at Leicester, Liverpool and Sheffield.

### Publications

(0) Selected books and monographs:

1. F. Neumann: Geometry of Algebraic Stacks and Moduli of Vector Bundles. to appear: IMPA Research Monographs, Springer Verlag, Berlin-New York, 250 pp.

2. F. Neumann, A. Pal (Eds.): Homotopy Theory and Arithmetic Geometry -- Motivic and Diophantine Aspects. Springer Lecture Notes in Mathematics Vol. 2292, Springer Verlag, Berlin-New York, 227 pp.

3. F. Neumann, S. Schroll (Eds.): Galois Covers, Grothendieck-TeichmÃ¼ller Theory and Dessins d'Enfants -- Interactions between Geometry, Topology, Number Theory and Algebra, Springer Proceedings in Mathematics & Statistics Vol. 330, Springer Verlag, Berlin-New York 2020, 248 pp.

Selected research articles:

1. I. Biswas, S. Chatterjee, P. Koushik, F. Neumann: Atiyah sequences and connections on principal bundles over Lie groupoids and differentiable stacks. to appear: Journal of Noncommutative Geometry

2. L. A. Barbosa-Torres, F. Neumann: Equivariant cohomology for differentiable stacks. Journal of Geometry and Physics 160 (2021), 103974.

3. I. Galvez-Carrillo, F. Neumann, A. Tonks: Gabriel-Zisman cohomology and spectral sequences. Applied Categorical Structures 29 (2021), 69-94.

4. S. Balchin, F. Neumann: On the number of rational points of classifying stacks for Chevalley group schemes. Springer Proceedings in Mathematics & Statistics Vol. 330, Springer Verlag, Berlin-New York, 2020, 9--30.

5. F. Neumann, M. Szymik: Spectral sequences for Hochschild cohomology and graded centers of derived categories. Selecta Mathematica 23 (2017), 1997-2018.

6. O. Mata-Gutierrez, F. Neumann: Geometry of moduli stacks of (k, l)-stable vector bundles over algebraic curves. Journal of Geometry and Physics 111 (2017), 54-70.

7. P. Frediani, F. Neumann: Ã‰tale homotopy types of moduli stacks of polarised abelian schemes. Journal of Homotopy and Related Structures 11 (4) (2016), 775-801.

8. I. Biswas, F. Neumann: Atiyah sequences, connections and characteristic forms for principal bundles over groupoids and stacks. Comptes Rendus Math. Acad. Sci. Paris Ser I 352 (2014), 59-64.

9. F. Neumann: Variations on the cohomology of loop spaces on generalized homogeneous spaces. Proceedings of the Steklov Institute of Mathematics 252 (2006), 205-211

10. P. Frediani, F. Neumann: Ã‰tale homotopy types of moduli stacks of algebraic curves with symmetries. K-Theory 30 (2003), 315-340.

11. J. P. May, F. Neumann: On the cohomology of generalized homogeneous spaces. Proceedings of the American Math. Society 130 (2002), no. 1, 267-270.

12. F. Neumann: A theorem of Tits, normalizers of maximal tori and fibrewise Bousfield-Kan completions. Publications RIMS Kyoto 35 (1999), no. 5, 711-723.

### Supervision

I have successfully supervised 8 PhD students some of them with external funding for example from the Colombian research council Colciencias. I am currently supervising four PhD students. Over the years I have also successfully supervised 18 Master students.

The following PhD research projects are aligned with my personal research interests in algebra, geometry and topology and I would be willing to supervise PhD students on any of the following topics:

1. Homotopy theory and cohomology of moduli stacks

2. Arithmetic geometry of algebraic stacks

3. Homological algebra of differential graded categories

4. Categorifying homological algebra

5. Differential geometry of differentiable stacks

### Teaching

1. MA1104 Elements of Number Theory

2. MA3153-MA4153 Number Theory

3. MA3121 Complex Analysis

4. MA3516 BSc Mathematics Project

I am also involved with teaching the MAGIC 064 Algebraic Topology course for PhD students as part of the MAGIC postgraduate course network of 21 UK universities. I am also involved with teaching master courses at the African Institute for Mathematical Sciences (AIMS) in Senegal and have taught various courses at international institutions in Germany, Spain, Mexico, Brazil, India, Ghana and Tanzania.### Press and media

### Activities

Selected activities, committee membership and other leadership roles:

1. Member-at-Large of the Council of the London Mathematical Society (LMS)

2. Member of the Research Grants Committee of the London Mathematical Society (LMS)

3. Member of the Nomination Committee of the London Mathematical Society (LMS)

4. Correspondent for the Isaac Newton Institute for Mathematical Sciences (INI) Cambridge and the International Centre for Mathematical Sciences (ICMS) Edinburgh

5. Associate Member of the European Mathematical Society (EMS) Committee for Developing Countries (CDC)

6. Chair of the Board for the LMS-IMU-AMMSI research initiative Mentoring African Research in Mathematics (MARM)

7. Chair of the Advisory Board for collaborative research and education projects between Norwegian Petroleum Geo-Services (PGS) The Norwegian Academy of Science and Letters (DNVA) Abel Prize Fund Kwame Nkrumah University of Science and Technology Kumasi Ghana (KNUST) and the National Institute for Mathematical Science Ghana (NIMS)

8. Board Member of the European Mathematical Society (EMS) Committee for European Solidarity

9. Member of the IMA-LMS-BSHM Committee for the 'Black Heroes in Mathematics' conferences

10. Referee and Reviewer for UKRI/EPSRC

11. Member of the London Mathematical Society (LMS)

12. Member of the American Mathematical Society (AMS)

### Conferences

Selected invited talks at workshops, conferences and congresses:

1. International Workshop on 'Geometry in Algebra and Algebra in Geometry VI (GAAG 2020)', UFF Niteroi, Brazil (12/2020)

2. LMS-IMU-AMMSI-UNAM MARM International Round Table on 'Mathematics and Society', UNAM Windhoek, Namibia (12/2020)

3. International Conference on 'Differential Algebraic and Topological Methods in Complex Algebraic Geometry', CIME Cetraro, Italy (09/2018)

4. LMS-IMU-AMMSI MARM Workshop: Around Algebra Combinatorics and Number Theory, Chancellor College University of Malawi Zomba, Malawi (08/2018)

5. Workshop and School on Algebraic Geometry, CCM-UNAM Morelia, Mexico (12/2017)

6. Algebraic Geometry in Mexico 2017, CMO-BIRS Oaxaca Mexico (11/2017)

7. SMF Algebraic Topology Conference in the Honour of Said Zarati, Tunis, Tunesia (10/2016)

8. Workshop and School on Algebraic Geometry, CCM-UNAM Morelia, Mexico (12/2015)

9. Workshop on 'Interactions between Arithmetic and Homotopy', Imperial College London, United Kingdom (09/2015)

Selected organised workshops, conferences and congresses:

1. BIRS Workshop on 'Moduli, Motives and Bundles - New Trends in Algebraic Geometry', Casa Matematica, Oaxaca, Mexico (09/2022)

2. ICMS/INI Research Webinar Series Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON) (since 05/2020)

3. International Centre for Mathematical Sciences (ICMS), Institute of Mathematics and its Applications (IMA) and London Mathematical Society (LMS) and British Society for the History of Mathematics (BSHM) Conference 'Black Heroes of Mathematics' (since 10/2020)

4. HIMR Heilbronn Institute for Mathematical Research Focus Workshop on 'Topological Methods in Group Representation Theory', Leicester, United Kingdom (11/2019)

5. 109th Transpennine Topology Triangle (TTT) Memorial Meeting for Sir Michael Atiyah, Leicester, United Kingdom (03/2019)

6. LMS-IMU-AMMSI MARM Workshop: Around Algebra, Combinatorics and Number Theory, Chancellor College, University of Malawi, Zomba, Malawi (08/2018)

7. LMS-CMI-HIMR Research School 'Homotopy Theory and Arithmetic Geometry - Motivic and Diophantine Aspects', Imperial College London, United Kingdom (07/2018)

8. LMS Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmueller Theory and Dessin d'Enfants', Leicester, United Kingdom (06/2018)