Lewis Topley

Reader and UKRI Future Leaders Fellow.

University of Bath.

Research interests:

• Ordinary and modular representation theory of Lie algebras and algebraic groups;

• Finite and affine W-algebras;

• Yangians in positive characteristics;

• Poisson algebras and deformation theory.

Postdocs and PhD students:

• Juan Jose Villarreal (Postdoc 2022-2024)

• Matt Chaffe (Phd, Birmingham 2020-2024)

• Lukas Tappenier (PhD, Bath 2022-)

Journal Articles

1. Invariants of centralisers in positive characteristic.
   Journal of Algebra, 399 (2014), pp. 1021-1050.   | Journal |  arxiv
   

2. Derived subalgebras of centralisers and finite W-algebras (with Alexander Premet).
   Compositio Mathematica 150 (2014), no. 9, pp. 1485-1548. | Journal | arxiv
   

3. A Morita theorem for modular finite W-algebras.
   Mathematishe Zeitschrift 285 (2017) 3-4, pp. 685-705. | Journal | arxiv
   

4. Harish-Chandra invariants and the centre of the reduced enveloping algebra.
   Journal of Pure and Applied Algebra 221 (2017), pp. 490-498. | Journal | arxiv
   

5. A Non-restricted counterexample to the first Kac-Weisfeiler conjecture.
   Proceedings of the American Mathematical Society, 45 (2016) 5, pp. 1937-1942. | Journal | arxiv
   

6. Modular finite W-algebras (with Simon M. Goodwin).
   International Mathematics Research Notices 18 (2019), pp. 5811-5853. | Journal | arxiv
   

7. The p-centre of the Yangian and shifted Yangians (with Jonathan Brundan).
   Moscow Mathematical Journal 18 (2018), no. 4, pp. 617-657. | Journal | arxiv
   

8. Transfer results for free Frobenius extensions (with Stephane Launois).
   Journal of Algebra 524 (2019), pp. 35-58. | Journal | arxiv
   

9.  On the semicentre of a Poisson algebra (with Cesar Lecoutre).
   Algebras and Representation Theory (2020), 23(3), pp. 875-886.  | Journal | arxiv
   

10. Minimal dimensional representations of reduced enveloping algebras for gl_n (With Simon M. Goodwin).
    Compositio Mathematica 155 (2019) pp. 1594-1617. | Journal | arxiv
    

11. The orbit method for Poisson orders (with Stephane Launois).
    Proceedings of the London Mathematical Society 120 (2020) pp. 65-94. | Journal | arxiv
    

12. A proof of the first Kac-Weisfeiler conjecture in large characteristics (with Ben Martin, David Stewart, Akaki Tikaradze).
    Representation Theory 23 (2019), pp. 278-293.  | Journal | arxiv
    

13. Restricted shifted Yangians and restricted finite W-algebras (with Simon M. Goodwin).
    Transactions of the American Mathematical Society Series B 8 (2021), pp. 190-228. | Journal | arxiv
    

14. Modular representations of Lie algebras of reductive groups and Humphreys' conjecture (with Alexander Premet).
    Advances in Mathematics 392 (2021), paper number 108024. | Journal | arxiv
    
    

15. Parabolic induction for Springer fibres (with Neil Saunders).
    Proceedings of the American Mathematical Society 151, no 8, (2023). | Journal | arxiv
    
    

16. One dimensional representations of finite W-algebras, Dirac reduction and the orbit method.
    Inventiones Mathematicae 234, (2023).  | Journal | arxiv
    
    

17.  Category O for truncated current Lie algebras (with Matt Chaffe).
    Canadian Journal of Mathematics (2023) | Journal | arxiv
    
    

18. Universal filtered quantizations of nilpotent Slodowy slices (with Filippo Ambrosio, Giovanna Carnovale, Francesco Esposito).
    Journal of Noncommutative Geometry (2023) | Journal | arxiv
    

Preprints

1. Smoothness of stabilisers in generic characteristic (with Ben Martin and David Stewart).
   arXiv:1810.12628 (2018).
   
   

2. The centre of the modular affine vertex algebra at the critical level (with Tomoyuki Arakawa and Juan Villarreal).
   arxiv:2305.17765 (2023).
   
   

3.  Equivariant deformation theory for nilpotent slices in symplectic Lie algebras (with Filippo Ambrosio).
   arxiv:2310.04773 (2023).
   
   

4. Modular representations of truncated current Lie algebras (with Matt Chaffe).
   arXiv:2311.08208 (2023).
   
   

5. On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras (with Matt Westaway and Simon M. Goodwin).
   arXiv:2311.10603 (2023).
   
   

6. Modular representations of the Yangian Y_2 (with Hao Chang and Jinxin Hu).
   arxiv.org:2403.18727 (2024).
   
   

7. Shifted twisted Yangians and Slodowy slices in classical Lie algebras (with Lukas Tappeiner).
   arXiv:2406.05492 (2024).

A selection of my professional activities  from 2015 onwards:

• In June 2024 I will speak at the conference "Vertex algebras, geometric representation theory and quantum groups" at CIRM Luminy.

• From October 2023 to September 2024, Hao Chang is visiting me from CCNU

• I organised the regional meeting of the LMS (South West and South Wales) in January 2024. 

• In August 2023 I was the local orgainser for the LMS-Bath Symposium ``Geometric and Categorical Representation Theory''. Later in the same month I co-organised a meeting at the International Centre for Mathematical Sciences on ``Geometric Representation Theory and W-algebras''.

• I was the organiser of the algebra section of the British Mathematical Colloquium, held in Bath in April 2023.

• From the 29th of May to the 18th of June 2023 I attended a research programme at the Newton Institute in Cambridge "Groups, representations and applications: new perspectives".

• During the summer term 2022 I delivered a TCC course in "Representation Theory and Lie Theory". Course webpage.

• In November 2021 I gave an online talk at CCNU, Wuhan, China. Watch the video here.

• I have now moved to the University of Bath and have hired my first PDRA Juan José Villarreal.

• On the 12th of May I spoke at the RepNet online seminar series. Watch the video here.

• In April 2021 I gave a talk in the Algebra and Representation Theory session of the British Mathematics Colloquium 2021.

• From August 2020 to June 2021 I was a lecturer and Birmingham fellow at the University of Birmingham.

• I have been awarded a UKRI Future Leaders Fellowship, to work on my research proposal ``Geometric Representation Theory and W-algebras''.  I will be hiring a postdoc to work with me on the project. Here are the  announcements from the UKRI and from the government.

• Between August 2019 and January 2020 I was a research fellow working with Simon Goodwin at the University of Birmingham.

• With Neil Saunders I co-organised a workshop on Springer Fibres and Geometric Representation Theory at the University of Greenwich. This was be funded by the  Heilbronn Institute's Focused Research Groups program.

• In July 2019 I visited Giovanna Carnovale and Francesco Esposito at the University of Padova. We started working on the theory of universal filtered quantisations of nilpotent Slodowy varieties.

• Together with Stéphane Launois and Omar León Sánchez, I organised a conference "Interactions Between Representation Theory and Model Theory" which was held at the University of Kent in July 2019.

• In May 2019 I gave a seminar at the conference Geometric and Automorphic aspects of W-algebras at the University of Lille.

• In May 2019 I visited Prof Roman Bezrukavnikov at Massachusetts Institute of Technology thanks to funding from the LMS.

• In April 2019 I organised a one day workshop on W-algebras at the University of Kent, together with Matteo Casati. 

• In November 2018 I participated in the conference Algebraic Groups: Geometry Actions and Structure which was officially the unofficial birthday conference for Prof Michel Brion.

• In 2017-2019, I am co-organising the seminar series “Algebra, Geometry and Topology” at the University of Kent, with Chris Bowman.

• In December 2017 I took part in the INdAM workshop in Rome on "Affine, vertex and W-algebras".

• In September 2017 I visited Tomoyuki Arakawa at Massachusetts Institute of Technology to start work on the theory of affine W-algebras and related vertex algebras in positive characteristics.

• In July 2017 I attended a summer school in Dijon "Current topics in the theory of algebraic groups".

• In January 2017 I took part in the winter school and subsequent conference on "Geometry and Representation theory" at the Erwin Schrödinger Institute in Vienna.

• In April 2016 I attended a conference in honour of my PhD supervisor Sasha Premet at the ICMS in Edinburgh "Representation theory and symplectic singularities". If you look carefully at the conference photos you can see the reflection of my spectacles floating like a spectre next to Gunter Malle's head!

• In July 2016 I attended the conference "Representation theory in Samos" at the University of the Aegean Sea, Samos.

• In May 2016 I visited Jon Brundan at the University of Oregon to start work on the theory of Yangians in positive characteristics.

• In 2016 I arranged a reading group in Padova on the subject of "Category O for symmetrisable Kac-Moody algebras" where we examined some combinatorial aspects of Kazhdan-Lusztig theory, mostly drawn from the work of Peter Fiebig.

• The above reading group was inspired by a series of lectures given by Prof Fiebig at a workshop attended in Marienheide, 2015, entitled "Representations of algebraic groups and Lie algebras in characteristic p".

• In August 2015 Simon Goodwin visited me in Padova and we started work on a series of papers on the theory of modular finite W-algebras and the representations of restricted Lie algebras.

• In January 2015 I gave a talk at the conference "Geometry and representations of Cherednik algebras, and category O" at Paris VII