Welcome to my personal web page!
I am a Postdoctoral Research Associate in the School of Mathematics, Statistics and Actuarial Science at the University of Kent, working with Andy Hone.
My research interest focuses on cluster algebras and their connections to representation theory, geometry and combinatorics.
I came to Kent in 2018. Previously, I was a Research Associate in the Department of Mathematical Sciences at Durham University, working with Anna Felikson, and a Research Assistant in the Representation Theory Group at Bielefeld University, under the supervision of Henning Krause. I received my PhD in 2011 from the University of Bonn, under the supervision of Jan Schröer.
Further information can be found in my CV.
School of Mathematics, Statistics and Actuarial Science
University of Kent
Canterbury, CT2 7FS
Telephone: +44 (0) 1227 82 4874
Email: P.B.Lampe at kent.ac.uk
Office: Sibson 272
Publications and preprints
- Exchange graphs for mutation-finite non-integer quivers of rank 3
Joint work with Anna Felikson. Preprint arXiv:1904.03928 (2019). [Link]
- Cluster algebras and discrete integrability
Joint work with Andy Hone and Thedoros Kouloukas. Preprint arXiv:1903.08335 (2019). [Link]
- An expansion formula for type A and Kronecker quantum cluster algebras
Joint work with İlke Çanakçı. Preprint arXiv:1807.07539 (2018). [Link]
- Factoriality and class groups of cluster algebras
Joint work with Ana Garcia Elsener and Daniel Smertnig. Preprint arXiv:1712.06512 (2017). [Link]
- Variations on Baur--Marsh's determinant
To appear in Journal of Combinatorial Theory, Series A. [Link]
- Maximum antichains in posets of quiver representations
Joint with Florian Gellert, Contributions to Algebra and Geometry 59 (2018), 1-20. [Link]
- On the approximate periodicity of sequences attached to noncrystallographic root systems
Experimental Mathematics 27 (2018), no. 3, 265-271.
- Diophantine equations via cluster transformations
Journal of Algebra 462 (2016), 320-337. [Link]
- Quantisation Spaces of Cluster Algebras
Joint with Florian Gellert, Glasgow Mathematical Journal 60, no. 2 (2018), 273-284.
- Acyclic cluster algebras from a ring theoretic point of view.
To appear in Communications in Algebra. [Link]
- Quantum cluster algebras of type A and the dual canonical basis
Proceedings of the London Mathematical Society 108 (2014), no. 1, 1-43. [Link
- A quantum cluster algebra of Kronecker type and the dual canonical basis
International Mathematics Research Notices 2011 (2011), no. 13, 2970-3005. [Link]
- The divisor class group of a cluster algebra
Oberwolfach Reports 8
(2014), 484-485. [Link]
- Quantum cluster algebras and dual canonical bases
Oberwolfach Reports 8 (2011), no. 10, 564-565. [Link]
Supervised PhD students
- Lecture Linear Mathematics, Spring 2019
- Tutorial for Linear Algebra I (Krause), Winter 2016/17
- Seminar Algebraic Methods, Summer 2016
- Tutorial for Representation Theory of Algebras III (Krause), Winter 2015/16
- Tutorial for Representation Theory of Algebras II (Voßieck), Summer 2015
- Seminar Mathematical Physics (with Kieburg), Summer 2015
- Tutorial for Representation Theory of Algebras I (Krause), Winter 2014/15
- Seminar Algebra (with Krause), Summer 2014
- Tutorial for Linear Algebra II (Bauer), Summer 2014
- Lecture Cluster Algebras, Winter 2013/14, Lecture Notes
- Seminar Combinatorics and Group Theory, Summer 2013, Lecture Notes
- Lecture Group Theory, Winter 2012/13
- Seminar Introduction to Cluster Algebras (with Krause, Mahrt), Summer 2012
- Tutorial for Linear Algebra II (Krause), Summer 2012
- Tutorial for Linear Algebra I (Krause), Winter 2011/12
- Tutorial for Introduction to Representation Theory (Krause), Summer 2011
- Tutorial for Analysis III (Franke), Winter 2005/06
- Tutorial for Analysis II (Franke), Summer 2005