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Dr Timothy Logvinenko
Reader
- LogvinenkoT@cardiff.ac.uk
- +44 29208 75546
- Abacws, Room Room 3.61, Senghennydd Road, Cathays, Cardiff, CF24 4AG
- Available for postgraduate supervision
Overview
My research is broadly in the fields of algebraic geometry and representation theory. My work focuses on studying DG-categories and derived categories associated to algebraic varieties and applying the knowledge of them to solve problems in various areas of algebraic geometry, including orbifolds and the McKay correspondence, categorification problems, mirror symmetry, moduli spaces and quiver representations.
Personal website
Publication
2024
- Anno, R. and Logvinenko, T. 2024. Unbounded twisted complexes. Journal of Algebra 647, pp. 794-822. (10.1016/j.jalgebra.2024.01.039)
2022
- Anno, R. and Logvinenko, T. 2022. On uniqueness of P-twists. International Mathematics Research Notices 14, pp. 10533-10554., article number: rnaa371. (10.1093/imrn/rnaa371)
2021
- Anno, R. and Logvinenko, T. 2021. Bar category of modules and homotopy adjunction for tensor functors. International Mathematics Research Notices 2021(2), pp. 1353-1462. (10.1093/imrn/rnaa066)
2017
- Anno, R. and Logvinenko, T. 2017. Spherical DG-functors. Journal of the European Mathematical Society 19(9), pp. 2577-2656. (10.4171/JEMS/724)
- Cautis, S., Craw, A. and Logvinenko, T. 2017. Derived Reid's recipe for abelian subgroups of SL3(ℂ). Journal für die reine und angewandte Mathematik 2017(727), pp. 1-48. (10.1515/crelle-2014-0086)
2016
- Anno, R. and Logvinenko, T. 2016. Orthogonally spherical objects and spherical fibrations. Advances in Mathematics 286, pp. 338-386. (10.1016/j.aim.2015.08.027)
2012
- Anno, R. and Logvinenko, T. 2012. On adjunctions for Fourier-Mukai transforms. Advances in Mathematics 231(3-4), pp. 2069-2115. (10.1016/j.aim.2012.06.007)
2010
- Logvinenko, T. 2010. Reid's recipe and derived categories. Journal of Algebra 324(8), pp. 2064-2087. (10.1016/j.jalgebra.2010.04.012)
2009
- Cautis, S. and Logvinenko, T. 2009. A derived approach to geometric McKay correspondence in dimension three. Journal für die reine und angewandte Mathematik (Crelles Journal) 2009(636), pp. 193-236. (10.1515/CRELLE.2009.086)
2008
- Logvinenko, T. 2008. Derived McKay correspondence via pure-sheaf transforms. Mathematische Annalen 341(1), pp. 137-167. (10.1007/s00208-007-0186-z)
- Logvinenko, T. 2008. Natural G-constellation families. Documenta Mathematica 13, pp. 803-823.
Articles
- Anno, R. and Logvinenko, T. 2024. Unbounded twisted complexes. Journal of Algebra 647, pp. 794-822. (10.1016/j.jalgebra.2024.01.039)
- Anno, R. and Logvinenko, T. 2022. On uniqueness of P-twists. International Mathematics Research Notices 14, pp. 10533-10554., article number: rnaa371. (10.1093/imrn/rnaa371)
- Anno, R. and Logvinenko, T. 2021. Bar category of modules and homotopy adjunction for tensor functors. International Mathematics Research Notices 2021(2), pp. 1353-1462. (10.1093/imrn/rnaa066)
- Anno, R. and Logvinenko, T. 2017. Spherical DG-functors. Journal of the European Mathematical Society 19(9), pp. 2577-2656. (10.4171/JEMS/724)
- Cautis, S., Craw, A. and Logvinenko, T. 2017. Derived Reid's recipe for abelian subgroups of SL3(ℂ). Journal für die reine und angewandte Mathematik 2017(727), pp. 1-48. (10.1515/crelle-2014-0086)
- Anno, R. and Logvinenko, T. 2016. Orthogonally spherical objects and spherical fibrations. Advances in Mathematics 286, pp. 338-386. (10.1016/j.aim.2015.08.027)
- Anno, R. and Logvinenko, T. 2012. On adjunctions for Fourier-Mukai transforms. Advances in Mathematics 231(3-4), pp. 2069-2115. (10.1016/j.aim.2012.06.007)
- Logvinenko, T. 2010. Reid's recipe and derived categories. Journal of Algebra 324(8), pp. 2064-2087. (10.1016/j.jalgebra.2010.04.012)
- Cautis, S. and Logvinenko, T. 2009. A derived approach to geometric McKay correspondence in dimension three. Journal für die reine und angewandte Mathematik (Crelles Journal) 2009(636), pp. 193-236. (10.1515/CRELLE.2009.086)
- Logvinenko, T. 2008. Derived McKay correspondence via pure-sheaf transforms. Mathematische Annalen 341(1), pp. 137-167. (10.1007/s00208-007-0186-z)
- Logvinenko, T. 2008. Natural G-constellation families. Documenta Mathematica 13, pp. 803-823.
- Anno, R. and Logvinenko, T. 2012. On adjunctions for Fourier-Mukai transforms. Advances in Mathematics 231(3-4), pp. 2069-2115. (10.1016/j.aim.2012.06.007)
- Logvinenko, T. 2010. Reid's recipe and derived categories. Journal of Algebra 324(8), pp. 2064-2087. (10.1016/j.jalgebra.2010.04.012)
- Cautis, S. and Logvinenko, T. 2009. A derived approach to geometric McKay correspondence in dimension three. Journal für die reine und angewandte Mathematik (Crelles Journal) 2009(636), pp. 193-236. (10.1515/CRELLE.2009.086)
- Logvinenko, T. 2008. Derived McKay correspondence via pure-sheaf transforms. Mathematische Annalen 341(1), pp. 137-167. (10.1007/s00208-007-0186-z)
Research
Research interests
My research focuses on studying DG-categories and derived categories associated to algebraic varieties and applying the knowledge of them to solve problems in various areas of algebraic geometry, including:
- Orbifolds and the McKay correspondence
- Categorification problems
- Mirror symmetry
- Moduli spaces
- Quiver representations
Research group
Teaching
Autumn semester
- Geometry (Year One)
Spring semester
- Algebra III: Fields (Year Three)
Biography
Education
- BA – Mathematics, University of Cambridge (Mathematical Tripos, Part IIB), 1999
- MMath – Mathematics, University of Cambridge (Mathematical Tripos, Part III), 2000
- DPhil – Mathematics, University of Bath, 2004
- MA – University of Cambridge, 2001
Professional memberships
- European Mathematical Society
- London Mathematical Society
Academic positions
- 2004-2006: JSPS Postdoctoral Fellowship (with Prof. Shigeru Mukai), RIMS, Kyoto University
- 2006 - 2008: Postdoctoral Fellowship, Institut Mittag-Leffler / KTH, Stockholm
- 2008 - 2010: Postdoctoral Fellowship, University of Liverpool, UK
- 2010 - 2013: Postdoctoral Researcher / Co-investigator (with Prof. Miles Reid) on an EPSRC research grant "Orbifolds and Birational Geometry", Mathematics Institute, University of Warwick, Coventry, UK
- 2013 - 2016: Lecturer, Cardiff University
- 2017 - 2020: Senior Lecturer, Cardiff University
- 2020 - present: Reader, Cardff University
Committees and reviewing
- EPSRC Peer Review College
Supervisions
Current supervision
Oscar Finegan
Research student