Timothy Logvinenko

I am a Reader at the School of Mathematics of Cardiff University. I've completed my PhD in 2004 at the University of Bath, and have since been a post-doctoral research fellow at RIMS (Kyoto), Institut Mittag-Leffler/KTH (Stockholm) and at the University of Warwick.

My full CV is available here.

Address:   School of Mathematics,   Cardiff University,   Senghennydd Road,   Cardiff, CF24 4AG,   UK Phone: +44 29 2087 5546 Fax: +44 29 2087 4199 E-mail:  LogvinenkoT at cardiff ac uk

Research

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

Seminars

• GiC Seminar Official Webpage

• COW Seminar Official Webpage

Conferences

• Geometry and Algebra of Orbifolds and the McKay Correspondence (Aug 9th-14th 2010 @ Uni of Warwick)
• Russian-British Winter School on the McKay Correspondence (Feb 20th-25th 2012 @ Uni of Warwick)
• AGTP: School on Algebraic Geometry and Theoretical Physics (Jul 9th-14th 2012 @ Uni of Warwick)
• Homological Projective Duality and Noncommutative Geometry (Oct 8th-13th 2012 @ Uni of Warwick)
  Lecture notes:
  • Alexander Kuznetsov - Homological Projective Duality (scans I)
  • Alexander Kuznetsov - Homological Projective Duality (scans II)
  • Alexander Kuznetsov - Homological Projective Duality (typeset, revised)
  • Dmitri Kaledin - Homological methods in Noncommutative geometry (scans)
  • Alexander Efimov - Homotopy finiteness of DG categories from algebraic geometry (scans)
  • Many thanks to Agnieszka Bodzenta-Skibińska and Mohammad Akhtar for providing the notes.
    The typeset version of the “Homological Projective Duality” notes is due to Agnieszka Bodzenta-Skibińska and Timothy Logvinenko.
• Categoricaly Cardiff: Derived Categories and Algebraic Geometry (18th Oct 2013 @ Cardiff Uni)
• EPSRC Warwick Symposium 2014-15: Derived Categories and Applications (Sep 2014 - Aug 2015 @ Uni of Warwick)
• 2CiC: Cow and Calf in Cardiff (23rd-24th Feb 2017 @ Cardiff Uni)
• Perverse schobers and categorical structures in algebraic geometry (30th Mar - 3rd Apr 2020 @ Cardiff Uni)
• Quivers, Clusters, Moduli and Stability (9th–13th January 2023@ University of Oxford)

Publications

• “A∞-structures in monoidal DG categories and strong homotopy unitality” with Rina Anno and Sergey Arkhipov,
    preprint arXiv:2303.11826. new!
• “Unbounded twisted complexes” with Rina Anno,
    J. Algebra 647 (2024), 794–822
• “The Heisenberg category of a category” with Ádám Gyenge and Clemens Koppensteiner,
    preprint arXiv:2105.13334.
• “P^n-functors” with Rina Anno,
    preprint arXiv:1905.05740.
• “On uniqueness of P-twists” with Rina Anno,
    Int. Math. Res. Not. 2022 (2022), no. 14, 10533–10554,
• “Bar category of modules and homotopy adjunction for tensor functors” with Rina Anno,
    Int. Math. Res. Not. 2021 (2021), no. 2, 1353–1462
• “Spherical DG-functors” with Rina Anno,
    J. Eur. Math. Soc. 19 (2017), 2577–2656
• "How to calculate A-Hilb C^n for 1/r(a,b,1...1)" with Sarah Davis and Miles Reid,
    submitted to the Rendiconti del Circolo Matematico di Palermo (special Alg Geometry volume), 37 pp., 2012
• "Derived Reid's recipe for abelian subgroups of SL3(C)" with Sabin Cautis and Alastair Craw,
    Journal für die reine und angewandte Mathematik 727 (2017), 1-48
• "Orthogonally spherical objects and spherical fibrations" with Rina Anno,
    Advances in Mathematics 286 (2016), 338–86
• "Erratum to ‘A derived approach to geometric McKay correspondence in dimension three’" with Sabin Cautis,
    Journal für die reine und angewandte Mathematik 689 (2014), 243-244
• "On adjunctions for Fourier-Mukai transforms" with Rina Anno,
    Advances in Mathematics 231 (2012), no. 3-4, 2069–2115
• "Reid's recipe and derived categories",
    Journal of Algebra 324 (2010), no. 8, 2064–2087
• "A derived approach to geometric McKay correspondence in dimension three" with Sabin Cautis,
    Journal für die reine und angewandte Mathematik 636 (2009), 193–236
• "Derived McKay correspondence via pure-sheaf transforms",
    Mathematische Annalen 341 (2008), no. 1, 137–167
• "Natural G-Constellation Families",
    Documenta Mathematica 13 (2008), 803–823,
• "Families of G-Constellations parametrised by resolutions of quotient singularities",
    University of Bath Ph.D. thesis, 140 pp., 2004
• "Families of G-constellations over resolutions of quotient singularities",
    preprint arXiv:math/0305194