Contact

University of Ljubljana
Institute of Mathematics, Physics and Mechanics
Faculty of Electrical Engineering
Tržaška cesta 25, 1000 Ljubljana, Slovenia

e-mail: matej.filip@fe.uni-lj.si

Research interests

I am a professor of mathematics at the University of Ljubljana. My research focuses on the classification of Fano manifolds using mirror symmetry and toric deformation theory.

Publications

1. with S. Felten, H. Ruddat: Smoothing toroidal crossing spaces, Forum of Mathematics, Pi 9 (2021) 1-36.
2. with A. Petracci, A. Corti: Mirror Symmetry and smoothing Gorenstein toric affine 3-folds , Facets of Algebraic Geometry volume in honour of William Fulton on the occasion of his 80th birthday (2022) 132-163.
3. with K. Altmann, A. Constatinescu: Polyhedra, lattice structures, and semigroups, Journal of the London Mathematical Society 106 (2022) 3938-4008.
4. with K. Altmann, A. Constatinescu: Versality in toric geometry , Journal of algebra 609 (2022) 1-43.
5. The Gerstehaber product of affine toric varieties, Communications in algebra 49 (2021) 1146-1162.
6. A differential graded Lie algebra controlling the Poisson deformations of an affine Poisson variety, Communications in algebra 48 (2020) 2183-2195.
7. Hochschild cohomology and deformation quantization of affine toric varieties, Journal of algebra 506 (2018) 188-214.
8. with G. Casnati, F. Malaspina: Rank two aCM bundles on the del Pezzo threefold of degree 7, Revista matematica complutense 30 (2017) 129-165
9. Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds, Geometriae dedicata 173 (2014) 331-346.

Preprints

10. Laurent polynomials and deformations of non-isolated Gorenstein toric sigularities
11. Deformations of a toric Gorenstein pair

Academic education

• 2018 - 2019: Postdoc in Mathematics, JGU Mainz. Supervisor: Prof. Dr. Helge Ruddat.
• 2014 - 2018: PhD in Mathematics, FU Berlin. Thesis: Noncommutative deformations of toric varieties. Supervisor: Prof. Dr. Klaus Altmann
• 2011-2013: MSc in Mathematics, University of Ljubljana. Thesis: Rank 2 ACM bundles on complete intersection Calabi-Yau varieties (in Slovene). Supervisors: Prof.~Dr.~Anita Buckley, Prof. Dr. Tomaž Košir
• 2008 - 2011: BSc in Mathematics, University of Ljubljana. Thesis: 27 lines on a smooth cubic surface (in Slovene). Supervisor: Prof. Dr. Tomaž Košir

Selected research talks

• Mutations and deformations, Conference: New developments in Singularity Theory: IMSA Miami, USA, Nov 10-Nov 14, 2025.
• Laurent polynomials and deformations of non-isolated Gorenstein toric singularities, Birational Geometry Seminar 2025: UCLA, USA, May 23, 2025.
• Laurent polynomials and deformations of non-isolated Gorenstein toric singularities, Conference: Fano varieties in Stavanger: Stavanger, Norway, Apr 2- Apr 4, 2025.
• Smoothing toric Gorenstein singularities using Laurent polynomials, Conference: Singularities from a homological perspective: IMSA Miami, USA, Nov 11-Nov 23, 2024.
• Smoothing Gorenstein toric singularities and mirror symmetry, TULSF meeting: SISSA Trieste, Italy, Nov 7, 2024.
• Mutations and smoothing of affine toric Gorenstein varieties, Autumn School and Workshop: Singularities and torus actions, University of Oldenburg, Germany, Sep 11-Sep 15, 2023.
• Mutations of Laurent polynomials and deformations of toric varieties, Conference: Toric degeneration and mirror symmetry in Kumamoto, University of Kumamoto, Japan, Oct 13-Oct 14, 2022
• Laurent polynomials and deformations of affine toric varities, Conference: Toric geometry, Oberwolfach, Germany, Mar 27-Apr 2, 2022
• The miniversal deformation of an affine toric Gorenstein threefold, Seminar at University of Nottingham (online talk), Jan 28, 2021
• Smoothing toroidal crossing spaces, Conference: Degenerations, algebraic surfaces, and related topics, University of Kobe, Japan, Dec 16-Dec 18, 2019
• Deformations of non-isolated toric singularities, Seminar at Imperial College London, UK, Oct 10, 2019
• The versal deformation for toric varieties in special lattice degrees, Seminar at FU Berlin, Germany, May 23, 2019
• Deformations of Gorenstein toric varieties, Seminar at SFU Vancouver, Canada, Feb 8, 2019
• Frobenious manifolds and formality of Lie algebras of polyvector fields, Spring School: Enumerative Invariants from Diferential Graded Lie Algebras and Categories, Tuscany, Italy, Mar 25-Mar 31, 2018
• Hochschild cohomology and deformation quantization of toric varieties, School on Deformation Theory, University of Turin, Italy, Jul 5-Jul 8, 2017
• Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds, Conference: ACM bundles on algebraic varieites, Ankara, Jun 16, 2015
• Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds, Seminar at Politecnico di Torino, Italy, May 14, 2014
• Rank 2 ACM bundles on complete intersection Calabi-Yau threefolds, Seminar TULSF at University of Ljubljana, Slovenia, Sep 19, 2013

Other Attended conferences

• Mid-Atlantic Geometry and Singularities Conference, Universidad de La Laguna, Tenerife, Spain, May 12- May 16, 2025
• Toric Degenerations, BIRS workshop, Banff, Canada, Dec 4-Dec 9, 2022
• Group Actions in Algebraic Geometry, Cetraro, Italy, Jul 10-16, 2022
• Mirror Symmetry and Fano Varieties II, Chicheley Hall, UK, Sep 25-27, 2019
• Introductionary workshop: Derived algebraic geometry and birational geometry and moduli spaces, MSRI, Berkeley, California, Jan 31-Feb 8, 2019
• Young perspectives in Deformation theory, University of Torino, Italy, November 27-30, 2018
• Instruments of Algebraic Geometry, University of Bucharest, Romania, Sep 11-22, 2017
• Workshop on Convexity in Algebraic Geometry, Fields Institute, Toronto, Oct 3-7, 2016
• Summer School on Poisson Geometry, University of Geneva, June 27-July 2, 2016
• Algebra and Geometry meeting IMUB, University of Barcelona, Spain, Dec 2-4, 2015
• Workshop Noncommutative Geometry and Higher Structures, University La Sapienza, Rome, Aug 31-Sep 4, 2015
• AMS Summer Institute in Algebraic Geometry, University of Utah, Salt Lake City, July 12-24, 2015
• Deformation Theory, Homological Mirror Symmetry and Noncommutative Geometry, University of Copenhagen, May 18-22, 2015
• Warwick EPSRC Symposium School on Derived Categories, Weyl Algebras and Hodge Theory, Warwick University, March 16-20, 2015

Teaching

• Mathematics 1,2,3: FE Ljubljana
• Algebraic Curves: FMF Ljubljana
• Introduction to Algebraic geometry: FMF Ljubljana

Student supervision

• Andras Sandor, Postdoc
• Izak Jenko, MSc
• Jure Markun: Deformation theory of toric varieties, MSc (2023)