Contact

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

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

Research interests

Algebraic geometry, deformation theory, convex geometry, toric varieties.

Preprints

10. Deformations of a toric Gorenstein pair

Publications

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

In preparation

• Deformation of gorenstein toric varieties and Laurent polynomials

Selected research talks

• Smoothing toric Gorenstein singularities using Laurent polynomials, Conference: Singularities from a homological perspective: IMSA Miami, USA, Nov 11-Nov 23, 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

• 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

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

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