Sefi Ladkani

During the years 2011-2014 I held a temporary position as a principal investigator at the Mathematical Institute of the University of Bonn within the framework of Priority Program SPP 1388 (Representation Theory) of the DFG (German Research Foundation).

Prior to that, I spent two years as a postdoctoral researcher at the Max-Planck-Institute for Mathematics in Bonn, Germany and one year at the Institut des Hautes Études Scientifiques at Bures-sur-Yvette, France. Part of my stay at these institutes was as an EPDI (European Postdoctoral Institute) Laureate.

I completed my Ph.D. studies in Mathematics at The Hebrew University of Jerusalem. My advisor was David Kazhdan.

Research

My research interests are in the areas of representation theory and homological algebra, with a focus on derived categories arising from combinatorial data. More specifically, I am interested in:

• Derived and triangulated categories.
• Representations of quivers and finite dimensional algebras.
• Tilting theory.
• Cluster categories.
• Categorification.
• Algebraic aspects of finite partially ordered sets and directed graphs.
• Sheaves on topological spaces, diagram categories, model categories.

Recent results

Some short notes, extended abstracts etc. of results announced at various meetings, arranged in reverse chronological order.

• On symmetric Jacobian algebras (pdf),
  abstract of a scheduled talk at the conference Advances in Representation Theory of Algebras (ARTA) 2013, Torun, September 2013, claiming in particular that the Jacobian algebras of the quivers with potentials arising from triangulations of closed surfaces are tame symmetric with periodic modules. A manuscript presenting the theory in a more general framework is in preparation.
• Derived equivalence classification of the gentle algebras arising from surface triangulations (pdf),
  talks at the Representation theory seminar, Bielefeld, July 2011 and at the Representation Theory Days, Hannover, November 2011.
• On fractionally Calabi-Yau algebras, coming soon,
  talks at the BIRS Workshop Test problems for the theory of finite dimensional algebras, Banff, September 2010, and at the workshop Projective Dimension 2, Bielefeld, October 2010.
• with Xiao-Wu Chen, The F-inflation category and its stable category, coming soon.

Publications

Arranged according to alphabetical order of the titles.

• Algebras of quasi-quaternion type (pdf)
• 2-CY-tilted algebras that are not Jacobian (pdf)
• Bounds on the global dimension of certain piecewise hereditary categories,
  J. Pure Appl. Algebra 212 (2008), no. 9, 2140-2145. (doi, pdf)
• Categorification of a linear algebra identity and factorization of Serre functors (pdf)
• with Janine Bastian and Thorsten Holm, Derived equivalence classification of cluster-tilted algebras of Dynkin type E
  Algebr. Represent. Theory. 16 (2013), no. 2, 527-551. (doi, pdf)
  Supplementary material to this paper, including complete lists of the derived equivalence classes, can be found here.
• Derived equivalences of triangular matrix rings arising from extensions of tilting modules,
  Algebr. Represent. Theory 14 (2011), no. 1, 57-74. (doi, pdf)
• Hochschild cohomology of gentle algebras (pdf)
• Hochschild cohomology of the cluster-tilted algebras of finite representation type (pdf)
• Mutation classes of certain quivers with potentials as derived equivalence classes (pdf)
• On cluster algebras from once punctured closed surfaces (pdf)
• On derived equivalences of categories of sheaves over finite posets,
  J. Pure Appl. Algebra 212 (2008), no. 2, 435-451. (doi, pdf)
• On derived equivalences of lines, rectangles and triangles
  J. London Math. Soc. 87 (2013), no. 1, 157-176. (doi, pdf)
• On Jacobian algebras from closed surfaces (pdf)
• On the periodicity of Coxeter transformations and the non-negativity of their Euler forms,
  Linear Algebra Appl. 428 (2008), no. 4, 742-753. (doi, pdf)
• Perverse equivalences, BB-tilting, mutations and applications (pdf)
• with Janine Bastian and Thorsten Holm, Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
  J. Algebra 410 (2014), 277-332. (doi, pdf)
• Universal derived equivalences of posets (pdf)
• Universal derived equivalences of posets of cluster tilting objects (pdf)
• Universal derived equivalences of posets of tilting modules (pdf)
• Which canonical algebras are derived equivalent to incidence algebras of posets?,
  Comm. Algebra 36 (2008), no. 12, 4599-4606. (doi, pdf)
• Which mutation classes of quivers have constant number of arrows? (pdf)

Ph.D. Thesis: Homological properties of finite partially ordered sets (pdf).

M.Sc. Thesis: On nilpotency problems in metabelian extensions of local fields (dvi , ps)

Presentations

Here are slides of some of my talks.

• On Jacobian algebras from closed surfaces, presentation at ICRA 2012, Bielefeld, August 2012 (pdf)
• Mutation classes of quivers with constant number of arrows and derived equivalences, talk at the BIRS Workshop Linking representation theory, singularity theory and non-commutative algebraic geometry, Banff, May 2012.
  A video recording of the talk is available here.
• Mutation classes of quivers with constant number of arrows and derived equivalences, presentation at the Conference of the DFG priority program 1388 "Representation Theory", Thurnau, March 2012 (pdf)
• Mutation classes of quivers with constant number of arrows and derived equivalences, slides accompanying my talk at the Workshop on Cluster Algebras and Combinatorics 2012, Graz, March 2012, as well as my talks at Hannover, Münster, Israel and Paris, from November 2011 to March 2012 (pdf)
• Perverse Morita equivalences are everywhere, presentation at ICRA XIV, Tokyo, Japan, August 2010 (pdf)
• Combinatorial aspects of derived equivalence, presentation at the Darstellungstheorie Schwerpunkttagung, Bad Honnef, April 2010 (pdf)
• On derived equivalences of simplices, prisms and boxes, slides accompanying my talk at the Conference on Homological and Geometrical Methods in Representation Theory, ICTP, Trieste, February 2010 (pdf)
• On derived equivalences of triangles, rectangles and lines, presentation at the Workshop on Triangulated Categories and Singularities, Paderborn, May 2009 (pdf)
• On derived equivalences of triangles, rectangles and lines, presentation at the Workshop on Representations and Cohomology, Cologne, March 2009 (pdf)
• Universal derived equivalences of posets and applications to cluster-tilting objects, poster for the 12th Midrasha Mathematicae on Higher Teichmuller Theory, Clusters and Quantization, Jerusalem, May 2008 (pdf)
• Generalized reflections and derived equivalences of posets, presentation at the Conference on Representations of Algebras, Groups and Semigroups, Bar-Ilan University, January 2008 (pdf)
• Posets, sheaves, and their derived equivalences, presentation at ICRA XII, Torun, Poland, August 2007 (pdf)
• Piecewise hereditary algebras and posets, presentation at ICRA XII, Torun, Poland, August 2007 (pdf)
• Constructions of derived equivalences of finite posets, presentation at the Workshop on Triangulated Categories, Leeds, UK, August 2006 (pdf)
• Derived equivalences of categories of sheaves over finite partially ordered sets, HUJI, May 2006 (pdf)

Teaching

During my Ph.D. studies I have been a teaching assistant at the Einstein Institute of Mathematics in the Hebrew University. Here is the list of the courses I taught.

• Algebraic structures 2 (Spring 2004, Spring 2005)
• Basic notions in noncommutative algebra (Fall 2003/4, Fall 2004/5, Fall 2005/6)
• Introduction to Logic (Fall 2006/7)