Sefi Ladkani
I hold a temporary position as a principal investigator
at the
Mathematical Institute
of the University of Bonn,
in 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
-
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.
Papers and Preprints
-
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
(pdf)
to appear in Algebr. Represent. Theory.
Supplementary material to this paper, including complete lists of the
derived equivalence classes, can be found
here.
-
with Janine
Bastian and
Thorsten Holm,
Derived equivalences
for cluster-tilted algebras of Dynkin type D
(pdf)
-
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 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)
-
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.