Ralf Schiffler

Department of Mathematics
University of Connecticut
Phone:(860) 486-8381
Fax: (860) 486-4238
Mailing address
Office: M-323

E-mail: schiffler(at)math(dot)uconn(dot)edu

Curriculum Vitae

Teaching

Spring 2013

5020Q Topics in Algebra: Tilting Theory



Students

Lucas David-Roesler
PhD 2012
Ilke Çanakçi
PhD 2013
Khrystyna Serhiyenko
PhD expected 2016
Ana Garcia Elsener
 PhD expected 2016 (co-advised with Sonia Trepode)
Stephen Zito
PhD expected 2016
Miki Oryu Masters 2011 (co-advised with Hiro-Fumi Yamada)

Research

My research focuses on Algebra, Representation Theory and Combinatorics. I am particularly interested in associative algebras, quiver representations, cluster algebras and quantum groups. My research is supported by NSF Grant DMS-1001637.

Citations in Google Scholar

I am the organizer of the Cluster Algebra Seminar at UConn.

Publications

1
 K. Lee, R. Schiffler : Positivity for cluster algebras of rank 3, 47 pages, to appear in Publ. Res. Inst. Math. Sci.
2
 I. Assem, M. J. Redondo, R. Schiffler : On the first Hochschild cohomology group of a cluster-tilted algebra, 30 pages, preprint.
3
 I. Assem, G. Dupont, R. Schiffler : On a category of cluster algebras, 37 pages, preprint.
4
 I. Canakci, R. Schiffler : Snake graph calculus and cluster algebras from surfaces, J. Algebra, 382, 240-281.
5
 I. Assem, J. C. Bustamante, K. Igusa, R. Schiffler : The first Hochschild cohomology group of a cluster-tilted algebra revisited, 14 pages, to appear in Internat. J. Algebra Comput.
6 I. Assem, M. A. Gatica, R. Schiffler : The higher relation bimodule, 20 pages, to appear in Algebras and Representation Theory, doi: 10.1007/s10468-012-9342-6.
7
 G. Musiker, R. Schiffler, L. Williams : Bases for cluster algebras form surfaces, Compositio Math 149, 2, (2013) 217-263.
8
 K. Lee, R. Schiffler : A Combinatorial Formula for Rank 2 Cluster Variables, J. Alg. Comb, 37, 1, (2013) 67-85.
9 K. Lee, R. Schiffler :  Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables, Compositio Math. 148, 6, (2012) 1821-1832.
10 M. Oryu, R. Schiffler : On one-point extensions of cluster-tilted algebras,  J. Algebra 357, (2012) 168-182.
11 R. Kinser, R. Schiffler : Idempotents in representation rings of quivers, Algebra Number Theory 6, No. 5, (2012), 967-994.
12
 L. David-Roesler, R. Schiffler : Algebras from surfaces without punctures, J. Algebra 350, (2012), 218-244.
13
 I. Assem, G. Dupont, R. Schiffler, D. Smith : Friezes, strings and cluster variables, Glasgow Math. J. 54, 1 (2012) 27-60.
14
 I. Assem, V. Shramchenko, R. Schiffler : Cluster automorphisms, Proc. Lond. Math. Soc. 104(6),  (2012), 1271-1302.
15
 G. Musiker, R. Schiffler, L. Williams : Positivity for cluster algebras from surfaces, Advances in Math. 227 (2011) 2241-2308.
16
 I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras without clusters, J. Algebra 324, (2010) 2475-2502.
17
 K. Igusa, R. Schiffler : Exceptional sequences and clusters,  J. Algebra 323, 8, (2010) 2183-2202.
18 G. Musiker, R. Schiffler : Cluster expansion formulas and perfect matchings, J. Alg. Comb. 32, 2, (2010) 187-209.
19
 R. Schiffler: On cluster algebras arising from unpunctured surfaces II, Advances in Math. 223 (2010) 1885-1923.
20
 R. Schiffler, Cluster algebras and cluster categories, lecture notes for the Latin American Colloquium, Sao Pedro, Brazil, (2009).
21
 G. Musiker, R. Schiffler : Cluster algebras of unpunctured surfaces and snake graphs, in DMTCS Proceedings, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009),  673-684.
22
 R. Schiffler, H. Thomas : On cluster algebras arising from unpunctured surfaces, Intern. Math. Res. Not. 17 (2009) 3160-3189.
23
 I. Assem, T. Brüstle, R. Schiffler : On the Galois covering of a cluster-tilted algebra, J. Pure Appl. Alg. 213, (7) (2009) 1450-1463.
24
 R. Schiffler : A cluster expansion formula (A_n case), Electron. J. Combin. 15 (2008) #R64 1.
25
 I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras and slices, J. of Algebra 319 (2008) 3464-3479.
26 I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras as trivial extensions, Bull. London Math. Soc. 40 (2008) 151-162.
27
 R. Schiffler : A geometric model for cluster categories of type D_n, J. Alg. Comb. 28, no. 1, (2008) 1-21.
28
I. Assem, T. Brüstle, R. Schiffler, G. Todorov : m-cluster categories and m-replicated algebras, J. Pure Appl. Alg. 212 (4) (2008) 884-901.
29 I. Assem, T. Brüstle, R. Schiffler, G. Todorov : Cluster categories and duplicated algebras, J. of Algebra 305 (2006) 548-561.
30
 P. Caldero, F. Chapoton, R. Schiffler : Quivers with relations and cluster tilted algebras, Algebras and Representation Theory 9, no. 4, (2006) 359-376.
31 P. Caldero, F. Chapoton, R. Schiffler : Quivers with relations arising from clusters (A_n case), Trans. Amer. Math. Soc. 358 , no. 3, (2006) 1347-1364.
32
R. Schiffler : On the multiplication in the quantized enveloping algebra of type A, in Representations of Algebras and Related Topics, Fields Institute Communications 45, (2005).
33
P. Caldero, R. Schiffler : Rational smoothness of varieties of representations for quivers of Dynkin type, Annales de l'Institut Fourier 54 (2), (2004) 295-315.
34
R. Schiffler : Projective rational smoothness of varieties of representations for quivers of type A, Representation Theory 7 (2003) 549-586.
35 R. Bédard, R. Schiffler : Rational smoothness of varieties of representations for quivers of type A, Representation Theory 7, (2003) 481-548.
36
R. Schiffler : Variétés de carquois et homologie d'intersection, Publications LACIM 30, Montréal (2003).