Ralf Schiffler

Department of Mathematics
University of Connecticut
Phone:(860) 486-8381
Fax: (860) 486-4238
Mailing address
Office: MONT-336

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

Curriculum Vitae


Teaching (Spring 2016)

MATH5211: Abstract Algebra II


Current students

Stephen Zito
PhD   2016
Ana Garcia Elsener
PhD expected 2017 (co-advised with Sonia Trepode)
Michelle Rabideau
PhD expected 2018
former students


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 the NSF CAREER Grant DMS-1254567.

Citations in Google Scholar

Conferences/seminars

International Conference on Representations of Algebras ICRA Syracuse, August 10-19, 2016.
Cluster Algebra Seminar at UConn.

Books

R. Schiffler : Quiver Represenations, CMS Books in Mathematics, Springer Verlag, 2014. There is a book review on page 7 of these CMS Notes.
R. Schiffler : Variétés de carquois et homologie d'intersection , Publications LACIM 30, Montréal, 2003.

Lecture notes

R. Schiffler : Lecture notes on cluster algebras from surfaces, CIMPA School, Mar del Plata, 2016.
R. Schiffler : Cluster algebras and cluster categories, lecture notes for the Latin American Colloquium, Sao Pedro, Brazil, 2009.

Articles

1
I. Canakci and  R. Schiffler : Cluster algebras and continued fractions, 28 pages.
2
I. Assem, R. Schiffler and  K. Serhiyenko : Modules over cluster-tilted that do not lie on local slices, 10 pages.
3
I. Assem, R. Schiffler and  K. Serhiyenko : Cluster-tilted and quasi-tilted algebras, 27 pages.
4
R. Schiffler and  K. Serhiyenko : Injective presentations of induced modules over cluster-tilted algebras, 24 pages.
5
A. Garcia Elsener and R. Schiffler : On syzygies over 2-Calabi-Yau tilted algebras, 21 pages.
6
R. Schiffler : Lecture notes on cluster algebras, by Robert J. Marsh, book review, Bull. Amer. Math. Soc. 53 (2016), 325-330.
7
I. Assem, M. A. Gatica, R. Schiffler, and R. Taillefer : Hochschild cohomology of relation extension algebras, J. Pure Appl. Alg. 220, 7, (2016), 2471–2499.
8
I. Canakci and R. Schiffler : Snake graph calculus and cluster algebras from surfaces III: Band graphs and snake rings, 51 pages.
8
R. Schiffler and  K. Serhiyenko : Induced and coinduced modules over cluster-tilted algebras. 27 pages.
10
I. Canakci, K. Lee, R. Schiffler : On cluster algebras from unpunctured surfaces with one marked point, Proc. Amer. Math. Soc Ser. B 2 (2015) 35-49.
11
I. Assem, M. J. Redondo, R. Schiffler : On the first Hochschild cohomology group of a cluster-tilted algebra, Algebr. Represent. Theory 18 (6), (2015), 1547-1576.
12
I. Canakci, R. Schiffler : Snake graph calculus and cluster algebras from surfaces II: Self-crossing snake graphs, Math. Z. 281 (1), (2015), 55-102.
13 K. Lee, R. Schiffler : Positivity for cluster algebras, Annals of Math. 182 (1), (2015) 73-125.
14
I. Assem, V. Shramchenko, R. Schiffler : Addendum to Cluster automorphisms and compatibility of cluster variables, Glasgow Math. J. 56 (3), (2014).
15
I. Assem, V. Shramchenko, R. Schiffler : Cluster automorphisms and compatibility of cluster variables, Glasgow Math. J. 56 (3), (2014) 705-720.
16
K. Lee, R. Schiffler : Positivity for cluster algebras of rank 3, Publ. Res. Inst. Math. Sci. 49, (2013) 601-649.
17
I. Assem, G. Dupont, R. Schiffler : On a category of cluster algebras, 37 pages, J. Pure Appl. Alg. 218 (3), (2013) 553-582.
18
I. Canakci, R. Schiffler : Snake graph calculus and cluster algebras from surfaces, J. Algebra, 382, (2013) 240-281.
19
I. Assem, J. C. Bustamante, K. Igusa, R. Schiffler : The first Hochschild cohomology group of a cluster-tilted algebra revisited,  Internat. J. Algebra Comput. 23 (4), (2013) 729-744.
20 I. Assem, M. A. Gatica, R. Schiffler : The higher relation bimodule, Algebras and Represent. Theory, 16, 4 (2013), 979-999.
21
G. Musiker, R. Schiffler, L. Williams : Bases for cluster algebras form surfaces, Compositio Math 149, 2, (2013) 217-263.
22
K. Lee, R. Schiffler : A Combinatorial Formula for Rank 2 Cluster Variables, J. Alg. Comb, 37, 1, (2013) 67-85.
23 K. Lee, R. Schiffler :  Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables, Compositio Math. 148, 6, (2012) 1821-1832.
24 M. Oryu, R. Schiffler : On one-point extensions of cluster-tilted algebras,  J. Algebra 357, (2012) 168-182.
25 R. Kinser, R. Schiffler : Idempotents in representation rings of quivers, Algebra Number Theory 6, No. 5, (2012), 967-994.
26
L. David-Roesler, R. Schiffler : Algebras from surfaces without punctures, J. Algebra 350, (2012), 218-244.
27
I. Assem, G. Dupont, R. Schiffler, D. Smith : Friezes, strings and cluster variables, Glasgow Math. J. 54, 1 (2012) 27-60.
28
I. Assem, V. Shramchenko, R. Schiffler : Cluster automorphisms, Proc. Lond. Math. Soc. 104(6),  (2012), 1271-1302.
29
G. Musiker, R. Schiffler, L. Williams : Positivity for cluster algebras from surfaces, Advances in Math. 227 (2011) 2241-2308.
30
I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras without clusters, J. Algebra 324, (2010) 2475-2502.
31
K. Igusa, R. Schiffler : Exceptional sequences and clusters,  J. Algebra 323, 8, (2010) 2183-2202.
32 G. Musiker, R. Schiffler : Cluster expansion formulas and perfect matchings, J. Alg. Comb. 32, 2, (2010) 187-209.
33
R. Schiffler: On cluster algebras arising from unpunctured surfaces II, Advances in Math. 223 (2010) 1885-1923.
34
R. Schiffler, Cluster algebras and cluster categories, lecture notes for the Latin American Colloquium, Sao Pedro, Brazil, (2009).
35
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.
36
R. Schiffler, H. Thomas : On cluster algebras arising from unpunctured surfaces, Intern. Math. Res. Not. 17 (2009) 3160-3189.
37
I. Assem, T. Brüstle, R. Schiffler : On the Galois covering of a cluster-tilted algebra, J. Pure Appl. Alg. 213, (7) (2009) 1450-1463.
38
R. Schiffler : A cluster expansion formula (A_n case), Electron. J. Combin. 15 (2008) #R64 1.
39
I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras and slices, J. of Algebra 319 (2008) 3464-3479.
40 I. Assem, T. Brüstle, R. Schiffler : Cluster-tilted algebras as trivial extensions, Bull. London Math. Soc. 40 (2008) 151-162.
41
R. Schiffler : A geometric model for cluster categories of type D_n, J. Alg. Comb. 29, no. 1, (2008) 1-21.
42
I. Assem, T. Brüstle, R. Schiffler, G. Todorov : m-cluster categories and m-replicated algebras, J. Pure Appl. Alg. 212 (4) (2008) 884-901.
43 I. Assem, T. Brüstle, R. Schiffler, G. Todorov : Cluster categories and duplicated algebras, J. of Algebra 305 (2006) 548-561.
44
P. Caldero, F. Chapoton, R. Schiffler : Quivers with relations and cluster tilted algebras, Algebras and Representation Theory 9, no. 4, (2006) 359-376.
45 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.
46
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).
47
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.
48
R. Schiffler : Projective rational smoothness of varieties of representations for quivers of type A, Representation Theory 7 (2003) 549-586.
49 R. Bédard, R. Schiffler : Rational smoothness of varieties of representations for quivers of type A, Representation Theory 7, (2003) 481-548.