## Ayse Sahin, Ph.D.

## Education History

B.A. in Mathematics, 1988, Mount Holyoke College

M.A. in Mathematics, 1992, University of Maryland at College Park

Ph.D. in Mathematics, 1994, University of Maryland at College Park

## Research Statement

Ergodic theory and dynamical systems; actions of amenable groups.

## Publications

Şahin, Ayşe; Schraudner, Michael; Ugarcovici, Ilie. A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings. Illinois Journal of Mathematics, *to appear*.

Cyr, Van; Kra, Bryna; Johnson, Aimee S.A.; Şahin, Ayşe. The complexity threshold for the emergence of Kakutani inequivalence. Israel Journal of Mathematics, *to appear*.

Johnson, Aimee; Madden, Kathleen; Şahin, Ayşe. Discovering discrete dynamical systems. Classroom Resource Materials Series. Mathematical Association of America, Washington, DC, 2017. xiii+116 pp.

Dykstra, Andrew; Şahin, Ayşe. The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer. J. Anal. Math. 132 (2017), 311–353.

Johnson, Aimee S. A.; Şahin, Ayşe A. Directional recurrence for infinite measure preserving Z^{d} actions. Ergodic Theory Dynam. Systems 35 (2015), no. 7, 2138–2150.

Kra, Bryna; Quas, Anthony; Şahin, Ayşe. Rudolph's two step coding theorem and Alpern's lemma for R^{d} actions. Trans. Amer. Math. Soc. 367 (2015), no. 6, 4253–4285.

Lightwood, Samuel; Şahin, Ayşe; Ugarcovici, Ilie. The structure and spectrum of Heisenberg odometers. Proc. Amer. Math. Soc. 142 (2014), no. 7, 2429–2443. 37B50

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. Rank-one Z^{d} actions and directional entropy. Ergodic Theory Dynam. Systems 31 (2011), no. 1, 285–299.

Şahin, Ayşe A. The Z^{d} Alpern multi-tower theorem for rectangles: a tiling approach. Dyn. Syst. 24 (2009), no. 4, 485–499.

del Junco, Andrés; Şahin, Ayşe. Dye's theorem in the almost continuous category. Israel J. Math. 173 (2009), 235–251.

Şahin, Ayşe; Ugarcovici, Ilie; Gidea, Marian. Preface [Research conducted in dynamical systems]. Discrete Contin. Dyn. Syst. Ser. S 2 (2009), no. 2, i–ii. 37-06

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. On the existence of Markov partitions for Z^{d} actions. J. London Math. Soc. (2) 69 (2004), no. 3, 693–706.

Quas, Anthony; Şahin, Ayşe A. Entropy gaps and locally maximal entropy in Z^{d} subshifts. Ergodic Theory Dynam. Systems 23 (2003), no. 4, 1227–1245.

Johnson, Aimee S. A.; Şahin, Ayşe A. Even Kakutani equivalence and the loose block independence property for positive entropy (Z^{d}) actions. Illinois J. Math. 45 (2001), no. 2, 495–516.

Park, Kyewon Koh; Şahin, Ayşe A. Even Kakutani equivalence via α→ and β→ equivalence in Z^{2}. Pacific J. Math. 201 (2001), no. 1, 205–221.

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. Modeling ergodic, measure preserving actions on Z^{d} shifts of finite type. Monatsh. Math. 132 (2001), no. 3, 237–253.

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. Mixing properties of nearly maximal entropy measures for Z^{d} shifts of finite type. Dedicated to the memory of Anzelm Iwanik. Colloq. Math. 84/85 (2000), part 1, 43–50.

Johnson, Aimee S. A.; Şahin, Ayşe A. Isometric extensions of zero entropy Z^{d} loosely Bernoulli transformations. Trans. Amer. Math. Soc. 352 (2000), no. 3, 1329–1343.

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. On the absence of invariant measures with locally maximal entropy for a class of Z^{d} shifts of finite type. Proc. Amer. Math. Soc. 127 (1999), no. 11, 3309–3318.

Şahin, Ayşe Arzu Tiling representations of R^{2} actions and α-equivalence in two dimensions. Ergodic Theory Dynam. Systems 18 (1998), no. 5, 1211–1255.

Johnson, Aimee S. A.; Şahin, Ayşe A. Rank one and loosely Bernoulli actions in Z^{d}. Ergodic Theory Dynam. Systems 18 (1998), no. 5, 1159–1172.

Johnson, Aimee S. A.; Şahin, Ayşe A. Finite rank Z^{d} actions and the loosely Bernoulli property. New York J. Math. 3A (1997/98), Proceedings of the New York Journal of Mathematics Conference, June 9–13, 1997, 125–134.

Sahin, Ayse Arzu Tiling representations of R(2) actions and alpha-equivalence in two dimensions. Thesis (Ph.D.)–University of Maryland, College Park. 1994. 95 pp.