Ayse Sahin, Ph.D.

Department:
Mathematics & Statistics
Title:
Professor and Chair
Address:
Math/Microbiology Bldg 120, 3640 Colonel Glenn Hwy, Dayton, OH 45435-0001

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 Zd 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 Rd 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 Zd actions and directional entropy. Ergodic Theory Dynam. Systems 31 (2011), no. 1, 285–299. 

Şahin, Ayşe A. The Zd 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 Zd actions. J. London Math. Soc. (2) 69 (2004), no. 3, 693–706. 

Quas, Anthony; Şahin, Ayşe A. Entropy gaps and locally maximal entropy in Zd 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 (Zd) 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 Z2. Pacific J. Math. 201 (2001), no. 1, 205–221. 

Robinson, E. Arthur, Jr.; Şahin, Ayşe A. Modeling ergodic, measure preserving actions on Zd 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 Zd 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 Zd 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 Zd shifts of finite type. Proc. Amer. Math. Soc. 127 (1999), no. 11, 3309–3318. 

Şahin, Ayşe Arzu Tiling representations of R2 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 Zd. Ergodic Theory Dynam. Systems 18 (1998), no. 5, 1159–1172.

Johnson, Aimee S. A.; Şahin, Ayşe A. Finite rank Zd 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.

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