William Mance

William Mance

Department:
Department of Dynamical Systems

Position:
adiunkt

room:
pok. 603

Phone number:
22 5228 221

e-mail:
e-mail

I'm a postdoc in the Institute of Mathematics at the Polish Academy of Sciences.  My research deals primarily with normal numbers and their relation to ergodic theoryfractal geometrynumber theory, and probability theory. Recently I have also started exploring questions about normal numbers relating to computability theory and descriptive set theory. My advisor was Vitaly Bergelson and I can be found here at the Mathematics Genealogy Project. You can see all of my papers here and some talks I've given here. This is my CV.

I was born and raised in Royal OakMichigan. I have also lived in PittsburghPennsylvaniaColumbusOhio, and DentonTexas before I moved to Warsaw, Poland

Assistant Professor, Mathematics, Polish Academy of Sciences (IMPAN)
Ph.D. (Mathematics), The Ohio State University (2010)
B.S. (Mathematics), Carnegie Mellon University (2003)

Videos of some talks

Here is Dylan Airey speaking on a recent paper that we are finishing with Stephen Jackson "Some complexity results on sets related to normal numbers" that relates normal numbers and desriptive set theory.

Here I am giving a talk on a recent paper I wrote with Dylan Airey "Normality of different orders for Cantor series expansions".

Publications

High school coauthors are marked with a † and undergraduate coauthors are marked with a *.  My papers can all be found on arXiv.org here.

  1. Some complexity results on sets related to normal numbers (with D. Airey* and Stephen Jackson), submitted arXiv preprint YouTube video
  2. Normality of different orders for Cantor series expansions (with D. Airey*), submitted arXiv preprint YouTube video
  3. Unexpected Distribution Phenomenon resulting from Cantor Series Expansions (with D. Airey†), Adv. Math. 279, 372--404 (2015) arXiv preprint
  4. Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions, Bull. Aust. Math. Soc. 92 (2), 205--213 (2015) (with Lior FishmanDavid Simmons, and Mariusz Urbanski), arXiv preprint
  5. On the Hausdorff dimension of countable intersections of certain sets of normal numbers, J. Théor. Nombres Bordeaux 27 (1), 199--217 (2015) arXiv preprint
  6. On the Hausdorff dimension of some sets of numbers defined through the digits of their Q-Cantor series expansions, to appear in J. Fractal Geom. (with D. Airey*) arXiv preprint
  7. Normal number constructions for Cantor series with slowly growing bases,to appear in Czechoslovak Math. J. (with D. Airey* and J. VandeheyarXiv preprint
  8. Normality preserving operations for Cantor series expansions and associated fractals, II, to appear in New York J. Math. (with D. Airey* and J. VandeheyarXiv preprint
  9. Normality preserving operations for Cantor series expansions and associated fractals, I, to appear in Illinois J. Math. (with D. Airey*) arXiv preprint
  10. Normal equivalencies for eventually periodic basic sequences, Indag. Math. 26 (3), 476--484 (2015) (with D. Airey*), to appear in Indag. Math arXiv preprint
  11. Number Theoretic Applications of a Class of Cantor Series Fractal Functions, II, Int. J. Number Theory 11 (2), 407--435 (2015) (with B. Li†) arXiv preprint
  12. Number Theoretic Applications of a Class of Cantor Series Fractal Functions, I, Acta Math. Hungar. 144 (2), 449-493 arXiv preprint
  13. Construction of μ-normal numbers (with M. Madritsch), to appear in Monatsh. Math. arXiv preprint
  14. Bounded Lüroth Expansions: Applying Schmidt Games where Infinite Distortion Exists (with J. Tseng) Acta Arith. 158, 33-47 (2013) arXiv preprint
  15. Cantor series constructions of sets of normal numbers, Acta Arith. 156, 223-245 (2012) arXiv preprint
  16. Typicality of normal numbers with respect to the Cantor series expansion, New York J. Math., 17, 601-617 (2011) Available Here
  17. Cantor Series Constructions Contrasting Two Notions of Normality (with C. Altomare), Monatsh. Math., 164, 1-22 (2011) arXiv preprint
  18. Construction of normal numbers with respect to the Q-Cantor series expansion for certain Q, Acta Arith. 148, 135-152 (2011) arXiv preprint
  19. Normal Numbers with Respect to the Cantor Series Expansion, Doctoral Dissertation (2010)

 

Instytut Matematyczny
Polskiej Akademii Nauk
ul. Sniadeckich 8
00--656 Warszawa, Poland

 

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