**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 theory, fractal geometry, number 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 Oak, Michigan. I have also lived in Pittsburgh, Pennsylvania, Columbus, Ohio, and Denton, Texas 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**

**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.

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

**Instytut Matematyczny**

Polskiej Akademii Nauk

ul. Sniadeckich 8

00--656 Warszawa, Poland