Pieter Allaart
University of North Texas
Mathematics
(940) 369-7313
Email:

Education

PhD, Vrije Universiteit Amsterdam, 1998.
Major: Mathematics & Computer Science
Dissertation Title: Ranges of vector measures and optimal-partitioning inequalities
MA, Free University, 1994.
Major: Mathematics; Master's thesis: A constant-sum characterization of Benford's Law

Professional Positions

Uncategorized
Associate Professor, University of North Texas. (2007 – Present).
GCOE Foreign Researcher, Kyoto University. (20092009).
Assistant Professor, University of North Texas. (20012007).
Visiting Assistant Professor, University of North Texas. (19982001).

Teaching

Teaching Experience

University of North Texas
MATH 1680, Elementary Probability and Statistics, 2 courses.
MATH 1710, Calculus I, 2 courses.
MATH 1720, Calculus II, 2 courses.
MATH 1780, Probability Models, 2 courses.
MATH 2510, Real Analysis I, 2 courses.
MATH 2700, Linear Algebra and Vector Geometry, 9 courses.
MATH 2730, Multivariable Calculus, 7 courses.
MATH 3000, Real Analysis I, 4 courses.
MATH 3010, Seminar in Problem Solving Techniques, 8 courses.
MATH 3180, Probability for Engineers, 1 course.
MATH 3410, Differential Equations I, 7 courses.
MATH 3510, Abstract Algebra I, 3 courses.
MATH 3680, Applied Statistics, 4 courses.
MATH 4610, Probability, 10 courses.
MATH 4650, Statistics, 2 courses.
MATH 4900, Special Problems, 4 courses.
MATH 5110, Introduction to Analysis, 2 courses.
MATH 5120, Introduction to Analysis, 2 courses.
MATH 5310, Real Analysis, 5 courses.
MATH 5320, Real Analysis, 7 courses.
MATH 5350, Markov Processes, 1 course.
MATH 5810, Probability and Statistics, 5 courses.
MATH 5820, Probability and Statistics, 1 course.
MATH 5900, Special Problems, 23 courses.
MATH 5910, Special Problems, 1 course.
MATH 6810, Probability., 5 courses.
MATH 6900, Special Problems, 10 courses.
MATH 6940, Individual Research, 1 course.
MATH 6950, Doctoral Dissertation, 27 courses.

Directed Student Learning

Directed Individual/Independent Study, Mathematics. (August 2023December 2023).

Other, Mathematics. (October 2023).

Doctoral Advisory Committee Chair,"Dimensions of statistically self-affine functions and random Cantor sets," Mathematics. (May 2023).

Directed Individual/Independent Study, Mathematics. (August 2022December 2022).

Directed Individual/Independent Study,"Groups as unions of proper subgroups," Mathematics. (September 2021November 2021).

Directed Individual/Independent Study, Mathematics. (January 2021August 2021).

Doctoral Advisory Committee Chair,"Optimal look-ahead stopping rules for simple random walk," Mathematics. (June 2021).

Directed Individual/Independent Study,"N/A," Mathematics. (January 2021May 2021).

Directed Individual/Independent Study, Mathematics. (July 2020December 2020).

Other, Mathematics. (August 2019December 2020).

Directed Individual/Independent Study, Mathematics. (January 2020May 2020).

Doctoral Advisory Committee Chair,"Prophet inequalities for multivariate random variables with cost for observations," Mathematics. (May 2019).

Other, Mathematics. (January 2019May 2019).

Directed Individual/Independent Study, Mathematics. (August 2018December 2018).

Other, Mathematics. (August 2018December 2018).

Doctoral Advisory Committee Chair,"A random walk version of Robbins' problem," Mathematics. (October 2018).

Other, Mathematics. (January 2018January 2018).

Other, Mathematics. (August 2017December 2017).

Dissertation Committee Member, Mathematics. (June 2017).

Directed Individual/Independent Study, Mathematics. (January 2017May 2017).

Other, Mathematics. (January 2017May 2017).

Doctoral Advisory Committee Chair, Mathematics. (December 2015).

Major Professor, Mathematics. (2015).

Major Professor, Mathematics. (2014).

Major Professor,"Project title: The optimal stopping time for the American call/put option using a multiplicative random walk," Mathematics. (20082008).

Research

Published Intellectual Contributions

Journal Article
Allaart, P. C., Kong, D. (2023). Critical values for the beta-transformation with a hole at 0. Ergodic Theory and Dynamical Systems. 43(6), 1785-1828.
Allaart, P. C., Jackson, S. C., Jones, R. T., Lambert, D. (2023). On the existence of numbers with matching continued fraction and decimal expansions. Monatshefte für Mathematik. 202(1), 1-30.
Allaart, P., Jones, R. T. (2023). Box-counting dimension and differentiability of box-like statistically self-affine functions. Journal of Mathematical Analysis and Applications. 521(2), Article 126909, 20 pages.
Allaart, P. C., Kong, D. (2022). Density spectrum of Cantor measure. Nonlinearity. 35(12), 6453–6484.
Allaart, P. C., Kong, D. (2021). Relative bifurcation sets and the local dimension of univoque bases. Ergodic Theory and Dynamical Systems. 41(8), 2241-2273.
Allaart, P. C., Kong, D. (2021). On the smallest base in which a number has a unique expansion. Transactions of the American Mathematical Society. 374(9), 6201-6249.
Norouzi Kandalan, R., Allaart, P. C., Namuduri, K. (2020). Mobility Accelerates Consensus-Building in Sensor Networks.. IEEE Sensors Letters. 4(12), 1-4.
Allaart, P. C. (2020). The pointwise Holder spectrum of general self-affine functions on an interval.. Journal of Mathematical Analysis and Applications. 488(2), Article 124096, 35 pages. Elsevier.
Allaart, P., Allen, A. (2019). A random walk version of Robbins' problem: small horizon. Mathematica Applicanda. 47(2), 293-312.
Allaart, P. (2019). An algebraic approach to entropy plateaus in non-integer base expansions. Discrete and Continuous Dynamical Systems. 39(11), 6507-6522.
Allaart, P., Kong, D. (2019). On the continuity of the Hausdorff dimension of the univoque set. Advances in Mathematics. 354, 24 pages.
Allaart, P., Kong, D., Baker, S. (2019). Bifurcation sets arising from non-integer base expansions. Journal of Fractal Geometry. 6(4), 301-341.
Allaart, P. (2018). Differentiability and Holder spectra of a class of self-affine functions. Advances in Mathematics. 328, 1-39.
Allaart, P. (2017). Differentiability of a two-parameter family of self-affine functions. Journal of Mathematical Analysis and Applications. 450, 954-968.
Allaart, P. (2017). On univoque and strongly univoque sets. Advances in Mathematics. 308, 575-598.
Allaart, P., Islas, J. A. (2016). A sharp lower bound for choosing the maximum of an independent sequence. Journal of Applied Probability. 53(4), 1041-1051.
Allaart, P. (2016). The infinite derivatives of Okamoto's function: an application of beta-expansions. Journal of Fractal Geometry. 3(1), 1-31.
Allaart, P. (2014). Correction and strengthening of ``How large are the level sets of the Takagi function?".
Allaart, P. (2014). Digital sum inequalities and approximate convexity of Takagi-type functions.
Allaart, P. (2014). Hausdorff dimension of level sets of generalized Takagi functions.
Allaart, P. (2014). On the level sets of the Takagi-van der Waerden functions.
Allaart, P. (2013). Level sets of signed Takagi functions. Acta Mathematica Hungarica.
Allaart, P. (2012). How large are the level sets of the Takagi function?.
Allaart, P. (2012). Predicting the supremum: optimality of "stop at once or not at all".
Allaart, P. (2012). The finite cardinalities of level sets of the Takagi function.
Allaart, P. (2012). The Takagi function: a survey.
Allaart, P. (2011). An inequality for sums of binary digits, with application to Takagi functions http://arxiv.org/abs/1009.1308 Related Links: http://arxiv.org/abs/1009.1308.
Kawamura, K., Allaart, P. C. (2011). Takagi function: Survey. Denton:.
Allaart, P. (2010). A general `bang-bang' principle for predicting the maximum of a random walk..
Allaart, P. (2010). How to stop near the top in a random walk.
Allaart, P. (2010). Optimal stopping rules for American and Russian options in a correlated random walk model..
Allaart, P. (2010). The improper infinite derivatives of Takagi's nowhere-differentiable function.
Allaart, P. (2009). A sharp ratio inequality for optimal stopping when only relative record times are observed.
Allaart, P. (2009). Injectivity of the Dubins-Freedman construction of random distributions.
Allaart, P. (2009). On a flexible class of continuous functions with uniform local structure.
Allaart, P. (2008). Distribution of the extrema of random Takagi functions.
Allaart, P. (2008). Optimal buy/sell strategies for directionally reinforced processes..
Allaart, P. (2007). Dimensions of the coordinate functions of space-filling curves.
Allaart, P. (2007). Prophet inequalities for i.i.d. random variables with random arrival times.
Allaart, P. (2006). Extreme values of some continuous, nowhere differentiable functions.
Allaart, P. (2006). Prophet regions for discounted, uniformly bounded random variables.
Allaart, P. (2005). On the coordinate functions of L´evy's dragon curve.
Allaart, P. (2005). Prophet regions for independent [0, 1]-valued random variables with random dis- counting.
Allaart, P. (2004). An application of prophet regions to optimal stopping with a random number of observations.
Allaart, P. (2004). Optimal stopping rules for correlated random walks with a discount.
Allaart, P. (2004). Stopping the maximum of a correlated random walk, with cost for observation.
Allaart, P. (2003). Moments of the mean of Dubins-Freedman random probability distributions.
Allaart, P. (2003). Pseudo-prophet inequalities in average-optimal stopping.
Allaart, P. (2001). Optimal stopping rules for directionally reinforced processes.
Allaart, P. (2000). Inequalities relating maximal moments to other measures of dispersion.
Allaart, P. (1999). A sharp non-convexity bound for partition ranges of vector measures with atoms.
Allaart, P. (1999). Bounds on the non-convexity of ranges of vector measures with atoms.
Allaart, P. (1998). Minimax risk inequalities for the location-parameter classification problem.
Allaart, P. (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability. 34, 288-291.

Presentations Given

Invited Talk

Allaart, P. (Author & Presenter), AMS Southeastern Sectional Meeting, The beta-transformation with a hole at zero, American Mathematical Society, Mobile, AL, United States of America. (2023).

Allaart, P. (Author & Presenter), Chongqing University Dynamical Systems Seminar, Differentiability and Holder spectrum of a class of self-affine functions, Chongqing University, online, China. (20232023).

Allaart, P. (Author & Presenter), American Mathematical Society Western Sectional Meeting, Density spectrum of Cantor measure, American Mathematical Society, online, United States of America. (20222022).

Allaart, P. C. (Author & Presenter), One World Numeration Seminar (online), On the existence of Trott numbers relative to multiple bases, online, United States of America. (20212021).

Allaart, P. C. (Author & Presenter), One World Numeration Seminar, On the smallest base in which a number has a unique expansion, Online, France. (2020).

Allaart, P. C. (Author & Presenter), Probability Seminar, On univoque and strongly univoque sets, University of Waterloo, Waterloo, Ontario (virtual seminar), Canada. (2020).

Allaart, P. C. (Author & Presenter), American Mathematical Society Southeastern Sectional Meeting, The pointwise Holder spectrum of self-affine functions, American Mathematical Society, Gainesville, Florida, United States of America. (2019).

Allaart, P. C. (Author & Presenter), Kyoto University Dynamical Systems Seminar, The pointwise Holder spectrum of self-affine functions, Kyoto, Japan. (2019).

Allaart, P. C. (Author & Presenter), Tsukuba University Number Theory Seminar, On univoque and strongly univoque sets, Tsukuba, Japan. (2019).

Allaart, P. (Author & Presenter), 60 years of dynamics and number expansions, On the local dimension of the univoque set, Pisa, Italy. (2018).

Allaart, P. (Author & Presenter), Symposium on Optimal Stopping, Some difficult to solve optimal stopping problems, Rice University, Houston, TX, United States of America. (2018).

Allaart, P. (Author & Presenter), Ergodic Theory Seminar, On univoque and strongly univoque sets, Warwick University (U.K.), United Kingdom. (2018).

Allaart, P. (Author & Presenter), Ergodic Theory Seminar, On univoque and strongly univoque sets, Leiden University, Netherlands. (2018).

Allaart, P. (Author & Presenter), Workshop on Ergodic Theory and Fractals, Differentiability and Holder spectra of a class of self-affine functions, Utrecht, Netherlands. (2018).

Allaart, P. (Author & Presenter), AMS Central Sectional Meeting, Differentiability and Holder spectra of a class of self-affine functions, American Mathematical Society, Denton, TX, United States of America. (2017).

Allaart, P. (Author & Presenter), Real Analysis Symposium, Differentiability and Holder spectra of a class of self-affine functions, Wooster, Ohio, United States of America. (20172017).

Oral Presentation

Allaart, P. (Author & Presenter), Geometry of Deterministic and Random Fractals, Density spectrum of Cantor measure, Budapest University of Engineering and Economics, Budapest, Hungary. (20222022).

Allaart, P. (Author & Presenter), AMS Southeastern Sectional Meeting, The infinite derivatives of Okamoto's function and beta-expansions, American Mathematical Society, Memphis, TN, United States of America. (2015).

Allaart, P. (Author & Presenter), Kyoto University Dynamical Systems Seminar, The infinite derivatives of Okamoto's function and beta-expansions, Kyoto, Japan. (2015).

Allaart, P. (Author & Presenter), AMS Sectional Meeting, Zero sets and maximum sets of randomized Takagi functions, American Mathematical Society, Lubbock, TX, United States of America. (2014).

Allaart, P. (Author & Presenter), Real Analysis Symposium, Zero sets and maximum sets of randomized Takagi functions, Prague, Czech Republic. (2014).

Allaart, P. (Author & Presenter), AMS Southeastern Sectional Meeting, The Hausdorff dimension of level sets of generalized Takagi functions, American Mathematical Society, Oxford, MS, United States of America. (2013).

Allaart, P. (Author & Presenter), Kyoto University Mathematics Department Colloquium, A new look at the Takagi function, Kyoto, Japan. (2012).

Allaart, P. (Author & Presenter), RTG Conference on logic, dynamics and their interactions, with a celebration of the work of Dan Mauldin, The Hausdorff dimension of level sets of generalized Takagi functions, Denton, TX, United States of America. (2012).

Allaart, P. (Author & Presenter), XVIII SIMMAC (International Symposium on Mathematical Methods Applied to the Sciences), Optimal prediction of the maximum of a stochastic process, San Jose, Costa Rica, Costa Rica. (2012).

Contracts, Grants and Sponsored Research

Grant - Research
Allaart, P. C. (Principal), "Non-integer base expansions and multifractal analysis," Sponsored by Simons Foundation, Private, $42000 Funded. (September 2020August 2025).
Allaart, P. (Principal), "Visitor grant for a 2.5 month research visit to Utrecht University," Sponsored by NWO (Dutch National Science Foundation), International, $7000 Funded. (March 2018June 2018).

Service

University Service

Chairperson, Real Analysis Qualifying Exam Committee. (June 2023 – Present).

Committee Member, Executive Committee. (August 2022 – Present).

Committee Member, Probability and Statistics Qualifying Exam Committee. (June 2018 – Present).

Member, Administrator Evaluation Committee. (October 2023December 2023).

Committee Member, Faculty Council. (September 2021December 2023).

Chairperson, Faculty Council. (August 2022June 2023).

Member, Chair Search Committee. (January 2023May 2023).

Committee Member, Real Analysis Qualifying Exam Committee. (June 2021May 2023).

Member, Statistics Search Committee. (January 2023March 2023).

Committee Member, Applied PDE search committee. (January 2022March 2022).

Committee Chair, Graduate Affairs Committee. (June 2020May 2021).

Committee Member, Executive Committee. (May 2019May 2021).

Committee Member, Faculty Senate Committee on Teaching Fellows and Teaching Assistants. (September 2015May 2021).

Committee Member, Graduate Affairs Committee. (June 2012June 2020).

Committee Chair, Ad-hoc grade appeal committee. (June 2019July 2019).

Committee Chair, Graduate Affairs Committee. (January 2019June 2019).

Committee Member, Applied PDE Search Committee. (September 2018May 2019).

Committee Member, Real Analysis Qualifying Exam Committee. (June 2017May 2018).

Committee Chair, Graduate Affairs Committee. (August 2017December 2017).

Committee Member, Probability and Statistics Qualifying Exam Committee. (June 2015May 2017).

Committee Member, Strategic Planning Committee. (June 2013May 2017).

Committee Chair, Real Analysis Qualifying Exam Committee. (June 2015May 2016).

Committee Chair, Graduate Affairs Committee. (20112013).

Other, Executive Committee. (20102012).

Committee Chair, Harmonic Analysis and Differential Equations Search Committee. (20072008).

Other, Undergraduate Curriculum Committee. (20062008).

Other, Undergraduate Affairs Committee. (20022008).

Other, UNT Stochastics Seminar. (20012005).

Professional Service

Workshop Organizer, Conference on Dynamical Systems and Fractal Geometry, Denton, TX. (June 2022 – Present).

Reviewer, Journal Article, Refereeing. (20192021).

Reviewer, Journal Article, American Mathematical Societry Math Reviews. (2005June 2020).

Reviewer, Book, American Mathematical Societry Math Reviews. (20182018).

Reviewer, Grant Proposal, Grant proposal to the Israel Science Foundation. (20072007).