Daniel grew up in Richmond, Vermont and graduated from Mount Mansfield Union High School in 2005. He earned his bachelor's degree in Mathematics and Computer Science from RPI and remained an extra year to get his MS in Mathematics. Daniel received his PhD in Mathematics from the University of Michigan in 2015 where his thesis advisor was Andreas Blass. He spent 3 years as a Visiting Assistant Professor (Postdoc) at the University of Denver before joining UVM in August 2018.
“Disjoint Infinity-Borel Functions”, In progress
“Bounding 2D Functions by Products of 1D Functions” with Francois Dorais, Submitted
“Classes of Barren Extensions” with Natasha Dobrinen, to appear in the Journal of Symbolic Logic, Final uploaded June 2020
“Generic Coding with Help and Amalgamation Failure” with Sy David Friedman, to appear in the Journal of Symbolic Logic, Final uploaded July 2020
“Perfect Tree Forcings for Singular Cardinals” with Natasha Dobrinen and Karel Prikry, Annals of Pure and Applied Logic, 171 (2020), no. 9, Article 102827.
“Forcing and the Halpern-Lauchli Theorem” with Natasha Dobrinen, Journal of Symbolic Logic, 85(2020), no 1, pp 87-102.
“Sacks Forcing and the Shrink Wrapping Property” with Osvaldo Guzman Gonzalez, Fundamenta Mathematicae, 248 (2020), no. 8, pp 33-47.
“Ramsey Theory on Generalized Baire Space”, Topology and Its Applications, 235(2018), pp 104-112.
“The Halpern-Lauchli Theorem at a Measurable Cardinal” with Natasha Dobrinen, Journal of Symbolic Logic, 82 (2017), pp 1560-1575.
“Disjoint Borel Functions”, Annals of Pure and Applied Logic, 168 (2017), no.8, 1552-1563.
“Weak Distributivity Implying Distributivity”, Journal of Symbolic Logic, 81(2016), pp 711-717.
“Combinatorics of Reductions Between Equivalence Relations” with Scott Schneider, Discrete Math. 338 (2015), no. 11, 2089-2094.
“A Simple C*-algebra with Finite Nuclear Dimension which is Not Z-stable” with Ilijas Farah, Takeshi Katsura, and Aaron Tikuisis, Jan 2013, Munster Journal of Mathematics 7 (2014) no. 2, 515-528.
“Continuity Induction”, College Mathematics Journal, May 2010.
Areas of Expertise and/or Research
Set Theory and Mathematical Logic
- PhD Mathematics, University of Michigan, 2015
- MS Mathematics, BS Mathematics and Computer Science, Rensselaer Polytechnic Institute, 2010
Innovation Hall E311
UVM: Applied Linear Algebra 122, Linear Algebra 124, Fundamentals of Calculus II 020, Calculus I 021, Real Analysis Math 141, Fundamentals of Mathematics 052
U of Denver: Calculus I & II, Differential Equations, Linear Algebra, Geometry, Multivariable Calculus
U of Michigan: Calculus I & II, Pre-Calculus