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.

## Lecturer

### Publications

• “Disjoint Infinity-Borel Functions”, In progress.

• “Bounding 2D Functions by Products of 1D Functions” In progress.

• “Perfect Tree Forcings for Singular Cardinals” with Natasha Dobrinen

and Karel Prikry, Submitted for Publication.

• “Generic Coding with Help and Amalgamation Failure” with Sy David

Friedman, to appear in the Journal of Symbolic Logic.

• “Forcing and the Halpern-Lauchli Theorem” with Natasha Dobrinen, to

appear in the Journal of Symbolic Logic.

• “Sacks Forcing and the Shrink Wrapping Property” with Osvaldo Guzman

Gonzalez, to appear in Fundamenta Mathematicae

https://www.impan.pl/en/publishing-house/journals-and-series/fundamenta-mathematicae/all//0/112892/sacks-forcing-and-the-shrink-wrapping-property,

DOI: 10.4064/fm688-2-20198.

• “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

### Education

- PhD Mathematics, University of Michigan, 2015
- MS Mathematics, BS Mathematics and Computer Science, Rensselaer Polytechnic Institute, 2010

### Contact

- 802-656-8121

Innovation Hall E311

### Courses Taught

UVM: Applied Linear Algebra 122, Linear Algebra 124, Fundamentals of Calculus II 020, Calculus I 021, Real Analysis Math 141

U of Denver: Calculus I & II, Differential Equations, Linear Algebra, Geometry, Multivariable Calculus

U of Michigan: Calculus I & II, Pre-Calculus

### Course Syllabi - Fall 2019

Real Analysis Section A Fall 2019 (PDF)

Applied Linear Algebra Section A Fall 2019 (PDF)