After graduating from Purdue University in 2018, I began

studying math as a graduate student at the University of Wisconsin - Madison.

I'm working with Tullia Dymarz and Chenxi Wu in the areas of

Geometric Group Theory and Dynamics.

I will be on the job market fall 2024. Here is a copy of my CV.

Feel free to contact me; my wisc dot edu e-mail address is "krenz3 at."

I have been investigating some categorical consequences of Stone-type dualities.

A particularly interesting generalization of Stone's duality theorem for Boolean algebras

is the duality between poc sets and median algebras. It happens that every Boolean algebra

is both a poc set and a median algebra in a canonical way, and moreover, these two kinds of

structure are reasonably compatible with one another. Surprisingly, any set supporting

suitably compatible poc set and median algebra structures is necessarily a Boolean algebra.

These same compatibility conditions can be used to define a tensor product of an arbitrary

poc set with an arbitrary median algebra as a quotient of a free Boolean algebra. When

this tensor product is appropriately defined, there is a two-variable tensor-hom adjunction

between the categories of poc sets (Poc), median algebras (Med), and Boolean algebras (Bool).

The dualization functors inducing the anit-equivalence between Poc and Med are the mutual

right adjoints present in this two-variable adjunction. The double dualization monads

induced by this adjunction are the codensity monads induced by inclusions of finite poc sets

into Poc and finite median algebras into Med. These patterns hold for other instances of stone

duality as well. One goal of my research is to devise a list of conditions one can impose on a

category that would guarantee analogues of the results described above.

Term | Course | Position |
---|---|---|

Fall 2018 | Math 221: Calculus and Analytic Geometry 1 | Teaching Assistant |

Spring 2019 | Math 221 | TA coordinator |

Fall 2019 | Math 234: Calculus -- Functions of Several Variables | TA coordinator |

Spring 2020 | Math 222: Calculus and Analytic Geometry 2 | TA coordinator |

Summer 2020 | Math 221 | Teaching Assistant |

Fall 2020 | Math 234 | TA coordinator |

Spring 2021 | Math 340: Elementary Matrix and Linear Algebra | Teaching Assistant |

Summer 2021 | Math 240: Introduction to Discrete Mathematics | Insructor of Record |

Fall 2021 | Math 112: Algebra | Instructor of Record |

Spring 2022 | Math 112 | Instructor of Record |

Summer 2022 | Math 222 | Instructor of Record |

Fall 2022 | Math 221 | TA coordinator |

Spring 2023 | Math 222 | Teaching Assistant |

Summer 2023 | Math 240 | Instructor of Record |

Fall 2023 | Math 320:Differential Equations and Linear Algebra | Teaching Assistant |

I have noticed certian browsers tend to omit some pen strokes (especially

single points/dots). This does not seem to be a problem for me when browsing

mobile Safari, for example.

FToC | U-Sub | By Parts | Trig |
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Partial Fractions | Linear ODEs |

Chapter 1 | Chapter 6 |
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