Andrew Krenz

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."

Research

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.

Teaching

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

Discrete Math Lecture Notes

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Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5
Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10
Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15
Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20
Lecture 21 Lecture 22 Lecture 23 Lecture 24 Currying

Calc 2 Lecture Notes

FToC U-Sub By Parts Trig
Partial Fractions Linear ODEs

Higgins: Categories & Groupoids

Chapter 1 Chapter 6