Biases in $k$-regular and $k$-indivisible Partitions
with Misheel Otgonbayar
UVA REU. July 2022.
slides
Abstract
Describes previous work using the circle method which gives an asymptotic for the number of
parts in partitions of $n$ which are congruent to $r$ mod $t$. Using similar methods, this talk
gives an asymptotic for the number of parts congruent to $r$ mod $t$ among partitions of $n$
which are $k$-regular (no part having multiplicity $k$ or more) and which are $k$-indivisible
(no part divisible by $k$). It then explores the properties of the implied biases towards
different congruence classes in either case before walking through the proofs using the circle
method and Euler-Maclaurin summation.
Incorporates research with Misheel Otgonbayar, under the advisement of William Craig and the
directorship of Ken Ono.
Reducibility of Sets in Generalized Settings
with Justine Dell and Henry Fleischmann
Young Mathematician's Conference. August 2021.
slides
Abstract
Describes additively irreducible sets in higher dimensions as well as in different bases, from
the perspective of the max-min semiring as well as lunar numbers.
Incorporates research with Benjamin Baily, Justine Dell, Henry L. Fleischmann, Leo Goldmakher,
Steven J. Miller, Ethan Pesikoff, and Luke Reifenberg.
The Complexity of the Zeckendorf Graph Game
with Benjamin Baily and Ethan Pesikoff
Young Mathematician's Conference. August 2021.
slides
Abstract
Explores the complexity of the Zeckendorf graph game, which we showed to be PSPACE-Complete by
reducing to the formula game.
Incorporates research with Benjamin Baily, Justine Dell, Henry L. Fleischmann, Steven J. Miller,
Ethan Pesikoff, and Luke Reifenberg.
The Bergman Game
with Ethan Pesikoff and Luke Reifenberg
Young Mathematician's Conference. August 2021.
slides
Abstract
Describes and explores the Bergman Game, a combinatorial game which produces base-$\varphi$
expansions of positive integers.
Incorporates research with Benjamin Baily, Justine Dell, Irfan Durmic, Henry Fleischmann,
Isaac Mijares, Steven J. Miller, Ethan Pesikoff, Luke Reifenberg, Alicia Smith Reina, and
Yingzi Yang.
Extensions of Conway's Game of Life
with Erya Du, Dianhui Ke, and Trey Smith
University of Michigan Lab of Geometry Poster Session. April 2021.
poster
Abstract
A poster concerning research on extensions of Conway's Game of Life, particularly probabilistic
and weighted extensions of the game.
Advised by Benjamin Riley, Carsten Sprunger, Katie Storey, and Joern Zimmerling.
You Need a Lemma
University of Michigan Directed Reading Program. April 2021.
slides
Abstract
Introduces category theory, thinking using universal properties, and the Yoneda Lemma.
Advised by Lukas Schweiller.
The Point at $\infty$: What is the Degree of $1/z$?
University of Michigan Math Club. April 2020.
slides
Advised by Christopher Zhang.