Maciej Piwowarczyk
Doctoral Student in Mathematics @ UNL
Shortcuts
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​Special Case Bijections on ASM's
Graph Constructions of Codes for Nanopore Sequencers in DNA Storage
12/3/24 - UNL Discrete Math Seminar (DisCo)
Storing data in synthetic DNA is an emerging storage technology. Specifically, nanopore sequencers have emerged as a strong contender for the retrieval and decoding of stored DNA, allowing for cheaper and faster, if currently error-prone, reading of DNA sequences. In this talk we will discuss the DNA code design problem for nanopore sequencers and provide a construction of a DNA graph code that accommodates the three primary restrictions imposed by nanopore sequencers. We also show that the proposed code is locally 1-deletion detecting.
Exploring Pseudorandomness
9/29/24 - UNL Math Dept. Graduate Student Seminar
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If I were to ask you to give me a random number between 1 and 10, how would you come up with a number? Would you give me the first number that comes to mind? Would you pull out your phone and ask Siri, or use a Google search? If I wanted a truly random number, would you be more reliably random or would a machine be? Why should we even care about a number being truly random? These are some of the questions that we will explore in this talk about psuedorandom number generation! We’ll learn about the history of the tools, try out a few methods ourselves, and explore the many ways in which psuedorandom number generators can affect our daily and professional lives.
Topics in Math Ed Research
Feb & Mar 2024 - MATH 993: Topics in Math Ed Research
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In the Spring 2024 semester, I got to take a course on topics in math education research at UNL. In this course, I got practice in parsing and presenting papers in this field.
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The topics that I got to present on included the effect of teacher expectations on student achievement, tools for assessing the quality of instruction, frames of the term "mathematics," and the idea of teaching math in an ethical and culturally relevant way.
P = NP? W/ MP
10/5/23 - UNL Math Dept. Graduate Student Seminar
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What do Sudoku, finding Hamiltonian circuits in graphs, and factoring large composite numbers have in common? Well, they’re all a piece of the puzzle that is the P NP problem! One of the Millennium Prize problems, P NP has been around since about the early 70’s. In this talk you’ll learn everything you need to know about this really cool problem, from baseline definitions to why we care about it. As this is a Maciej Piwowarczyk™ presentation, you can also be guaranteed bad memes, good history, and a dollop of graph theory.
Equity in the Classroom
8/17/23 - UNL Math Dept. GTA Orientation
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All Graduate Teaching Assistants (GTAs) in UNL's math department who are at least about to enter their second year of studies are instructors of record. In preparation or in support of this role, GTAs participate in a orientation session focused on creating equitable learning spaces for our student. This year the focus was on identity, and how the same event can be experienced in significantly different ways.
Special Case Bijections on Alternating Sign Matrices
4/21/23 - Pt. 2 in MATH 958: Alternating Sign Matrices
4/7/23 - Pt. 1 in MATH 958: Alternating Sign Matrices
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These two presentations were on papers exploring bijections on Alternating Sign Matrices (ASMs). Though the number of ASM's is well understood, it is generally very difficult to find a bijection between ASM's and classes of objects with the same size. With every new bijection comes a statistic that is not preserved that prevents the general case from being realized. Jessica Striker and Markus Fulmek study a special case in which a bijection is possible to find.
Private Info Retrieval With Side Information
12/6/22 - MATH 958: Info Theory
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A message that you want to retrieve is stored on some amount of remote databases. However, you do not want to reveal which message you are retrieving. One way to protect your message is to download everything in the database. It's inefficient, but it would certainly keep your interests secret.
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Swanand Kadhe et al. in their paper Private Information Retrieval with Side Information consider the scenario where the user already has access to some of the info in the databases. Can we still keep our intentions secret without downloading everything?
One-Cut Origami
3/23/23 - UNL Undergraduate Math Club
9/12/22 - UNL Math Dept. Graduate Student Seminar
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The noble pursuit of origami has been around for centuries. Throughout that time, there has been one question that’s been burning inside of everyone’s head: Given a straight-edge polygon, can you fold the shape such that all of its lines lie on top of each other? It took a few hundred years to sort out the details, but we’ll go over it by the end of this talk. That is, not before we go over the history of the problem and the many people who have contributed to it. Audience participation is encouraged and appreciated!
Algebraic Graph Theory
11/15/22 - UNL Discrete Math Seminar
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One of the beautiful things about Graph Theory is that there are so many ways to represent a graph and each representation tells us something a little different. In this talk we’ll be looking at a graph through its adjacency matrix. At the same time we’ll be building up some algebraic structure. Eventually we’ll put the two together and explore some results that I find pretty cool, like how the diameter of a graph can give you information about the eigenvalues of its adjacency matrix. Time permitting I would also love to share how some special graphs, like complete and bipartite ones, can tell us even more!
The Link Between Vincent, Math, and You!
2/18/20 - DePaul Undergraduate Math Club
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St. Vincent de Paul was a pretty cool guy who did some pretty cool stuff about four centuries ago. In this talk, we’re going to bring him into the present and talk about some of the underlying connections between what he was doing all that time ago and what we do today as mathematicians. We’ll start with a general history of the crucial Vincentian figures, dive into the details of their work and how it connects to our own, and end with some ways to use some tried and tested Vincentian knowledge in our professional lives.
