Spring 2026

Math Honors Presentations

Speakers: Nishant Ajitsaria, Mason McElroy, Noah Siekierski, Hutch Smith 

Tuesday, April 28

Abstracts: 

Hutch Smith -  Conditions on the Expansion of Monomials as Summands of SEMs

This talk will introduce some combinatorial objects and concepts before diving into the algebra of symmetric polynomials. We will examine different bases for the symmetric polynomials and prove part of a conjecture on the appearance of a given monomial in the expansion of an Standard Elementary Monomial (SEM) using a variety of visual and combinatorial arguments. 

Nishant Ajitsaria - Maximal Convex Chains

Given a random set of points in a square, the problem of the longest increasing (monotone) path from the bottom-left to the top-right has been extensively studied. What happens if we add another geometric constraint to this? What if we require that the path not only be increasing, but convex (increasing slopes) too? We call this new problem the search for the Maximal Convex Chain.  We get to see some novel results due to this added constraint. As the number of points tends to infinity, we find that the optimal path converges asymptotically to a limiting curve. The number of points on the chain increases predictably. The path closes in on its true potential, the theoretical optimizer.  Previously, these chains had been studied under a uniform distribution. We extended this analysis to the non-uniform case, to study how the underlying distribution affects the shape and size of the optimal chain. Through this new perspective, we saw some phenomena that might have never been observed under a uniform distribution.

Mason McElroy - Avoidance Couplings: How to Mathematically Dodge Fate

A random walk is a process we can apply on any graph, where a “walker” starts at a single point and randomly chooses an edge to follow on each “turn.” A coupling of walkers then attempts to place two or more random walkers on a single graph. If the walkers are independent (on a finite graph), it’s well known that they will eventually intersect. However, by allowing them to be dependent on each other, we can construct avoidance couplings - pairs of walkers that do not intersect. Avoidance couplings are understood for certain classes of graphs, and in this paper we introduce a construction on a new category of graph - finite subsets of a square lattice. Further, two independent random walkers on the infinite square lattice are known to intersect each other infinitely often. However, we’ve found a construction that allows dependent walkers to not only avoid each other, but put an arbitrarily large distance between them. In fact, they manage to do this surprisingly quickly! 

Noah Siekierski - Approximate Message Passing for Quantum State Tomography 

Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), an algorithmic framework for sparse signal recovery, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large sparse recovery problems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction error by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.  

5 Minute Math

Speakers: Many Undergraduate Students!

Thursday, April 23

Join us for 5 Minute Math, a special event presented by UUG in collaboration with the SUM seminar series. Participants in UUG's Directed Reading Program share the results of a semester’s worth of research across diverse math disciplines, all in just 5 minutes each. Seven groups of talented students have been working hard all semester to explore advanced math topics with their graduate student mentors. This event is their chance to share that work with all of you!  Come ready to learn something new, celebrate student-driven projects, and support your peers. If you're interested in participating in the Directed Reading Program next year, this is a great opportunity to network, meet potential mentors/mentees, and see what kind of projects you could be working on.  (Questions? Contact Stephanie Stewart at smstewa7@ncsu.edu)  Be there or b^2.

3D Bioprinting: The Future of Plant Science

Speaker: Stephanie Stewart (Biomath)

Thursday, March 26

Plants rule the world. They feed us, fuel us, and sustain life on Earth. But breeding better crops to meet global food demand is slow and inefficient. This project addresses global food demand challenges by developing a 3D bioprinting pipeline to enhance plant regeneration from protoplasts. We sample from different seed tissue sources with high regenerative capability, but these cells are challenging to sustain post-harvest. We test different enzyme solutions to isolate these cells, then arrange them precisely in three dimensions using a bioprinter. By controlling cell density, layering, and spacing, we replicate the natural cues that tell cells what to become. Over months, we watch single cells divide into clusters, form tissues, and grow into tiny plantlets. We are building a faster, smarter, and more resource-effective pipeline to improve the crops which support humanity.

All horses are black

Speaker: Dr. Irina Kogan

Thursday, February 26

I will prove that all horses are the same color, that 1=2, that a nickel equals a half dollar, and, if time permits, some other unbelievable statements. Nonsense? Of course. . . but can you catch the mistakes in my arguments? This talk will be accessible to all undergraduates.

How To Do Math With Words

Speakers: Dylan Ferguson and Adelaide Nebeker SLIDES PROOF STYLE GLOSSARY

February 5, 2026

Proofs are hard. Have you ever seen the logic of a proof, but still struggled to actually write it down?  We’re here to help.  How To Do Math With Words is a workshop on the style of writing proofs.  We’ll help identify common blocks math students encounter with proofs, and give you some strategies to help overcome them.  This is a beginner workshop, so we don’t expect you to solve anything.  If you want to get better at putting one word in front of another when it comes to proof writing, How To Do Math With Words is for you.

The REU-niverse Explained

A panel featuring faculty and REU alumni (and pizza)

January 15, 2026

Are you curious about mathematical research?  Would you like to travel somewhere new this summer?  If so, you should consider applying to a Research Experience for Undergraduates (REU).  These summer programs typically last 8-10 weeks and take place at colleges and universities all over the country.  They are fun and also exceptionally rewarding, both intellectually and professionally.  There are many possible mathematical topics, with opportunities for students in every academic year.  This panel will be a crash course on finding REUs, creating a competitive application, and eventually succeeding in your research experience. 

Application deadlines are approaching quickly, so get a head start and check out the links here: https://www.ewbates.com/links.

SLIDES (about the DRUMS REU, not presented at this event)

Fall 2025

Undergraduate Honors Presentations

Speakers: Sydney Hughes, Paris Lewis, Camden Toumbleston

December 2, 2025

Tiling the Aztec diamond with Dominoes

Speaker: Nathan Reading

Thursday, November 20

Abstract: The study of domino tilings goes back to early 20th century physicists, who used domino tilings in a statistical-mechanical model of diatomic molecules on a surface.  A domino is a 2x1 rectangle.  Tiling a region in the plane by dominoes means completely covering the region with non-overlapping dominoes. Consider the following simple question:  How many ways can a given region of the plane be tiled by dominoes? For example, there are two domino tilings of a 2x2 square.  For a general rectangular region, the formula looks strange and is difficult to prove.  For a different planar region called the Aztec diamond, the formula is quite simple.  We'll discuss and illustrate a beautiful proof of the formula due to Elkies, Kuperberg, Larsen, and Propp.  Time permitting, we'll also see what domino tilings have to do with the Arctic Circle.  The talk will be accessible to all undergraduates.  No prior knowledge of tilings will be assumed.

The shape of relations: games, knots and other stories

Speaker: Radmila Sazdanovic

October 30, 2025

Abstract: Literature Nobel prize winner A. Solzhenitsyn wrote: "Topology! The stratosphere of human thought! In the XXIV century it might just possibly be of use to somebody, ...".  Developed in the XXI century,  Topological Data Analysis (TDA) offers powerful methods for uncovering patterns in complex datasets by analyzing their shape. In this talk, we will explore tools for visualizing high-dimensional maps and detecting relations between data sets with expected correlations. We will demonstrate the utility of these tools with real-world examples from game theory and cancer genomics, as well as from theoretical mathematics: knots and their invariants.

Career successes & mistakes, big & small

A panel featuring faculty, students, and alumni

October 9, 2025

Abstract: Some of the best ingredients for a successful and meaningful career are role models who provide an example of destinations we might like to reach.  If we are lucky, our role models can also illuminate the journey toward those destinations.  So in this event, we will hear from panelists on the ups and downs of pursuing various types of mathematical careers.  Everyone is welcome to be inspired by their successes, learn from their mistakes, and ask questions on everything in between.

Beyond the Paper Donut

Speaker: Stepan Paul

September 18, 2025

Abstract: In principle, the surface of a donut--called a torus--can be obtained by gluing the opposite edges of a rectangle to each other. So, what about in practice? Is it possible to literally bend/fold/roll a flat piece of paper and tape the opposite edges together? What about other surfaces? We'll explore these questions and illustrate with 3D models some of the mathematical concepts that underlie them. 

Tips, Tricks, and Other Thoughts on Applying to Graduate School

A panel featuring faculty and current graduate students

August 28, 2025

Whether you are a freshman or a senior, it is never too early to begin thinking about graduate school applications.  With application season just around the corner, this event will provide timely advice and insights on the process from start to finish.  Attendees will hear from faculty who have served on admissions committees, and from students who recently navigated the application process.  Even if you are not sure about pursuing a graduate degree, this event is an opportunity to ask questions and to learn what you can do now to prepare yourself for success.