Mailing List: https://forms.gle/a1wLPUWCF3uGmimQA
When: Tuesday 3:35 - 4:25
Where: Ford 170
Organizers: Aidan (joh18354 AT umn.edu), Demetri (case0242 AT umn.edu), Son (nguy4309 AT umn.edu)
Retired organizer: Harper (nierg001 AT umn.edu)
Note: This is a mirror site of the official website here.
The Undergraduate Math Research Seminar (UMRS) is a seminar aimed to create a welcoming undergraduate research community at UMN. We will have opportunities for students to give low-stakes talks on the research and reading they’ve done as well as hold sessions devoted to learning what research is like, the different areas of math research and how to create research presentations. If you’d like to be updated on the seminar, see the mailing list above. See here for the 2021-2022 schedule.
Jan 24: Research opportunities panel
We will have a panel of undergraduates with research experience sharing their tips on finding research opportunities and REU applications.
Jan 31: Anthony Kirby. "Knot Theory From All Angles"
An introduction to knots with emphasis on invariants in various spaces.
Feb 7: Michael Cauthorn. "Bruhat Ordering and Pipe Dreams";
Son Nguyen. "Bumpless Pipe Dreams, Alternating Sign Matrices and beyond"
Michael's talk: "An ordering on permutations shows up in 3 different contexts."
Son's talk: "Bijections between alternating sign matrices and various objects."
Feb 14: Valentine's Break
Feb 21: Michael Cauthorn. "Lattice Models"
An introduction to and generalization of ice models.
Feb 28: Samuel Coyle. "The Fundamental Group and Methods for Calculations"
This talk will begin with an introduction to the Fundamental Group and the motivation behind its development and use in Algebraic Topology. Then, we will develop some tools to calculate the Fundamental Group of a Space including group actions and Van Kampen's theorem. We will conclude by looking into one application of the Fundamental Group with a brief proof of Brouwer's Fixed Point Theorem and end by viewing some limitations of the Fundamental Group.
Mar 7: Spring break!
Mar 14: Dinh-Quan Tran. "The Fourier Transform and Applications"
An introduction to Fourier Series and the Fourier Transform, highlighting its applications in solving partial differential equations and in signal analysis.
Mar 21: AJ Harris. "Bulgarian Solitaire and Its Variants"
An overview of the mathematics behind the game Bulgarian Solitaire and an introduction to a few of its variants.
Mar 28: Connor McCausland. "VC Dimensions of Geometric Families"
The Vapnik-Chervonenkis (VC) dimension is a quantification of the complexity of families of sets, with applications in combinatorics and machine learning. In this talk, we will discuss the VC dimensions of several natural geometric families and methods for determining them.
Apr 4: Anthony Kirby. "Examples from Algebraic Topology"
A high-level overview of algebraic topology with visual explanations. Topics include homology theory, Universal Coefficient Theorem of Cohomology, free groups of graphs, graded rings, and more!
Apr 11: Harper Niergarth. "Numerical semigroups and the Kunz cone"
In the past, McDonald’s sold chicken nuggets in packs of 6,9, and 20. This means you can not order exactly 10 nuggets, but you have a few ways of ordering 18 (three 6 packs or two 9 packs). Eventually, you might want to list all the numbers you can get by adding copies of 6, 9, and 20. If you did, you would have what is called the McNugget semigroup, an example of a numerical semigroup. In this talk, we will give an overview of numerical semigroups and discuss some surprisingly deep connections to polyhedral geometry.
Apr 18: Break!
Apr 25: DRP Presentations
Sep 13: Intro to different fields of math
For our first meeting, a panel of undergraduates with research experience will be giving an overview of fields of math such as Algebra, Combinatorics, Analysis, Topology, and Geometry as well as recommend introductory readings on those topics.
Sep 20: Son Nguyen. "Fun with Tableaux"
This is the first of a two-week series on column-strict tableaux (CST). In this session, we will have fun activities with CST.
Sep 27: Son Nguyen. "Bender-Knuth Involutions, Promotion and Evacuation on Column-Strict Tableaux and Linear Extensions of Posets"
This is the second of a two-week series on column-strict tableaux (CST). In this session, we will introduce Bender-Knuth involutions on CST as well as promotion, jeu-de-taquin and evacuation on CST. We will also extend these actions to linear extensions of posets if time permits.
Oct 4: Aidan Johnson. "FOMO on Graphs : Failed Skew Zero Forcing Numbers "
This talk will discuss the skew forcing rule on graphs and how it contributes to create the failed skew zero forcing number, $F^-(G)$. In particular, the characterization of all graphs where $F^-(G)=1$. As well as, looking at the failed skew zero forcing numbers for powers of paths and cycles.
Oct 11: Harper Niergarth. "Spectral Faux Trees"
“A spectral faux tree with respect to a given matrix is a graph which is not a tree but has the same eigenvalues as a tree for the given matrix. For this talk, we consider the existence of spectral faux trees for several matrices, with emphasis on constructions, and find strikingly different results for each matrix studied. This talk is intended to be accessible for anyone who knows what an eigenvalue is!”
Oct 18: Archan Sen. "Generalized Markov Numbers "
This talk will discuss Markov tuples in the generalized case -- numbers that satisfy the Diophantine equation $x^2+y^2+z^2+xy+xz+yz = 6xyz$. We talk about the solutions to these tuples, patterns in Markov families, and the graphical representation of Markov numbers. We start with the ordinary case and compare the similarities and differences.
Oct 25: Demetrios Case. "Tropical Geometry"
This talk will discuss algebra in a tropical semiring, properties of tropical polynomials, and the affine space of tropical polynomials This talk is one of a two-part series which will provide the mathematical intuition and toolset to describe and analyze tropical Hyperplane arrangements.
Nov 1: Halloween Special
For this Halloween, get prepared for the spookiest thing ever: grad school application!!! We will have a panel of survivor who are willing to come and share their experience going through this nightmare. Your worst nightmare is coming for you, muahahahahahahaha.
Nov 8: Voting break!
Nov 15: Grant Silewski. "The k-Domination of the Cartesian Product of Complete Graphs "
Let G=(V(G), E(G)) be a finite undirected graph. A set S of vertices in V is said to be total k-dominating if every vertex in V is adjacent to at least k vertices in S. The k-domination number, γ_k(G), is the minimum cardinality of a k-dominating set in G. In this work we study the k-domination number of Cartesian products of two complete graphs, which is a lower bound of the total k-domination number of Cartesian product of any two graphs with the same number of vertices. We obtain new lower and upper bounds for the k-domination number of Cartesian product of two complete graphs. Some asymptotic behaviors are obtained as a consequence of the bounds we found.
Nov 22: Thanksgiving break!
Nov 29: DRP Speed Run
We will have students from the Directed Reading Program coming to give short presentations on what they have read this semester.
Dec 6: Social Event
No talk, just have fun!