We will have a panel of undergraduates with research experience sharing their tips on finding research opportunities and REU applications.

An introduction to knots with emphasis on invariants in various spaces.

Michael's talk: "An ordering on permutations shows up in 3 different contexts."

Son's talk: "Bijections between alternating sign matrices and various objects."

An introduction to and generalization of ice models.

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.

An introduction to Fourier Series and the Fourier Transform, highlighting its applications in solving partial differential equations and in signal analysis. 

An overview of the mathematics behind the game Bulgarian Solitaire and an introduction to a few of its variants. 

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.

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! 

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.

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. 

This is the first of a two-week series on column-strict tableaux (CST). In this session, we will have fun activities with CST.

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.

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. 

“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!” 

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. 

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.

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.

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. 

We will have students from the Directed Reading Program coming to give short presentations on what they have read this semester.

No talk, just have fun!