Games and Patterns with Stable Tamari Order
Abstract: The Tamari Poset, introduced by Dov Tamari in the 1960s, is a fundamental structure in combinatorics, particularly known for its connection to binary trees, Catalan numbers, and associative operations. This poset not only serves as a combinatorial model for various algebraic and geometric structures but also plays a significant role in the study of lattice theory and planar triangulations. Building on this classical framework, we expand the poset to all non-negative integer sequences of the same length and explore further properties and structures.
In this talk, I will focus on the lower order ideal of sequences of the form (a,b,a) where a < b. I will explore surprising results regarding the size of these lower order ideals and the number of intervals they contain. Interestingly, these results lead to sequences that correspond to known entries in the OEIS (the online encyclopedia for integer sequences), hinting at deeper connections to other combinatorial objects. I will also discuss open problems and potential directions for further research. This is research completed during an REU last summer.
Inspiring Women and Unlocking Opportunities at NCUWM
Abstract: The weekend of January 31st, 2025, two William Smith students, Colleen Jump (2027) and Van Tran (2025), had the opportunity to escape the cold in Geneva to enjoy a moment of spring in Lincoln Nebraska for the Nebraska Conference for Undergraduate Women in Mathematics (NCUWM). Now in its 27th year, this conference has long served as a platform for encouraging and empowering women in mathematics. It brought together over 300 students in mathematics from across the country, fostering an environment of collaboration, learning, and mutual support. The event provided attendees with invaluable opportunities to explore various career paths, research areas, and graduate programs in mathematics, while also hearing from inspiring women mathematicians. This colloquium will be presented by Colleen and Van, reflecting on their personal experiences and key takeaways from the conference, as well as shedding light on the broader impact of NCUWM in encouraging diversity and inclusion within the field of mathematics.
We will have colloquium talks presented by our candidates for our Visiting Assistant Professor in Computer Science position. Please see your instructor for details!
Panel: Mathematicians in Industry
Abstract: Yu, Cassano and Bryce all graduated from HWS with majors in mathematics. Currently, Cassano is a Senior Consulting Actuary at USI Consulting Group, Bryce is a Senior Data Developer at Mathematica, Inc., and Yu is a Senior Actuarial Analyst for the Global Atlantic Financial Company. They will share their stories and answer questions in this panel!
The panel will be followed by a pizza dinner to facilitate additional discussion with the alums. If you plan on staying for the dinner, please RSVP to Professor King (eking@hws.edu) to insure sufficient food.
This panel is supported by National Science Foundation Award #2331555 led by Professors Hebb and Metz, and cosponsored by the Salisbury Center for Career, Professional and Experiential Education.
Film Screening: Counted Out
Information on the movie can be found here and here.
Understanding Stochastic Oscillators through Linear Algebra
Abstract: Many rhythmic phenomena in natural and engineered systems may be approximately described by limit cycles -- closed, periodic solutions of systems of nonlinear ordinary differential equations. When working with real data, one often confronts irregular rhythmic oscillations that are best modeled by stochastic differential equations. In this talk, I will discuss recent work on how to generalize concepts from deterministic dynamical systems, such as phase reduction, to stochastic (noisy, irregular) dynamical systems.
The Magic of Matrices and Their Eigenvalues
Abstract: Graphs and their associated matrices are powerful tools for modeling connections and relationships between objects. Depending on the nature of the modeling, various matrices can be linked to the graph. In this talk, we will focus on two key matrices: the adjacency matrix and the Laplacian matrix.
In the context of square matrices, eigenvalues and eigenvectors are essential for analyzing the model and its potential solutions. We will focus on the eigenvalues and eigenvectors of the matrices mentioned above, with particular emphasis on the Laplacian matrix.
For a given graph, the Laplacian matrix has an important eigenvector called the Fiedler vector, which plays a crucial role in numerous applications. In this presentation, we will discuss some of the key properties of the Fiedler vector and its applications.