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.
(Title in Progress; Topic: Alums in Industry)
Abstract: (In Progress)
This talk will be followed by an informal pizza dinner, also in Gulick 2000.
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.
(Title in Progress)
Abstract: (In Progress)