### Friday, May 10 — Holt 175, 4:00pm

#### Anastasia Chavez — Saint Mary's College of California

**Title:** The valuation polytope of the zig-zag poset

**Abstract:** The summer 2021 Latinx Mathematical Research Community (LMRC) served as a catalyst for several research projects in various areas of mathematics. This talk will introduce the research of one such project. Geissinger defined the valuation polytope as the set of all [0,1]-valuations on a finite distributive lattice. We study the valuation polytope, V(Z_n), arising from the height 2 up-down poset on n elements, referred to as the zig-zag poset Z_n. Dobbertin showed that the valuation polytope of any poset can be described as the convex hull of vertices characterized by all the chains of that poset. It follows that the dimension of the valuation polytope is the number of elements of the corresponding poset. We discuss our combinatorial results of V(Z_n) such as its normalized volume, the existence of a unimodular triangulation, and facet enumeration. Additionally, we discuss current work towards describing the f-vector and underlying matroidal description. This is joint work with Federico Ardila, Anastasia Chavez, Jessica De Silva, Pamela E. Harris, Jose Luis Herrera Bravo, and Andrées R. Vindas-Meléndez.

### Friday, April 26 — Holt 175, 4:00pm

#### Laura Starkston — UC Davis

**Title:** Breaking down symplectic 4-manifolds

**Abstract:** We will talk about ways to understand and encode 4-dimensional spaces, with the geometric data of a symplectic structure. Historically, there are various ways of breaking down a manifold into simpler pieces where the gluings can be encoded diagrammatically. We will talk about old and new ways of doing this, leading up to multisections with divides. This is based on joint work with Gabriel Islambouli.

### Friday, April 12 — Holt 175, 4:00pm

#### Bethany Johnson — Cal Poly Humboldt

**Title:** Chaos in the Wild: Unveiling Nature’s Dynamic Patterns

**Abstract:** In the 1970s, Robert May proposed that population dynamics could be explained by chaos theory, offering a glimpse into the intricate fluctuations of natural ecosystems. Despite decades of research, it is widely believed that ecological chaos is rare, and fluctuations in natural populations are often attributed to 'noise.' However, the rarity of chaos in complex ecosystems is a mystery, potentially obscured by limitations of traditional models. In this talk, we will embark on a reevaluation of chaos in natural ecosystems, leveraging modern data-driven methodologies and a global database of population dynamics. We will uncover evidence suggesting that chaos may be more prevalent than previously thought, particularly among short-lived taxa. These findings not only challenge existing paradigms in ecology but also have profound implications for ecosystem forecasting and management.

### Friday, March 29 — Holt 175, 4:00pm

#### Mario Bencomo — CSU, Fresno

**Title:** Introduction to inverse problems with examples and research applications

**Abstract:** Inverse problems are a classification of mathematical problems in engineering and science that involve estimating model parameters/inputs relative to a “forward/direct” problem. In this talk I will present several examples of inverse problems to elucidate the definition and highlight typical mathematical challenges. I will also discuss an application in the field of exploration seismology where such inverse problems require mathematical tools from numerical optimization and differential equations.

### Friday, March 8 — Holt 175, 4:00pm

#### Michael Coons and John Lind — CSU, Chico

**Title:** A question on aperiodic order for NSF Research Experiences for Undergraduates

**Abstract:** In this talk, I will start by defining the Stern sequences and Takagi function. Then we will come upon two pictures that looks strangely similar. The idea of the problem is to understand how these two pictures are so similar. This single problem falls in the intersection of analysis, combinatorics, number theory, dynamical systems and fractal geometry.

**Title:** A question on knots and graphs for NSF Research Experiences for Undergraduates

**Abstract:** There is a mysterious connection between knots and directed graphs, defined in terms of the regions in a knot diagram. I will explain how to translate information between the world of knots and the world of graphs using this connection. Some classic knot invariants, such as the Alexander polynomial, correspond to well-understood aspects of graph theory. This will lead us to ask how other, more recently discovered, knot invariants might be understood in terms of graphs.

### Friday, February 23 — Holt 175, 4:00pm

#### Nick Franceschine — Sonoma State University

**Title: **Fermat’s Polygonal Number Theorem

**Abstract: **We will explore the back alleys of number theory as we learn the history of this curious but rarely-discussed result, with an All-Star cast of mathematicians. This talk will be suitable for undergraduate students, who are encouraged to attend.

### Friday, February 2 — Holt 175, 4:00pm

#### Oscar Vega — CSU, Fresno

**Title:** Introduction to the Cal-Bridge Scholarship

**Abstract:** Oscar Vega is the CSU Co-Director of Cal-Bridge Math. Cal-Bridge is a scholarship program that supports only CSU students interested in pursuing a PhD in Physics Astronomy, Computer Science, or any of the Mathematical Sciences (pure, applied, statistics, math ed, etc). In this presentation, Oscar will introduce to students and faculty what Cal-Bridge does, how it does it, who should apply, and what kinds of support it offers (besides the scholarship money). Cal-Bridge requires a faculty member at the campus the scholar attends to serve as their mentor. Hence, faculty interest in being a Cal-Bridge mentor is crucial for an applicant to be eligible for funding. Scholarships are for up to $15,000 per year for up to two years. Rising Juniors of any major, interested in getting a PhD in Physics and Astronomy, Computer Science, or any of the Mathematical Sciences, are encouraged to apply. The deadline to apply will be in the late spring semester.