Feb. 18: Organizational Meeting

Feb. 25: BUGCAT Informational Meeting

**Abstract: **This year, we will host our 14th annual Binghamton University Graduate Conference in Algebra and Topology (BUGCAT). As the name suggests, this conference is largely run by graduate students, and helping organize the conference is a great experience (that also looks good on your CV). At this meeting, we'll discuss the conference and what's involved in making it happen. If you are interested in BUGCAT but can't attend, please feel free to email me (alamour1@binghamton.edu).

Mar. 4: Chris Chia, *Duality and Trace*

**Abstract: **I will talk about duality and trace in category theory and how it relates to fixed point theory. The examples will mostly be linear algebra.

**Mar. 18: Uly Alvarez, ***A bow tie, a twirl, in a ball*

**Abstract: **I will analyze the order complex of a certain topological poset that arises from a generalization of a field.

**Mar. 25: Meenakshy Jyothis, ***Geodesic Currents*

**Abstract:** The talk will introduce geodesic currents. I will try to explain why we can think of the space of geodesic currents as a generalized space that contains both Teichmuller space and the set of simple closed curves up to homotopy.

**Apr. 1: Andrew Lamoureux, ***Differential Algebra*

**Abstract:** This talk will explore the basics of differential algebra, such as differential rings, differential ideals, and the ring of differential polynomials. I will then focus on differential field theory, emphasizing its parallels to ordinary field theory.

**Apr. 8: Chris Eppolito, ***A Sequence of Unseemly Examples: The Hopeless Hyperfields*

**Abstract:** Hyperfields are essentially fields with a multivalued addition. We explore the rudiments of hyperfield theory, with an emphasis on a zoo of examples.

**Apr. 15: Josh Carey, ***Graded Dimension, MacDonald's Identity and Theta Functions*

**Abstract:** I will talk about different ways to calculate the graded dimension of Lie modules and about an interesting connection between formulas of Lepowsky and MacDonald using theta functions.

**Apr. 29: Andrew Lamoureux, ***Differential Algebra (continued)*

**Abstract:** This is a continuation of my talk from April 1. In particular, I will discuss the basics of differential Galois theory and then p-derivations, which are arithmetic analogues of derivations.

**May 6 (4:15pm): Sayak Sengupta, ***Nilpotent modulo polynomials*

**Abstract: **We will start with the definitions of some "special" subvarieties of affine varieties over a finite field F. Then we will attempt to convert (to be very loose with the word) this problem into an algebraic theory of Nilpotent modulo polynomials (over Z) which we hope would induce new polynomial maps. Although a very rough idea but I think this one has quite a few interesting aspects of its own.