Math and Cookies is an undergraduate research seminar and Department seminar is for math faculty members.
Math and Cookies and Department seminar will alternate each week.
These seminars are partly supported by NSF LEAPS-MPS (DMS-2532394).
If you are interested in giving a talk (or you know somebody), please let me know!
The following is the list of the speakers for the seminar for Fall 2025.
We meet: Wednesdays 1:00 pm - 2:00 pm (or 2:00 pm - 3:00 pm) at Coykendal Science Building 320.
Oct 1 (Department Seminar): Chris Eppolito (SUNY New Paltz) - 1:00 pm - 2:00 pm at CSB 320.
Title: Matroids from the ground(set) up
Abstract: Matroids are combinatorial objects which abstract properties of linear independence among vectors in a vector space. Which properties we choose to abstract give us completely different looking structures and axioms for these objects. This underlies the true power of matroids: their different descriptions provide us with a variety of different ways of constructing them and proving properties thereof. This talk will survey the most common axiomatizations of matroids, together with motivating examples and interesting constructions.
Oct 8 (Math and Cookies): Han-Bom Moon (Fordham University) - 2:00 pm - 3:00 pm at CSB 320.
Title: Let's count points!
Abstract: A fascinating fact in mathematics is that there are many interesting connections between seemingly different mathematical disciplines. In this talk, I will present a surprising formula counting integral points on polygons and sketch its proof. We will see a delightful interaction between algebra, geometry, and combinatorics. No prerequisite is assumed beyond single variable calculus. Everyone is welcome!
Oct 22 (Math and Cookies): Phanuel Mariano (Union College) - 2:00 pm - 3:00 pm at CSB 320.
Title: The isoperimetric inequality and its connection to probability
Abstract: The isoperimetric inequality is a geometric result relating the square of the circumference of a closed plane curve to the area it encloses, along with various generalizations of this relationship. There is a connection between inequalities that come up in probability and the classical isoperimetric inequality. The connection is through Brownian motion, which is a mathematical model for the random movement of a particle. It was first observed by Robert Brown in 1827 while looking at pollen grains through a microscope. I will discuss some classical isoperimetric problems related to the expected lifetime of Brownian motion from a domain.
Oct 29 (Department Seminar): Vladmir Shpilrain (The City College of New York) - 1:00 pm - 2:00 pm at CSB 320.
Title: Tropical cryptography
Abstract: D. Grigoriev and I introduced a new area of "tropical cryptography" in 2014. What it means is that we used min-plus algebras (a.k.a. tropical algebras) as platforms for various cryptographic primitives. That is, we replaced the usual operations of addition and multiplication by the operations min(x,y) and x+y, respectively. An obvious advantage of using tropical algebras as platforms is unparalleled efficiency because in tropical schemes, one does not have to perform any multiplications of numbers since tropical multiplication is the usual addition. The focus therefore is entirely on the security of tropical cryptographic schemes. I will discuss several NP-hard problems in tropical algebras that one can use to build cryptographic primitives.
Nov 5 (Math and Cookies): Mee Seong Im (Johns Hopkins University) - 2:00 pm - 3:00 pm at CSB 320.
Title: Entropy, cocycles, and diagrammatics and parabolic induction for Springer fibers of type C
Abstract: In the first part of my talk, I will discuss how cocycles appear in a graphical network. Furthermore, the Shannon entropy of a finite probability distribution has a natural interpretation in terms of diagrammatics. I will explain the diagrammatics and their connections to infinitesimal dilogarithms and entropy. This is joint work with Mikhail Khovanov.
In the second part of my talk, I will discuss the geometry of nilpotent orbits. Nilpotent orbits are important objects in geometric representation theory since they appear in Springer’s construction of Weyl group representations, associated varieties of primitive ideals of enveloping algebras, conical symplectic singularities, and modular representation theory of Lie algebras, to name a few. The theory of Lusztig-Spaltenstein induction is a geometric process for constructing nilpotent orbits in the Lie algebra of a reductive group from the nilpotent orbits in Levi subalgebras. I will discuss the parabolic induction for Springer fibers of type A as well as some progress made involving the parabolic induction for Springer fibers of type C. This is joint with Neil Saunders and Arik Wilbert.
Nov 12 (Department Seminar): Cameron Wright (University of Washington) - 10:00 am - 11:00 pm at CSB 320. (Special Time)
Title: Categories of Matroids with Coefficients
Abstract: A matroid is a combinatorial gadget that generalizes a finite configuration of vectors in a vector space over a field. However, many matroids cannot be realized in this way. By allowing for coefficients in more general objects than fields, we obtain an approach to matroid theory which allows us to use much of our intuition from linear algebra even on non-realizable matroids. In this talk, I will give an account of this perspective and survey recent work with Jaiung Jun and Alex Sistko in which we leverage this approach to explore matroid theory through the lens of category theory. If time permits, we will also discuss relations between these categories, tropical geometry, and algebraic K-theory.
Nov 19 (Math and Cookies): Kei Kobayashi (Fordham University) - 2:00 pm - 3:00 pm at CSB 320.
Title: Brownian motion, stochastic differential equations, and anomalous diffusions
Abstract: Brownian motion and associated stochastic differential equations have been employed to model a number of random time-dependent quantities observed in many different research areas. However, these classical stochastic models have several drawbacks; one notable shortcoming is that they do not allow the quantities to be constant over any time interval of positive length. To describe such constant periods, one can introduce a random time change, which gives rise to a new class of stochastic differential equations representing the so-called "anomalous diffusions."
The first half of the talk will be devoted to an introduction to Brownian motion and classical stochastic differential equations, with emphasis on how they arise in applications, what properties they have, and their connections with partial differential equations. Toward the end of the talk, a new class of stochastic differential equations will be presented, along with some of my contributions to this area.
Dec 3 (Department Seminar): Jeungeun Park (SUNY New Paltz) - 1:00 pm - 2:00 pm at CSB 320.
Title: Mathematical Approaches to Understanding Bacterial Movement
Abstract: Bacteria move through their environments using a variety of physical and biochemical mechanisms. In this talk, we discuss how mathematical tools can be used to model bacterial movement across different scales—from the motion of individual cells to collective behaviors in populations. We will also illustrate how modeling helps us interpret experimental observations and uncover key principles governing microbial motility.