2021 Past Events
 Tuesday, December 14, 2021

Tuesday, December 7, 2021
Justin Shin, University of Pittsburgh
Hegeman 102 4:00 pm – 5:00 pm EST/GMT5
US law recognizes that statistical evidence can play an important role in determining whether or not an organization is guilty of discrimination. At the same time, legal scholars have cast doubts on the appropriateness of mathematical evidence and probabilistic standards in jurisprudence. As Laurence Tribe famously notes, mathematical evidence poses a special danger because it is often both impressive and inscrutable to the typical juror. How do we square concerns about statistical evidence with its use in discrimination law? One solution is to recognize the causal nature of discrimination and understand the concerns with statistical evidence as concerns to do with causal relevance. With recent developments in causal modeling, new kinds of statistical evidence give rise to fresh concerns about the role of statistics in law while breathing new life into old complaints. Discrimination has inescapable causal baggage, and some reform in discrimination law and jurisprudence as a whole is needed if evidence from causal modeling is to be appropriately digested by US courts.

Tuesday, November 16, 2021
Hegeman 102 4:00 pm – 5:00 pm EST/GMT5
Tina Giorgadze
"Building an Agentbased Computational Model of Chimeric Antigen Receptor (CAR) TCell Immunotherapy in TripleNegative Breast Cancer Using Binary Distribution of Antigens"
Hannah Kaufmann
"Minimal Presentation Sizes of Numerical Semigroups"
A numerical semigroup is a subset of integers closed under addition, while a minimal presentation is a choice of minimal relations between generators of the numerical semigroup. It is a wellknown fact that if m is the smallest positive element, then the size of the minimal presentation is at most m choose 2. Finding the possible minimal presentation sizes of numerical semigroups whose smallest positive element, or multiplicity, is m has been a longstanding open problem. In this talk, we introduce the role of embedding dimension in determining the attainable minimal presentation sizes. For each pairing of multiplicity and embedding dimension, we present multiple classes of numerical semigroups and pose upper and lower bounds. Our methods are not only combinatorial, but also involve posets and betti elements.
Verity Scheel
"Embedding Dimensions of Simplicial Complexes on Few Vertices"
As the result of summer research with Steve Simon (Bard) and Florian Frick (CMU), we found a straightforward characterization of simplicial complexes on few vertices that embed into the dsphere. Simplicial complexes can be studied both as geometric objects embedded into space and as combinatorial set systems, and our result provides a simple combinatorial property that corresponds to topological characteristics of the same object. In particular, a simplicial complex on d+3 vertices embeds into the dsphere if and only if its nonfaces do not form an intersecting family. Like the case of planar graphs, we show in addition that such complexes satisfy the rigidity property that continuous and linear embeddability are equivalent.

Wednesday, November 3, 2021
Hegeman 308 12:30 pm – 1:30 pm EDT/GMT4
Talia Willcott, Ansel Tessier, Rachael Yoder, Andrew Stafford, Verity Scheel, Julia Sheffler

Tuesday, November 2, 2021
Amalia Culiuc, Amherst College
Hegeman 102 4:00 pm – 5:00 pm EDT/GMT4
In 1807, JeanBaptiste Joseph Fourier's study of the theory and flow of heat led to the publication of his "Mémoire sur la propagation de la chaleur dans les corps solides" (Treatise on the propagation of heat in solid bodies). This work, which introduced the notion of representing continuous functions in terms of sums of trigonometric functions, continues to be celebrated today as a foundational collection of ideas for the modern mathematical field of harmonic analysis. With applications ranging from signal processing to medical imaging, Fourier theory remains an active area of research to this day. In this talk we will give a brief introduction to Fourier series, their convergence properties, and the beautiful mathematics they helped create. No background beyond a second semester calculus course will be assumed.
 Friday, October 22, 2021

Friday, October 22, 2021
Dani Schultz
Merck Pharmaceuticals
ReemKayden Center Laszlo Z. Bito '60 Auditorium 12:10 pm – 1:10 pm EDT/GMT4
Aspects of this session will highlight my journey from a small town in northern Wisconsin to the bustling east coast where leaning into discomfort has been critical in driving my career at Merck and the chemistry that I have pursued. Throughout my career, I have tapped into my ability to forge meaningful collaborations, internally and externally, to challenge the status quo and drive disruptive thinking – both in chemistry but also in improving STEM culture. I’ll briefly touch upon some recently completed academicindustrial research collaborations that aimed to empower earlycareer female professors and provide a platform to mentor and train female professors and students in pharmaceutical research. Throughout all of this, I have a passion for diversity, equity and inclusion and will share how I’ve navigated raising important, and at times difficult, topics and how to influence workplace culture. I’ve learned a lot through failed experiments along the way and I am looking forward to an active discussion with fellow changemakers!
Dani Schultz received her PhD from the University of Michigan working with Professor John Wolfe and was an NIH postdoctoral fellow at the University of WisconsinMadison with Professor Tehshik Yoon. Since joining Merck in 2014, Dani has been a member of Process Chemistry and Enabling Technologies in Rahway, NJ and as of 2021 became the Director of the Discovery Process Chemistry group in Kenilworth, NJ. Throughout her time at Merck, Dani has been involved in the development of synthetic routes for drug candidates spanning HIV and oncology – forging meaningful collaborations, both internally and externally, to address the synthetic challenges that occur during pharmaceutical development. Most recently, she has served as cohost to the Pharm to Table podcast that aims to elevate the people and stories behind #MerckChemistry.

Thursday, October 21, 2021
Chuck Doran, University of Alberta
Olin 306 3:00 pm – 4:00 pm EDT/GMT4
Starting from a humble pair of points, we will “twist” our way up CalabiYau fibered spaces, through the hidden geometries of String Theory and Mathematics. Along the way, we’ll explore the subtle interplay between geometry, algebra, and topology. This talk is designed to be broadly accessible to undergraduates. All are welcome.

Tuesday, October 19, 2021
Miriam Kuzbary, Georgia Institute of Technology
Hegeman 102 4:00 pm – 5:00 pm EDT/GMT4
Knot theory is a rich and active area of research involving questions of interest both to mathematicians and to researchers outside of mathematics, and many of these questions boil down to a single essential query: how can one tell when two knots are different? In this talk, we will discuss why this is a difficult question to answer. In particular, we will learn about polynomials used to detect properties of knots and the surprising geometric implications of some knot polynomials.

Wednesday, October 6, 2021
Join MoMath for "QUADS: a SET®like game" featuring Lauren Rose, Associate Professor of Mathematics at Bard College
Online Event 4:00 pm – 5:00 pm EDT/GMT4
How good are your patternrecognition skills? Find out as you learn this exciting, new SET®like card game, QUADS. Join us for an evening of fun as Lauren Rose, Associate Professor of Mathematics at Bard College, shares the rules of this engaging game she coinvented, then dive beneath the surface to see how combinatorics, probability, and algebra are the underlying mathematical engines that drive the fun.
Special introduction by Liz McMahon, Professor of Mathematics at Lafayette College, and Gary Gordon, Marshall R. Metzgar Professor of Mathematics at Lafayette College.
You can join in by participating in a livestream broadcast of the event.
Registration is free. Choose from two sessions:
Math Encounters (online)
Register for 4:00 pm ET (New York) session
Register for 7:00 pm ET (New York) session
Math Encounters (mathencounters.org) is MoMath's popular free public presentation series celebrating the spectacular world of mathematics, produced with support from the Simons Foundation.

Tuesday, October 5, 2021
John Cullinan, Mathematics Program
Hegeman 102 4:00 pm – 5:00 pm EDT/GMT4
Much of modern number theory involves studying solutions to equations with integer coefficients. By combining techniques of geometry and abstract algebra, mathematicians have been able to solve fundamental questions, such as Fermat's Last Theorem and the SatoTate Conjecture.More recently, statistics has become an important tool for studying number theoretic problems that resist classical techniques. In this talk, we will introduce this area of mathematics by focusing on three specific examples taken from three different areas of number theory. We will also do some realtime computation and data generation. This talk should be accessible to anyone who has taken Proofs and Fundamentals.
 Tuesday, September 21, 2021

Tuesday, September 21, 2021
Orsola CapovillaSearle, University of CaliforniaDavis
Hegeman 102 4:00 pm – 5:00 pm EDT/GMT4
Contact topology arose from the study of Hamiltonian dynamics, and is a field with applications to dynamics, optics, thermodynamics, fluid mechanics, geometry, and topology. A 3dimensional space with a contact structure is a space with a plane associated to every point where the planes twist in a specific way. Legendrian submanifolds of a contact 3dimensional space are special submanifolds that lie tangent to the planes in the contact structure.
A knot in 3dimensional space is a tangled string whose endpoints have been glued together. A link is a disjoint union of knots. A Legendrian knot is a knot that also lies tangent to the planes in the contact structure in the 3dimensional space. Two Legendrian knots are distinct if I can't "wiggle" one to the other while always staying tangent to the planes in the contact structure.
If one considers a 4dimensional space X with a 3dimensional boundary Y , one can study surfaces in X whose boundary is a link in Y. By adding geometrical constraints to such a space X and the surface, the link can be Legendrian. I will talk about some results on Lagrangian surfaces whose boundary are Legendrian links.
**Following the seminar, please join us in the Ludlow tent for the Math Program Open House! Refreshments available!**

Tuesday, September 7, 2021
Adam Lowrance, Vassar College
Hegeman 102 4:00 pm – 5:00 pm EDT/GMT4
Take off your shoelaces, tie them up, and fuse the two ends together to form a continuous lace without ends. Now you have a mathematical knot. Two knots are the same if you can move, bend, and stretch one until it looks exactly like the other. Now take a flashlight and point it at your knot. The shadow of your knot on the wall is called a knot diagram or a knot projection.
One common way to study knots is via their invariants, quantities that are associated with the knot that do not change regardless of how the knot is presented. One such invariant is the Jones polynomial. In this talk, we define the Jones polynomial of a knot and discuss what the Jones polynomial tells us about a knot.

Thursday, May 20, 2021
Join our graduating seniors in presenting their research!
Main Commencement Tent 5:30 pm – 7:00 pm EDT/GMT4
Please see the abstract booklet below for full descriptions of students' research.
Download: Senior Project Poster session booklet S21.pdf 
Wednesday, May 5, 2021
Ismar Volić, Wellesley College
Online Event 3:00 pm – 4:00 pm EDT/GMT4
Simplicial complexes are versatile objects in the intersection of graph theory, combinatorics, topology, and geometry. While mathematicians have always appreciated the fact that simplicial complexes are extremely powerful in spite of being easy to define and relatively easy to work with, their usefulness in realworld applications has increased dramatically just in the last decade or so.
In this talk, I will first discuss the definition and the basic constructions that can be performed with simplicial complexes, toggling back and forth between combinatorics and topology. I will then give an overview of some of their recent applications in signal processing, neuroscience, data analysis, and social sciences. I will in particular describe ongoing work by several undergraduates at Wellesley College in which certain types of political systems and their interactions are modeled by simplicial complexes.
This talk should be accessible to anyone who has had some exposure to combinatorics (basics of combinations and permutations).
Zoom Info: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, April 28, 2021
Mona Merling '09, University of Pennsylvania
Online Event 3:00 pm – 4:00 pm EDT/GMT4
To avoid misleading anyone, this talk will not be about the sociology of topologists! "Social choice" is a model for decision making in economic, social, and political contexts. For example: suppose that each person gets to vote on their favorite location where they would like to place a statue on an island. Is there a fair way based on these votes to choose the location? This will turn out to be a topological, even a homotopical, problem, depending on the topology of the island. In this talk we will explore social choice models and answer the question about when they exist using algebraic topology.
The purpose of this talk is to serve as an advertisement for algebraic topology and basic category theory. I will not assume any background other than calculus (in particular the notion of continuity so that I can give an intuition about topology). Familiarity with abstract algebra will help, but I will err on the side of defining what a group is, and I will give a crash course in category theory.
Zoom Info: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 74261

Wednesday, April 21, 2021
Hala Nelson, James Madison University
Online Event 3:00 pm – 4:00 pm EDT/GMT4
Today's popular AI is mostly software, algorithms, and big data processing. Mathematics powers most of these AI techniques that are rapidly integrated into every aspect of our society and are useful for a vast array of applications. AI agents only understand numbers, more specifically, blobs of zeros and ones. In this talk we will use undergraduate mathematics to make an AI agent process our natural language, recognize what she sees, and make intelligent decisions. We will work out simple examples that have wide applications in the Artificial Intelligence sphere. This is an extremely undergraduate friendly talk and you only need to have calculus and linear algebra backgrounds.
Zoom Info: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, April 14, 2021
Florian Frick, Carnegie Mellon University
Online Event 1:30 pm – 2:30 pm EDT/GMT4
How do you fairly divide rent among roommates, a necklace among thieves, or a pizza between friends? Such questions of fair division can often be understood with the tools of geometry and topology — even for those problems that are not geometric to begin with. We will discuss how to do this, and why topology is useful for problems that appear to be unrelated to topology. In particular, we will explore a relation between fairly splitting a necklace and inscribing shapes into curves. No prior knowledge of topology is needed, and this talk is available to all who are familiar with some linear algebra or multivariable calculus.
https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, April 7, 2021
Galen DorpalenBarry '15, University of Minnesota
Online Event 3:00 pm – 4:00 pm EDT/GMT4
In 1943, J. L. Woodbridge of Philadelphia submitted the following problem to American Mathematical Monthly: “Show that n cuts can divide a cheese into as many as $(n+1)(n^2  n + 6)/6$ pieces.”
This question and its solution are deeply connected to the study of collections of lines in $mathbb{R}^2$, planes in $mathbb{R}^3$, and more generally hyperplanes in $mathbb{R}^n$. We will explore the solution and a more general version: given n (hyper)planes in a real, ddimensional vector space, how can we figure out the number of chambers of an arrangement of hyperplanes, without necessarily being able to see and count them?
There are many wonderful solutions to this question. We present one provided by the VarchenkoGel’fand ring, which is the ring of functions from the chambers of the arrangement to the integers with pointwise addition and multiplication. Varchenko and Gel’fand gave a simple presentation for this ring, which can be computed using simple facts about linear algebra.
We will assume very little background but expect that the audience is familiar with linear independence and dependence. We will give a ringtheoretic solution to this problem, so it may be helpful (but not necessary) to be familiar with quotient rings.
Zoom Info: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, March 31, 2021
Ethan Bloch, Bard College
Online Event 3:00 pm – 4:00 pm EDT/GMT4
In this talk we discuss the interplay between curvature and the distance between points on polyhedra. We start by discussing the curvature of polyhedra, which is concentrated at the vertices, and we then consider the question of whether or not a shortest path between two points on a polyhedron can pass through a vertex. We then discuss an attempt, not yet successful, at finding a polyhedral analog of Myers' Theorem for smooth surfaces, which relates positive curvature to distances between points. Along the way we consider some questions about the unfolding of polyhedra (for example, unfolding a cardboard box so that it is flat). This talk is open to all.
Zoom Info: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, March 17, 2021
Lauren Rose, Bard College
Online Event 3:00 pm – 4:00 pm EDT/GMT4
Generalized splines on a graph G with edge weighted by ideals a commutative ring R are Rvertex labelings such that if two vertices share an edge in G, the vertex labels are congruent modulo the edge ideal. When R is a principal ideal domain, we introduce collapsing operations that reduces any simple graph to a single vertex and carries along the edge ideal information. This corresponds to a sequence of surjective maps between the associated spline modules, and leads to an explicit construction of an Rmodule basis in terms of the edge ideals. We also solve an interpolation problem, i.e., given a partial vertex labeling, when can it can be extended to a generalized spline?
Zoom: https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619

Wednesday, March 3, 2021
Pablo Soberón, Baruch College
Online Event 3:30 pm – 4:30 pm EST/GMT5
Given a family of convex sets in R^d, how do we know that their intersection has a large volume or a large diameter? A large family of results in combinatorial geometry, called Hellytype theorems, characterize families of convex sets whose intersections are not empty. During this talk we will describe how some bootstrapping arguments allow us to extend classic results to describe when the intersection of a family of convex sets in R^d is quantifiably large. The work presented in this talk was done in collaboration with undergraduate students.
Join Zoom Meeting
https://bard.zoom.us/j/86398169686?pwd=M0pvT25ETmFhbUhkb1FUc2FuaGl0QT09
Meeting ID: 863 9816 9686
Passcode: 742619