News + Events

Reem-Kayden Center Lobby  5:00 pm – 6:30 pm EST/GMT-5
Join us in celebrating our December graduating seniors as their present their work!

Zoe Wellner, Carnegie Mellon University
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
Often, continuous and discrete are treated as opposites of each other. The Borsuk--Ulam theorem states that for any continuous map  from the sphere to Euclidean space, $fcolon S^dto R^d$, there is a pair of antipodal points that are identified, so $f(x)=f(-x)$. This theorem deals with continuous objects, is fundamentally topological, and yet, it has numerous applications to discrete results. We will look at how these methods apply to some problems, including chromatic numbers of Kneser graphs (like the Petersen graph which you see pictured) and the Ham Sandwich theorem: given a $d$-dimensional sandwich with $d$ ingredients, with a single cut you can split your sandwich in half such that every ingredient is exactly halved as well. We will also look at what it means to take a colorful generalization of a result and why it is helpful.

  RKC 111  6:00 pm – 7:00 pm EST/GMT-5

  RKC 111  12:00 pm – 1:00 pm EDT/GMT-4

Reem-Kayden Center  4:00 pm – 6:00 pm EDT/GMT-4

Reem-Kayden Center Laszlo Z. Bito '60 Auditorium  5:00 pm – 7:00 pm EDT/GMT-4
Majoring (or interested) in science or math but unsure about whether grad school is right for you?  

The Bard Interdisciplinary Science Research Accelerator is sponsoring a panel discussion, Q&A, and networking event with admissions administrators and faculty from across the region.  

We’ll talk about what master’s and PhD programs are out there, what they are like, and how to optimize the rest of your time spent at Bard.  

Panelists:

Delilah Gates
Gravity Initiative Postdoctoral Associate Research Scholar, Princeton University

Andrew Harder
Director of Graduate Admissions, Mathematics Department, Lehigh University

Emily Harms
Senior Associate Dean, The Rockefeller University

Felicia Keesing
David and Rosalie Rose Distinguished Professor of Science, Mathematics, and Computing, Bard College

Chris Lafratta
Professor of Chemistry, Bard College

Chuck Doran
Distinguished Visiting Professor of Mathematics and Physics, Bard College

Open to all Bard students, especially those moderated in mathematics or the sciences.

Adam Sheffer, CUNY
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
The Szemerédi–Trotter theorem is a simple statement about points on lines in the plane. Surprisingly, this result turned out to be surprisingly useful. Over the past 20 years, it has been used to prove impressive results in combinatorics, number theory, harmonic analysis, model theory, theoretical computer science, and more.

In this talk, we will introduce the Szemerédi–Trotter theorem and see how it can be used in unexpected places. We will also chat about the current research front—how mathematicians are currently trying to extend this theorem. 
 

Jen Gaudioso ’95, Sandia National Labs
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Dr. Jen Gaudioso, the director of computing research at Sandia National Labs, will take you on a journey covering the breadth of computing and information science research at Sandia. She’ll cover the full spectrum of computer science, from fundamental research to real-world applications that impact crucial areas like energy security, climate science, engineering, and national security missions. Dr. Gaudioso will highlight some of the exciting possibilities that lie ahead in these fields such as quantum computing, neuromorphic computing, codesign strategies, and the ever-evolving realms of artificial intelligence and machine learning. Discover how these breakthroughs are reshaping our world and driving innovation. Join us to hear about the key research questions and collaborative partnerships essential to overcoming these complex challenges.

Jennifer Gaudioso ’95 is currently director of the Center for Computing Research at Sandia National Laboratories. She oversees research in discrete mathematics, data analytics, cognitive modeling, and decision support materials. Previously, Jen has served as director of the Center for Computation and Analysis for National Security, and also the International Biological and Chemical Threat Reduction Program. She served on two National Academies Committees that addressed biodefense issues. In addition to her Bard degree, Jen has a masters degree and PhD in physical chemistry from Cornell University.
 

  RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Meenakshi McNamara, "Generalizations of the ErdH os--Ginzburg--Ziv Theorem Via Topology”
Skye Rotstein, “Billiard Dynamics on the Double Pentagon”
Josef Lazar, “Machine Learning for Emotional Text to Speech Modeling”

Chris Elliott, Amherst College
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
I'll give an introduction to the mathematics behind supersymmetry. Supersymmetry is a novel idea in physics for a symmetry that relates two different sorts of elementary particle: "bosons", which describe the fundamental forces of nature, and "fermions", which make up matter. In mathematics we can study "super" versions of objects such as vectors, which have bosonic and fermionic components. I'll introduce some of these ideas, and end by presenting some novel calculations in the world of superalgebra developed by my undergraduate research students Osha Jones and Ziji Zhou this summer, which have applications to quantum physics in three dimensions.

  RKC 111  12:00 pm – 1:00 pm EDT/GMT-4

Come meet math faculty and fellow math majors! Refreshments will be served!
3rd floor Albee Math Lounge  5:00 pm – 6:00 pm EDT/GMT-4

RKC 111  11:50 am – 1:10 pm EDT/GMT-4
Eat Pizza and Meet Faculty and Students!

Susan D'Agostino, '91
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Long before Susan D’Agostino wrote, How to Free Your Inner Mathematician: Notes on Mathematics and Life (Oxford University Press, 2020), she was a student at Bard College in the late 1980s and early 1990s. There, she majored in anthropology, took nearly as many classes in film, and avoided the math department. She also filled countless journals sitting on the back steps of Manor House, nurturing a burning desire to write. But Bard writing faculty, including William Weaver, Chinua Achebe, John Ashbery, Mona Simpson, and Robert Kelly exuded a gentle, if unspoken, message that she needed more life experience to give her writing soul. And so, upon graduating from Bard, she moved into a small cabin 50 feet from a barn housing 42,000 chickens, took a job traveling through Central and South America, and began studying theoretical mathematics. Susan’s post-college path took her far from Annandale-on-Hudson, but the life perspective she cultivated at Bard continues to provide a true north in her life. In this talk, attendees will hear stories from her book that are focused on defining success for oneself in both math and life.  

Susan D’Agostino is a science writer and mathematician whose work has been published in The Atlantic, Washington Post, Inside Higher Ed, Scientific American, Wired, Quanta, BBC, Nature, National Public Radio, and other outlets. She is the author of How To Free Your Inner Mathematician (Oxford University Press, 2020). Susan is the technology reporter at Inside Higher Ed, where she provides substantive analysis on pressing issues facing higher education today for 2.3 million monthly readers. Her writing has been recognized with fellowships from the Columbia University School of Journalism, Reuters Institute at Oxford University, the National Association of Science Writers, the Council for the Advancement of Science Writing, and the Heidelberg Laureate Forum Foundation. She earned a PhD in mathematics at Dartmouth College, an MA in science writing at Johns Hopkins University, and a BA in anthropology at Bard College.
 

Allison Stanger, Visiting Professor of Technology and Human Values
RKC 111  12:00 pm EDT/GMT-4

  John L. Bell, Western University
Hegeman 107  12:00 pm – 1:00 pm EDT/GMT-4
The concept of the continuum is one of the oldest in philosophy and mathematics. A continuum is conceived of as a continuous entity possessing no gaps or interruptions. We commonly suppose that space, time and motion are continua. The continuum concept was first systematically investigated by Aristotle c. 350 B.C. His major conclusion was that a continuum cannot be reduced to a discrete entity such as a collection of points or numbers. In the 17th century Leibniz’s struggle to understand the continuum led him to term it a labyrinth. In modern times mathematicians have formulated a set-theoretic, or “arithmetic” account of the continuum in discrete terms, although certain important thinkers, such as Brentano, Weyl and Brouwer rejected this formulation, upholding to Aristotle’s view that continua cannot be reduced to discreteness.

Closely allied to the continuum concept is that of the infinitely small, or infinitesimal. Traditionally, an infinitesimal has been conceived of, geometrically, as a part of a continuous curve so small that it may be regarded as “straight”, or, numerically, as a “number” so small that, while not coinciding with zero, is smaller than any finite nonzero number. The development of the differential calculus from the 17th century until the 19th century was based on these concepts.

In my talk I shall present a historical survey of these ideas.

Kristina Striegnitz, Union College
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Data plays an increasing role in shaping our lives. It is, therefore, important to help non-experts understand, evaluate and draw inferences based on data. Data is often represented as graphs. However, prior research has shown that many people struggle with graph comprehension. We compared the effectiveness of presenting data as a graph to a text summary and to a combination of the two. Furthermore, we explored whether, in the combined presentation, color-coding or graph annotations helped non-expert readers better understand the underlying data.


Kristina Striegnitz is an associate professor of computer science at Union College in Schenectady, NY.  Before coming to Union she did a postdoc with Justine Cassell at Northwestern University. Kristina has a joint PhD from Saarland University in Germany and University Henri Poincare, Nancy 1 in France. Her research is in natural language generation and dialog systems. She is particularly interested in embodied interactive systems that are situated in physical or virtual environments.

Alicia Lamarche, University of Utah
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4

Alan Thompson, Loughborough University
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
A pseudolattice is a (multidimensional) grid of points, equipped with a function that takes two points from the grid and returns an integer. A simple example would be the grid of points (x,y) in the plane with integer coordinates x and y, along with the dot product which takes two such points (a,b) and (c,d) and returns the integer ac+bd. I begin with a gentle introduction to the theory of pseudolattices, before presenting two settings in which they show up in geometry. The first describes configurations of points and curves on surfaces, whilst the second encodes the geometry of families of tori over a disc. Interestingly, despite the fact that the two settings seem unrelated, the pseudolattices that show up in each setting are identical. This is an example of the general phenomenon of "mirror symmetry," first discovered by theoretical physicists, which says that many geometric objects which seem to be unrelated nonetheless share fascinating properties.

  Ursula Whitcher, American Mathematical Society
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Adinkras are decorated graphs that encapsulate information about the physics of supersymmetry. If we color the edges of an Adinkra with a rainbow of shades in a specific order, we obtain a special curve that we can study using algebraic and geometric techniques. We use this structure to characterize height functions on Adinkras, then show how to encapsulate the same information using data from our rainbow. This talk describes joint work with Amanda Francis.

Karen Lange, Wellesley College
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
You can make a simple family tree by starting with a person at the root and then adding two branches for her parents, and then adding two branches for the parents of each of  her two parents, and so on.  Such a family tree is an example of  a binary tree because each level of the tree has at most two branches.  We'll see that every binary tree with infinitely many nodes has an infinite path; this result is called Weak Kőnig's Lemma.   But just because we know a path exists, doesn't mean we can find it.  Given Weak Kőnig's Lemma, it's natural to ask whether we can compute a path through a given binary tree with infinitely many nodes.  It turns out the answer to this "Path Problem"  is "no", so we say that the problem is not "computable".  But then what exactly is the computational power of this Path Problem?
Using the Path Problem as a test case, we will explore the key ideas behind taking a "computable" perspective on mathematics (over an "existence" one) and describe an approach for measuring the computational power of mathematical problems.  We'll see that the computational power of problems varies widely  and studying problems' power helps to illuminate what really makes problems "tick". This talk will highlight ideas from graph theory, theoretical computer science, and logic, but no background in any of these subjects is necessary.  

Rylan Gajek-Leonard, '16, Union College
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
We all have an intuitive notion of 'distance' between two numbers. For example, we might say that the distance between the numbers 3 and 5 is 2, and the distance between -5 and 1 is 6. But what do we really mean by 'distance'? Are there other ways to measure numbers? It turns out that the answer is yes: for every prime number p, there is a way to measure numbers in terms of their divisibility by p. In doing this, we are led to the world of "p-adic numbers", a strange place where all triangles are isosceles and where every point in a circle is its center. The theory of p-adic numbers permeates nearly all aspects of modern number theory. In this talk, we will define and gain intuition for the p-adic numbers and see some of their applications to problems in number theory.

Rylan completed his bachelor's degree in mathematics and music performance at Bard College, where he was also a cellist in the conservatory. He obtained a master's degree from the University of Cambridge, where he also performed with the Cambridge Philharmonic, and a PhD from UMass Amherst. Rylan currently teaches at Union College in Schenectady, New York. His research is in algebraic number theory and arithmetic geometry.

  James Marshall, Sarah Lawrence College
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
Since the 1920s, physicists and philosophers have been trying to understand the strangeness of the subatomic world as revealed by quantum theory, but it wasn't until the 1980s that computer scientists first began to suspect that this strangeness might represent a source of immense computational power. This realization was soon followed by key theoretical advances, including the discovery of algorithms that harness the quantum phenomena of superposition and entanglement, enabling quantum computers in principle to solve certain problems far more efficiently than any conventional computer. Around the same time, researchers built the first working quantum computers, albeit on a very small scale. Today the multidisciplinary field of quantum computing lies at the intersection of computer science, mathematics, and physics, and is one of the most fascinating areas in science, with potentially far-reaching consequences for the future. In this talk I will give an overview of the basic mathematical ideas behind quantum computing, and use them to illustrate two particularly interesting results: the quantum search algorithm, and quantum teleportation.

Alejandro Morales, University of Massachusetts
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
Flow polytopes are an important class of polytopes in combinatorics whose lattice points and volumes have interesting properties and relations to other parts of geometric and algebraic combinatorics. These polytopes were recently related to (multiplex) juggling sequences of Butler, Graham, and Chung. The Chan-Robbins-Yuen (CRY) polytope is a flow polytope with normalized volume equal to the product of consecutive Catalan numbers, one of the most well-known sequences in combinatorics. Zeilberger proved this by evaluating the Morris constant term identity, but no combinatorial proof is known. In this talk we will talk about the connection between juggling and (flow) polytopes and introduce a new refinement of the Morris identity with combinatorial interpretations both in terms of lattice points and volumes of flow polytopes. 

Alejandro Morales is originally from Colombia and got his B.Math. from the University of Waterloo and a Ph.D. from MIT, working with Professor Alexander Postnikov. After postdocs at Université du Québec à Montréal and UCLA, he started a tenure-track position at UMass, Amherst where he is part of the Discrete Mathematics group. Morales works in enumerative and algebraic combinatorics and uses bijections, symmetric functions, and tools from algebra to study several objects including linearizations of posets, polytopes associated to graphs, and factorizations of permutations. Morales' research is funded by grants of the National Science Foundation and is a handling Editor of the mathematician owned journal Combinatorial Theory. You can see videos, slides, code, and conjectures of the work of Morales here: ahmorales.combinatoria.co
 

Anca Radulescu, SUNY New Paltz
RKC 111  12:00 pm – 1:00 pm EST/GMT-5

Tifin Calcagni, The Global Math Circle
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
Magic squares are mathematical structures that have been known since ancient times; most likely many of their properties are still left undiscovered. Magic squares are an ideal topic for mathematical exploration and discovery with participants of all levels. Since 2020, Global Math Circle has carried out this activity with various groups. This topic was the foundation of a whole circle project in Colombia. We made five versions in which children of the United States 2020-I, 2022-II, Colombia 2020-I (urban online), Colombia/Peru 2021-II (urban online), 2022-II Colombia (Rural Face-to-face). Exploration of magic squares lead to discussions ranging from basic arithmetic, combinatorics, geometry, vector spaces, and more. We want to show you how to use magic squares as a springboard topic to get at larger mathematical explorations with students of diverse backgrounds and readiness levels.

 

Brandon Look, University of Kentucky
Olin 204  12:00 pm – 1:00 pm EST/GMT-5
In his book on Leibniz's philosophy, Bertrand Russell writes that his first reaction to Leibniz's metaphysics was to think of it as "a kind of fantastic fairy tale, coherent perhaps, but wholly arbitrary." Upon further study, though, he saw that "this seemingly fantastic system could be deduced from a few simple premises, which, but for the conclusions which Leibniz had drawn from them, many, if not most, philosophers would have been willing to admit."  While Russell's logicist interpretation of Leibniz has, to a degree, fallen out of favor among Leibniz scholars, I want to show that there is something right about reading Leibniz this way.  In my talk, then, I shall present the core premises of Leibniz's thought and show how his metaphysics follows from them.    

RKC 111  11:50 am – 1:10 pm EST/GMT-5
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