News + Events

Reem-Kayden Center  4:00 pm – 5:30 pm EST/GMT-5
Join our December graduating seniors as the present their work!

Leon Horsten, Universitat Konstanz
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
In my talk, I consider the kinds of reasons that a mathematician has for believing in mathematical statements. Moreover, we investigate some of the epistemic concepts that are connected to these reasons, such as justification, mathematical justification, proof, formal proof, philosophical proof.
This area is the battleground of the disputes between the philosophers of mathematical practice on the one hand, and the ‘traditional’ philosophers of mathematics on the other hand. I will argue for a middle road in this debate. 

Jeff Suzuki, Brooklyn College
RKC 111  12:00 pm – 1:00 pm EST/GMT-5
Everyone knows that calculus was invented by Newton. Or Leibniz. Actually, the real inventor was Isaac Barrow (Newton’s teacher), but Pierre de Fermat (1601–1661) solved all three of the main problems of calculus:  finding tangents, extreme values, and areas under a curve. We’ll introduce Fermat’s method, then show how it leads to the familiar result that the integral of 1/x is ln x, and e as the base of the natural logarithmic function.
 
Jeff Suzuki was probably born indecisive, and double majored in history and mathematics with a concentration in physics. He avoided having to choose between them by writing a dissertation on the history of celestial mechanics. Since then, he’s done everything possible to avoid specialization, venturing into constitutional law, patents, and mathematics education, and as of this past weekend, is looking into the possibility of developing an open-world game based around mathematics.
 

Lisa Shabel, Ohio State University
Barringer House  12:00 pm – 1:00 pm EDT/GMT-4
Kant’s metaphysical project is framed by his revolutionary claim that some judgments are both synthetic and a priori knowable: one must seek their justification independent of sense experience (i.e., they are a priori) and yet the meaning of such judgments cannot be grasped via conceptual analysis (i.e., they are non-analytic). Kant claims further that allmathematical truths have this distinctive character, and he came to this view by reflecting on mathematical practice. We will discuss how to understand Kant’s view of mathematical truth in light of the mathematics with which he was engaged.

RKC 111  11:45 am – 1:00 pm EDT/GMT-4

Andrew Gregory, University College London
Hegeman 204  12:00 pm – 1:00 pm EDT/GMT-4
Plato's use of number in his music theory, theory of matter, and cosmology raises some interesting questions in metaphysics and philosophy of science. What is the relation between mathematics, physics, and the world? Is there a beauty and simplicity to some mathematics and does that capture the nature of the world? What is the distinction (historical, philosophical) between mathematical physics and numerology? This paper looks at the nature and influence of Plato's views.

James D. Lewis, University of Alberta
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
In topology, there is the notion of a linking number of two oriented disjoint curves in affine 3-space. An algebraic generalization is the concept of a height pairing, which lies at the confluence of arithmetic and geometry. We explain a motivating example situation in an algebraic geometric setting. This talk is targeted to a general audience.

  Reem-Kayden Center  4:00 pm – 6:00 pm EDT/GMT-4
Join our summer research students as they present their work!


Download: BSRI abstract booklet F22-3.pdf

Karin Reinhold Larsson, SUNY Albany
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Canadian-American astronomer Simon Newcomb was the first to notice the curious fact that the ten digits do not occur with the same frequency in logarithmic tables. This weird fact was observed on other sequences in nature such as the  Fibonacci sequence, powers of two and factorials. We will learn a little of the history of Benford’s Law (BL) and do some simulations that will give us an insight to understand the reason behind BL. It turns out that many real life datasets follow BL. Understanding which processes follow BL has provided useful applications of BL into financial fraud detection. 

Karin Reinhold Larsson is an associate professor at the University at Albany, SUNY. She was born in Argentina, obtained a licenciatura in mathematics from the University of Buenos Aires and a PhD in mathematics from Ohio State University. Her main research interests are in Ergodic Theory with connections to probability and harmonic analysis. She has served as president of the University Senate and she is involved the local community serving as statistical consultant in our own Peace Project. 

Elana Kalashnikov, University of Waterloo
RKC 111  5:00 pm – 6:30 pm EDT/GMT-4
Algebraic geometry is the study of ‘shapes’ cut out by polynomial equations. One of the major open problems facing mathematicians today is how to classify these shapes. More complicated shapes can be broken into basic building blocks - so to classify all varieties it suffices to classify the basic building blocks. In this talk, we’ll explain how insights in string theory have given mathematicians a promising way of classifying the building blocks using Mirror Symmetry. The key idea is that each building block should correspond to certain decorated polytopes. Given a building block, the question is then how to produce such a polytope: this is done by degenerating the equations cutting out the shape of the building block. We’ll discuss what’s known about this approach, and what’s left to do, along with explicit examples.

  RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Antu Santanu “Towards a Universal Gibbs Phenomenon”
Felicia Flores & Darrion Thornburgh “2-Caps in the Game of EvenQuads”
Tina Giorgadze “Simplifying Text Using Sentence Fusion Graph”
Hannah Kaufmann “Data Assimilation for Geophysics Models: Glaciers and Storm Surge”
Josef Lazar “A Closer look at Projective SET”
Daniel Rose-Levine "Fun with Quads"

Pamela E. Harris, University of Wisconsin-Milwaukee
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
Multiplex juggling sequences are generalizations of juggling sequences (describing throws of balls at discrete heights) that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Kostant’s partition function is a vector function that counts the number of ways one can express a vector as a nonnegative integer linear combination of a fixed set of vectors. What do these two families of combinatorial objects have in common? Attend this talk to find out!

Liz McMahon, Lafayette College
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
The card game SET is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game; understanding that mathematics enhances our appreciation for the game, and the game enhances our appreciation for the mathematics!  We’ll look at questions in combinatorics, probability, linear algebra, and especially geometry.  There's also a Daily Puzzle, and we have found some interesting things out about that.  If you’d like some practice before the talk, go to www.setgame.com (which will redirect you) for the rules and the Daily Puzzle.

Moshe Cohen, SUNY New Paltz
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4
A line arrangement is a finite collection of lines in the plane.  We can study a line arrangement using algebra and geometry by looking at equations of lines as in high school algebra.  We can study this using combinatorics by looking at the points that are intersections of lines.  We can study this using topology by looking at the complement -- the leftover space.  We can ask if the combinatorial information forecasts the topological information of the complement by studying the moduli space of all geometric realizations. I will introduce several fun problems for us to work on to help acquaint ourselves with this topic and its many complexities.  No specific background is required.

  Learn about the math major, meet other math students and faculty, learn about our weekly seminar, and have pizza!
 
RKC 111  12:00 pm – 1:00 pm EDT/GMT-4

  Reem-Kayden Center Laszlo Z. Bito ‘60 Auditorium  4:00 pm – 6:00 pm EDT/GMT-4
Questions about the Math Placement? Confused about what math course to take? Japheth Wood, Director of Quantitative Literacy, will be available to answer your questions.

  Reem-Kayden Center, Laszlo Z. Bito ‘60 Auditorium  4:00 pm – 6:00 pm EDT/GMT-4
Questions about the Math Placement? Confused about what math course to take? Japheth Wood, Director of Quantitative Literacy, will be available to answer your questions.

Reem-Kayden Center  5:00 pm – 6:30 pm EDT/GMT-4
Abstract booklet below!


Download: Senior Project Poster session booklet S22-1.pdf

  Andrew Schultz, Wellesley College
Hegeman 204A  12:00 pm – 1:00 pm EDT/GMT-4
Binomial coefficients are a staple in the world of combinatorics. Their usefulness in enumeration is nearly unparalleled, but their humble beginnings belie intricate structure and surprising depth. In the pursuit of understanding binomial coefficients more completely, one can encode them in a family of polynomials called Gaussian coefficients. Do these Gaussian coefficients have their own structure and depth? In this talk we'll introduce the Gaussian coefficients and see some surprising ways in which they are (almost!) as nice as their more famous brethren (and maybe a way or two in which they are even nicer).

Matt Kerr
Washington University-St. Louis
Hegeman 204A  12:00 pm – 1:00 pm EDT/GMT-4
Then first you'll have to construct the table, which game regulations insist must pass through five given points. When you're done with that I’ll pick N<10, and to beat me you have to shoot the ball (from wherever I put it) so it returns in exactly N steps to where it started.

If you're not put off by a vector space of polynomials, you can make the elliptic table; and if you know how to spot a complex torus, then (with practice and foci) you can win. This is how I trap unsuspecting students into learning a bit of algebraic geometry.

Because the real title of this talk is: two theorems on conics in the plane!

Shira Zerbib, Iowa State University
Hegeman 204A  12:00 pm – 1:00 pm EDT/GMT-4
The KKM theorem, due to Knaster, Kuratowski and Mazurkiewicz in 1929, is a topological lemma reminiscent of Sperner's lemma and Brouwer's fixed point theorem. It has numerous applications in combinatorics, discrete geometry, economics, game theory and other areas. Generalizations of this lemma, in several different directions, were proved over the years (e.g., by Shapley, Gale, Komiya, Soberon) and have been widely applied as well. We will discuss a recent common generalization of all these theorems. We will also show two very different applications of KKM-type theorems: one is a proof of a conjecture of Eckhoff from 1993 on the line piercing numbers in certain families of convex sets in the plane, and the other is a theorem on fair division of multiple cakes among players with subjective preferences.

Marcus Michelen, University of Illinois-Chicago
Hegeman 204A  12:00 pm – 1:00 pm EDT/GMT-4
Consider a polynomial of degree n whose coefficients are -1 or 1 independently and randomly chosen. What do its roots typically look like?  It turns out that random polynomials are an example of a very common phenomenon: large random structures typically exhibit a lot of predictable behavior. I'll discuss some common examples of this phenomenon, discuss the case of random polynomials, and also explain some applications of these random objects to other fields of math and computer science. No experience in probability will be expected or required; the goal is to give a gentle introduction to some deep facts.

Natalie Frank, Vassar College
Hegeman 204A  12:00 pm – 1:00 pm EDT/GMT-4
"Aperiodic order" is the study of highly ordered structures that fall just short of being periodic. Geometric questions in mathematics and decidability questions in logic provided early theoretical models of such structures. The Nobel Prize-winning discovery of physical quasicrystals in the 1980s led to the wider interest in aperiodically ordered structures. This talk will describe the mathematics of symmetry, the central role symmetry played in the discovery of quasicrystals, and the mathematical models that are used to describe quasicrystals today. 

Caitlin Leverson, Math Program
Hegeman 204A  12:00 pm – 1:00 pm EST/GMT-5
Knots, which you can think of as a string knotted up with the ends glued together, are simple to define but are challenging to tell the difference between. We will discuss a few interesting invariants, algorithms to associate a number to a knot, which we can use to help differentiate between knots. We will also talk about a related notion of knots, called Legendrian knots, where we add a geometric condition. No previous knowledge of knots will be assumed.

  Andrew Harder, Lehigh University
Hegeman 107  12:00 pm – 1:00 pm EST/GMT-5
An elliptic Lefschetz fibration is a smooth 4-manifold M (possibly with boundary) which admits a map to a surface S (possibly with boundary), and so that all but a finite number of fibers are diffeomorphic to a 2-torus, and the rest are homeomorphic to a “pinched” 2-torus. The classification of elliptic Lefschetz fibrations can be reduced to a (hard) problem in linear algebra whose solution is known in several cases — for instance, a theorem of Moishezon and Livné says that if S is just the 2-sphere then it is known that any elliptic Lefschetz fibration has 12n fibres which are pinched 2-tori for some integer n, and that the topology of M is completely determined by n.

Surprisingly, the situation where S is a 2-dimensional disc, despite being well studied, is not completely understood. In this talk, I will discuss an answer to this problem under certain conditions on the boundary of M and on the number of fibres which are singular. We reduce this problem to a question about linear algebraic objects called pseudo-lattices and apply a theorem of Kuznetsov to give a concrete description of a class of elliptic Lefschetz fibrations. Finally I will discuss my motivation for considering this problem and how this classification theorem reflects the numerical classification of weak del Pezzo surfaces in algebraic geometry. This is based on joint work with Alan Thompson.