2022 Past Events

Wednesday, November 16, 2022
Leon Horsten, Universitat Konstanz
RKC 111 12:00 pm – 1:00 pm EST/GMT5
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.

Wednesday, November 9, 2022
Jeff Suzuki, Brooklyn College
RKC 111 12:00 pm – 1:00 pm EST/GMT5
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 openworld game based around mathematics.

Friday, November 4, 2022
Lisa Shabel, Ohio State University
Barringer House 12:00 pm – 1:00 pm EDT/GMT4
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 nonanalytic). 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.
 Wednesday, November 2, 2022

Friday, October 28, 2022
Andrew Gregory, University College London
Hegeman 204 12:00 pm – 1:00 pm EDT/GMT4
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.

Monday, October 24, 2022
James D. Lewis, University of Alberta
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
In topology, there is the notion of a linking number of two oriented disjoint curves in affine 3space. 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.

Friday, October 21, 2022
ReemKayden Center 4:00 pm – 6:00 pm EDT/GMT4
Join our summer research students as they present their work!
Download: BSRI abstract booklet F223.pdf 
Wednesday, October 19, 2022
Karin Reinhold Larsson, SUNY Albany
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
CanadianAmerican 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.

Tuesday, October 4, 2022
Elana Kalashnikov, University of Waterloo
RKC 111 5:00 pm – 6:30 pm EDT/GMT4
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.

Wednesday, September 28, 2022
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
Antu Santanu “Towards a Universal Gibbs Phenomenon”
Felicia Flores & Darrion Thornburgh “2Caps 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 RoseLevine "Fun with Quads"

Wednesday, September 21, 2022
Pamela E. Harris, University of WisconsinMilwaukee
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
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!

Wednesday, September 14, 2022
Liz McMahon, Lafayette College
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
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.

Wednesday, September 7, 2022
Moshe Cohen, SUNY New Paltz
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
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.

Wednesday, August 31, 2022
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/GMT4

Wednesday, August 17, 2022
ReemKayden Center Laszlo Z. Bito ‘60 Auditorium 4:00 pm – 6:00 pm EDT/GMT4
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.

Tuesday, August 16, 2022
ReemKayden Center, Laszlo Z. Bito ‘60 Auditorium 4:00 pm – 6:00 pm EDT/GMT4
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.

Tuesday, May 17, 2022
ReemKayden Center 5:00 pm – 6:30 pm EDT/GMT4
Abstract booklet below!
Download: Senior Project Poster session booklet S221.pdf 
Wednesday, May 11, 2022
Andrew Schultz, Wellesley College
Hegeman 204A 12:00 pm – 1:00 pm EDT/GMT4
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).

Monday, May 9, 2022
Matt Kerr
Washington UniversitySt. Louis
Hegeman 204A 12:00 pm – 1:00 pm EDT/GMT4
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!

Wednesday, April 20, 2022
Shira Zerbib, Iowa State University
Hegeman 204A 12:00 pm – 1:00 pm EDT/GMT4
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 KKMtype 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.

Wednesday, April 13, 2022
Marcus Michelen, University of IllinoisChicago
Hegeman 204A 12:00 pm – 1:00 pm EDT/GMT4
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.

Wednesday, March 16, 2022
Natalie Frank, Vassar College
Hegeman 204A 12:00 pm – 1:00 pm EDT/GMT4
"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 Prizewinning 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.

Wednesday, February 23, 2022
Caitlin Leverson, Math Program
Hegeman 204A 12:00 pm – 1:00 pm EST/GMT5
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.

Friday, February 11, 2022
Andrew Harder, Lehigh University
Hegeman 107 12:00 pm – 1:00 pm EST/GMT5
An elliptic Lefschetz fibration is a smooth 4manifold 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 2torus, and the rest are homeomorphic to a “pinched” 2torus. 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 2sphere then it is known that any elliptic Lefschetz fibration has 12n fibres which are pinched 2tori for some integer n, and that the topology of M is completely determined by n.
Surprisingly, the situation where S is a 2dimensional 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 pseudolattices 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.