2023 Past Events

Wednesday, March 15, 2023
Rylan GajekLeonard, '16, Union College
RKC 111 12:00 pm – 1:00 pm EDT/GMT4
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 "padic numbers", a strange place where all triangles are isosceles and where every point in a circle is its center. The theory of padic numbers permeates nearly all aspects of modern number theory. In this talk, we will define and gain intuition for the padic 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.

Wednesday, March 8, 2023
James Marshall, Sarah Lawrence College
RKC 111 12:00 pm – 1:00 pm EST/GMT5
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 farreaching 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.

Wednesday, March 1, 2023
Alejandro Morales, University of Massachusetts
RKC 111 12:00 pm – 1:00 pm EST/GMT5
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 ChanRobbinsYuen (CRY) polytope is a flow polytope with normalized volume equal to the product of consecutive Catalan numbers, one of the most wellknown 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 tenuretrack 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
 Wednesday, February 15, 2023

Wednesday, February 8, 2023
Tifin Calcagni, The Global Math Circle
RKC 111 12:00 pm – 1:00 pm EST/GMT5
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 2020I, 2022II, Colombia 2020I (urban online), Colombia/Peru 2021II (urban online), 2022II Colombia (Rural Facetoface). 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.

Friday, February 3, 2023
Brandon Look, University of Kentucky
Olin 204 12:00 pm – 1:00 pm EST/GMT5
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.
 Wednesday, February 1, 2023