Mathematics Department

Colloquium

Upcoming Seminar

November 29, 4:40 PM in Eliot 314
Daniel Dugger, University of Oregon

Most Thursday afternoons during the academic year, the Reed College Department of Mathematics hosts a math talk. The talks are directed to our mathematics majors but are usually accessible on a variety of levels. Refreshments are served before the talks.

2018-19 Schedule

Fall

4:40-5:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.

Aug 30Meeting with Majors

Topics to be discussed:
Faculty evaluation procedure
Senior thesis project
Graduate schools
…and, whatever else comes up!

Photos will be taken of junior & senior mathematics majors for the department bulletin board.

All students welcome. Refreshment will be provided.

Sept 6AI is Coming.....
David Krueger, University of Montreal

How can we build advanced artificial intelligence (AI) systems that behave as we intend and expect? ("AI alignment") How can we know whether the AI we've built is safe? ("AI safety")  What will happen if it's not?  Although nobody knows if or when we will develop human-level artificial general intelligence (AGI), recent progress in machine learning (ML), in particular deep learning (DL) and reinforcement learning (RL) have led to a massive surge of interest in AI, with billions of dollars going into research with the explicit aim of building AGI.  This has coincided with increased concern over the transformative social impacts of AI technology, most notably the possibility of human extinction ("AI-Xrisk").  I'll give background on machine learning and AI alignment, safety, and Xrisk; and I'll talk a bit about my research in these areas.

All are welcome. Free and open to the public.  Refreshment will be provided

Sept 13Summer Research Presentations

Reed students will present overviews of research in mathematics, statistics, and computer science they completed during summer 2018:

Ira Globus-Harris and Marika Swanberg - Differentially private analysis of variance

Simon Couch and Zeki Kazan - Differentially private non-parametric hypothesis testing

Maxine Calle - Putting the "k" in curvature: k-plane constant curvature conditions

Henry Blanchette - Citations and collaborations among computer systems publications

Sept 20Summer Research Presentations

Reed students will present overviews of research in mathematics, statistics, and computer science they completed during summer 2018:

Zichen Cui - Minimally intersecting filling pair origamis

David Tamas-Parris and Livia Xu - Generators and relations for the equivariant Barratt-Eccles operad

Yevgeniya Zhukova - A look at the functors Ext and Tor

Nick Chaiyachakorn - De Rham cohomology is singular cohomology: de Rham's theorem

Sept 27Bitcoins and Blockchains
Adam Groce, Reed College

Cryptocurrencies like Bitcoin attempt to create an electronic "object" that functions as the equivalent of cash, allowing people to carry out electronic transactions without the need for an intermediary (like a bank or credit card company).  This talk will explain what these cryptocurrencies are and the blockchain technology that makes them work.  The focus will be on understanding the really innovative cryptography that makes them function, but we'll also talk about the economic and policy issues that they raise.  A good technical understanding of how cryptocurrencies really work is crucial if one wants to separate their true promise from the groundless hype.

Oct 4Spaces of Commuting Matrices
José Manuel Gómez, Universidad Nacional de Colombia
In this talk I will introduce the space of commuting matrices associated to different groups of matrices both with real and complex coefficients. We will consider different explicit examples. We will pay particular attention to the problem of computing the number of path-connected components in such spaces. At the end of the talk I will try to explain the geometric relevance of such spaces and the geometric significance of the number of path-connected components.
Oct 11Inversion generating functions for signed pattern avoiding permutations
Naiomi Cameron, Lewis and Clark College
We consider the classical Mahonian statistics on the set Bn(Σ) of signed permutations in the hyperoctahedral group Bn which avoid all patterns in Σ, where Σ is a set of patterns of length two. In 2000, Simion gave the cardinality of Bn(Σ) in the cases where Σ contains either one or two patterns of length two and showed that |Bn(Σ)| is constant whenever |Σ| = 1, whereas in most but not all instances where |Σ| = 2, |Bn(Σ)| = (n+1)!. We answer an open question of Simion by providing bijections from Bn(Σ) to Sn+1 in these cases where |Bn(Σ)| = (n+1)!. In addition, we extend Simion’s work by providing a combinatorial proof in the language of signed permutations for the major index on Bn(21, ̄2 ̄1) and by giving the major index on Dn(Σ) for Σ = {21, ̄2 ̄1} and Σ = {12, 21}. The main result of this paper is to give the inversion generating functions for Bn(Σ) for almost all sets Σ with |Σ| ≤ .
Oct 25An Introduction to the Bernoulli Numbers, from Pythagoras to Present
Ellen Eischen, University of Oregon

Consider these basic questions: What can we say about whole number solutions to polynomial equations? What about finite sums of powers of whole numbers? Infinite sums of powers of fractions? What about factorizations into primes?

In the setting of certain interesting families of examples, fractions called "Bernoulli numbers" unify these seemingly unrelated questions. After an introduction to the Bernoulli numbers, we will explore related developments for these intertwined problems, which lead to central challenges in number theory and beyond.

Nov 1Preperiodic points in complex and arithmetic dynamics
John Doyle, Louisiana Tech University
The study of complex dynamical systems was begun about a century ago, and interest was renewed in the 1980's by work of Douady, Hubbard, and others. Noting analogies between dynamical systems and various objects in algebraic geometry and number theory, Morton and Silverman began to develop an arithmetic theory of dynamical systems in the early 1990's. I will discuss preperiodic points for polynomial maps, motivated by the problem of counting the number of such points in both the complex and arithmetic settings, and I will survey various results on questions of this type.
Nov 8Using Topological Invariants to Distinguish Objects
Courtney Thatcher, University of Puget Sound
A common question asked in topology is whether or not two objects are the same. One way to try to answer this is by looking at the intrinsic properties of the objects such as the number of pieces, how many holes it contains, and how it is twisted. These properties, known as topological invariants, are shared by spaces that are considered the same, but they may not be able to distinguish between spaces that are different. In this talk, we will take a closer look at a particular invariant known as the Euler characteristic and see how it is used to distinguish 2-dimensional objects (the classification of surfaces). Some additional invariants and classification problems will also be presented.
Nov 15Prime numbers and their biases
Stephan R. Garcia, Pomona College
We survey some classical and modern results about prime numbers.  In particular, we highlight remarkable biases displayed by prime pairs that were recently discovered by Pomona undergraduates.
Nov 29Daniel Dugger, University of Oregon

Spring

4:40-5:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.

Jan 31Spyridon Michalakis, California Institute of Technology
Feb 7Blair Davey, City College of New York
Feb 21David Krumm, Reed College
Feb 28Jonathan May, University of Southern California
Mar 7Dino Lorenzini, University of Georgia
Mar 14Niles Johnson, Ohio State University
Mar 21Josh Gancher, Cornell University
Apr 4Chris Piech, Stanford University
Apr 11Nathan Ilten, Simon Fraser University
Apr 18Adam Smith, Boston University
Apr 25John Palmieri, University of Washington
May 2Mike Hill, UCLA

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Phone: 503-777-7710
Fax: 503-788-6691

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