Colloquium
Upcoming Seminar
January 31,
4:30 PM
in
Vollum Lecture Hall
The Shape of the Quantum Realm
Spyridon Michalakis, California Institute of Technology
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.
201819 Schedule
Fall
4:405:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.
Aug 30  Meeting with Majors Topics to be discussed: Photos will be taken of junior & senior mathematics majors for the department bulletin board. All students welcome. Refreshment will be provided. 

Sept 6  AI 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 humanlevel 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 ("AIXrisk"). 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 13  Summer Research Presentations Reed students will present overviews of research in mathematics, statistics, and computer science they completed during summer 2018: Ira GlobusHarris and Marika Swanberg  Differentially private analysis of variance Simon Couch and Zeki Kazan  Differentially private nonparametric hypothesis testing Maxine Calle  Putting the "k" in curvature: kplane constant curvature conditions Henry Blanchette  Citations and collaborations among computer systems publications 
Sept 20  Summer 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 TamasParris and Livia Xu  Generators and relations for the equivariant BarrattEccles operad Yevgeniya Zhukova  A look at the functors Ext and Tor Nick Chaiyachakorn  De Rham cohomology is singular cohomology: de Rham's theorem 
Sept 27  Bitcoins 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 4  Spaces 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 pathconnected 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 pathconnected components. 
Oct 11  Inversion 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 25  An 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 1  Preperiodic 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 8  Using 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 2dimensional objects (the classification of surfaces). Some additional invariants and classification problems will also be presented. 
Nov 15  Prime 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 29  Scissors congruence and Hilbert's Third Problem Daniel Dugger, University of Oregon In 1900 Hilbert posed a (now wellknown) list of 23 problems that he thought should guide future research for the next century. The third problem concerned whether it was possible to chop up a certain tetrahedron (into a finite number of pieces) and reassemble them to form a cube. The story behind this strange question dates back to Euclid and the early foundations of geometry, and in some form continues to the present day. This was the first of Hilbert's problems to be solved, by Max Dehn. The solution hinged on being able to define and manipulate a new type of "number system". I will describe this story from the beginning and give a sketch of Dehn's work. The talk will assume little in the way of prerequisites; it can probably be understood by anyone who has taken high school geometry. 
Spring
4:405:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.
Jan 31  Please note change in time. Please note change in location. The Shape of the Quantum RealmSpyridon Michalakis, California Institute of Technology Time: 4:30 PM Location: Vollum Lecture Hall At the turn of the century, a list of thirteen significant open problems at the intersection of math and physics was posted online by the president of the International Association of Mathematical Physics. But with problems such as NavierStokes on the list, quick progress seemed unreasonable. Indeed, a decade later, with only one problem partially solved and despite the progress yielding two Fields Medals, the list was all but forgotten. Then, in 2008, as a young mathematician at Los Alamos National Lab, I was tasked with solving the second problem on the list, which asked for a rigorous explanation of the Quantum Hall effect, an important phenomenon in physics with applications to quantum computing and beyond. The solution, which would involve a deep connection between topology and quantum physics, would come a year later. I want to share that journey with you, focusing on insights gained along the way about the relationship of mathematics to physics.


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