Colloquium
Upcoming Seminar
October 26,
4:40 PM
in
Eliot 314
Azumaya Algebras: Bridging Algebra and Topology
Ben Williams, University of British Columbia
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.
201718 Schedule
Fall
4:405:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.
Aug 31  Please note change in location. Meeting with majorsLocation: Psychology 105 

Sept 7  Lattices, finite subsets of the circle, and the trefoil knot Kyle Ormsby, Reed College I will explore a remarkable correspondence between
Along the way, we will encounter modular forms, Voronoi cells, and open book decompositions. The talk should be accessible to anyone who knows how to multiply complex numbers.

Sept 14  How to Win the Lottery David Roe, Department of Mathematics, University of Pittsburgh From 2005 through 2012, three groups in Massachusetts earned millions of dollars playing a lottery game called Cash Winfall. I'll describe how the game worked, explain why it was exploitable, give connections with projective geometry and share stories from my participation in one of the pools. You'll also learn why almost every other lottery is not worth playing. 
Sept 21  A New Approach to Euler Calculus for Continuous Intergrands Carl McTague, University of Rochester The Euler characteristic satisfies an inclusionexclusion principle χ(X∪Y)=χ(X)+χ(Y)χ(X∩Y), which lets one regard it as a measure – a peculiar one where a point has measure 1 while a circle has measure 0. One can use it to integrate simple functions (in the sense of measure theory), and the resulting integral calculus has deep roots in algebraic geometry and has recently found surprising applications to data analysis. However, since it is only finitely – not countably – additive, it does not fit into the framework of Lebesgue integration, and there are problems integrating even the most elementary nonsimple functions. I will describe a new approach to this calculus, based on differential geometry, which makes it possible to integrate a large class of nonsimple functions, and which hints at new ways to apply differential geometry to data analysis. 
Sept 28  Cancelled Bicolored Trees, Shabat Polynomials and Monodromy Groups Uniquely Determined by PassportNaiomi Cameron, Lewis & Clark College Location: Physics 123 In this talk, I will discuss the results of an undergraduate research project focused on socalled dessin d'enfants. Roughly speaking, a dessin d'enfant (or dessin for short) is a bicolored graph embedded into a Riemann surface. Dessins which are trees can be associated analytically to preimages of certain polynomials, called Shabat polynomials, and also algebraically to their monodromy group, which is the group generated from rotations of edges about its vertices. One known invariant for dessins is called the passport, which is the multiset of the degrees of its vertices and faces. The focus of this project was to determine the Shabat polynomials and monodromy groups for trees uniquely determined by their passport. 
Oct 5  Homotopy Types as a Foundation for Mathematics Emily Riehl, Johns Hopkins University The CurryHoward correspondence formalizes an analogy between computer programs and mathematical proofs. This talk will introduce alternative foundations for mathematics animated by this analogy. The basic object is called a type, which can be simultaneously interpreted as something like a set or as something like a mathematical proposition. Homotopy type theory refers to the recent discovery that a type can also be interpreted as something like a topological space. We will discuss the implications of this homotopy theoretic interpretation for the socalled univalent foundations of mathematics.

Oct 12  Classifying Manifolds: Applications of Topology to Geometry and Physics Christine Escher, Oregon State University A fundamental and deep problem in mathematics is a classification of the objects of study: which objects are the same, which are different. The tools for the classification of this talk come from algebraic topology but the interest and motivation for the classifications come from differential geometry and theoretical physics. I will give an overview over which objects we study and what we mean by "the same" and "different". In particular, I will discuss the classification of Euclidean spaces and spheres. 
Oct 19  Fall Break 
Oct 26  Azumaya Algebras: Bridging Algebra and Topology Ben Williams, University of British Columbia Since the discovery of Quaternions by Hamilton in 1843, noncommutative division algebras have been a topic of study in algebra. In the mid20th century, they were generalized considerably by several people, culminating in an abstract and general definition of "Azumaya algebra" by Grothendieck in 1968. In this formulation, certain algebraic problems may admit solutions by geometric, or strictly speaking, topological, methods. I will explain what the algebraic terms mean, how Grothendieck's idea works and why it is ingenious, and how you can use it to solve problems. 
Nov 2  Mariana Smit Vega Garcia, University of Washington 
Nov 9  
Nov 16  
Nov 23  Thanksgiving Break 
Nov 30  Mike Rosulek, Oregon State University 
Spring
4:405:30pm in Eliot 314 (unless marked otherwise). Directions to Reed.
Jan 25  Jonathan Campbell, Vanderbilt University 

Feb 1  
Feb 8  
Feb 15  
Feb 22  
Mar 1  
Mar 8  Symmetries of Noncommutative Algebras: The What? The How? And the Why Care? Chelsea Walton, Temple University & University of Illinois UrbanaChampagne 
Mar 15  Spring Break 
Mar 22  
Mar 29  
Apr 5  
Apr 12  Location: Physics 123 
Apr 19  
Apr 26 