Mathematics Department

Colloquium

Upcoming Seminar

September 28, 4:40 PM in Physics 123
Bicolored Trees, Shabat Polynomials and Monodromy Groups Uniquely Determined by Passport
Naiomi Cameron, Lewis & Clark College

In this talk, I will discuss the results of an undergraduate research project focused on so-called 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 pre-images 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.

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.

2017-18 Schedule

Fall

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

Aug 31
Please note change in location.
Meeting with majors
Location: Psychology 105
Sept 7Lattices, finite subsets of the circle, and the trefoil knot
Kyle Ormsby, Reed College
I will explore a remarkable correspondence between
  • lattices in the complex plane (up to homothety),
  • nonempty subsets of the circle with at most three elements, and
  • the complement of the trefoil knot in the 3-sphere.
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 14How 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 inclusion-exclusion 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 non-simple functions. I will describe a new approach to this calculus, based on differential geometry, which makes it possible to integrate a large class of non-simple functions, and which hints at new ways to apply differential geometry to data analysis.

Sept 28Bicolored Trees, Shabat Polynomials and Monodromy Groups Uniquely Determined by Passport
Naiomi Cameron, Lewis & Clark College
Location: Physics 123
In this talk, I will discuss the results of an undergraduate research project focused on so-called 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 pre-images 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 Curry-Howard 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 so-called univalent foundations of mathematics.
Oct 12Classifying 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 19Fall Break
Oct 26Ben Williams, University of British Columbia
Nov 2Mariana Smit Vega Garcia, University of Washington
Nov 9
Nov 16
Nov 23Thanksgiving Break
Nov 30Mike Rosulek, Oregon State University

Spring

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

Jan 25Jonathan Campbell, Vanderbilt University
Feb 1
Feb 8
Feb 15
Feb 22
Mar 1
Mar 8Symmetries of Noncommutative Algebras: The What? The How? And the Why Care?
Chelsea Walton, Temple University & University of Illinois Urbana-Champagne
Mar 15Spring Break
Mar 22
Mar 29
Apr 5
Apr 12
Location: Physics 123
Apr 19
Apr 26

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