Talks (unless otherwise indicated) are in Davis 301 from 4–5 PM on Mondays. Refreshments begin at 3:30 on the second floor of Davis.

To make sure you get email updates, add yourself to the mathstu (if a student) or mathothers (if not) email groups. Or check the Colby Math&Stats facebook page.

You can see last semester’s schedule.

**September 11**

Wes Viles and Evan Randles

Colby College

*Meet Our New Faculty
*

### Title

### Abstract

**September 18**

No Colloquium

*We encourage you to go to the talks on mathematics and gerrymandering at Bowdoin.
*

**September 25**

Fernando Gouvêa, Colby

*Polynomial Endoscopy: What can you know if you can’t find the roots?
*

### Title

### Abstract

**October 2**

Rosa Orellana, Dartmouth

*Graphs, Symmetry and Coloring
*

### Title

### Abstract

The polynomial that we obtain which encodes all possible ways to properly color a graph is called the symmetric chromatic polynomial. The number of variables in the polynomial is the number of vertices. It is called symmetric because it doesn’t change when we permute the variables. In this talk, I will describe several properties of this polynomial and some unsolved problems related to this polynomial.

This talk will not assume any graph theory knowledge.

**October 6 (Friday!)**

Pamela Harris, Williams

*Invisible Lattice Points
*

**October 9**

Patricia Cahn, Smith

*Stranger Strings
*

### Title

### Abstract

**October 30**

TBA

**November 6**

Chris Chong, Bowdoin

*The nonlinear mass-spring system: A simple homework problem, or the start of a scientific revolution?
*

### Title

### Abstract

**November 7**

Andrew Sage, Iowa State

*A Walk Through a Random Forest
*

### Title

### Abstract

Talk at 3:30 pm, Davis 201.

Refreshments at 3:00 pm, outside of Davis 216.

**November 13**

Gregory Dungan, USMA

*Introduction to Topological Data Analysis and Applications
*

### Title

### Abstract

**November 14**

Wes Viles, Colby

*Network Characterization through Composite and High-order Interactions
*

### Title

### Abstract

Tuesday, November 14, starting at 3:30 pm, Davis 201

Refreshments at 3:00 pm, outside of Davis 216

**November 16**

Jerzy Wieczorek, Carnegie Mellon

*Model-Selection Properties of Forward Selection with Sequential Cross-Validation
*

### Title

### Abstract

Thursday, November 16, starting at 3:30 pm, Davis 301

Refreshments at 3:00 pm, outside of Davis 216

**November 27**

Jianing Yang ’18, Colby

*Jianing will be giving two 20 minute talks about research she did at Williams this past summer
*

### Title

### Abstract

**Talk 1: Limiting Distributions in Generalized Zeckendorf Decompositions**

Zeckendorf’s Theorem states that every positive integer can be uniquely decomposed into a sum of nonadjacent Fibonacci numbers. Interestingly this property can be used as a definition of the Fibonacci numbers, and thus it is natural to consider extensions to other recurrence sequences and decomposition laws. In addition to unique decomposition, these sequences led to Gaussian behavior in the distribution of number of summands in decompositions, and geometric decay in the probability of a gap of length $g$. We extend these arguments to allow the bin sizes $b_n$ and the legal number of summands chosen from the $n$th bin to vary. We further generalize by examining cases where we place adjacency conditions on the bins, where we use a Central Limit Theorem type result to study the limiting behavior.

**Talk 2: Biases in Fourier coefficients of elliptic curve and cuspidal newform families**

Random Matrix Theory, originally developed to model energy levels of heavy nuclei, has had remarkable success in predicting the main term of the behavior of zeros of $L$-functions. Unfortunately these models cannot see the lower order terms, where the arithmetic of the family lives. We prove results on lower order terms for many families of $L$-functions. In some one-parameter families of elliptic curves, where these terms are related to excess rank, we observe that the second moment of the Fourier coefficients has a negative bias. We extend these techniques to more general families of elliptic curves as well as higher moments and prove the bias is present there as well. We also compute all higher moments of Fourier coefficients from cuspidal newform families.

**December 4**

Ben Mathes, Colby

*Orthogonal Polynomials
*