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.

Sept. 10
Scott Taylor
Colby College
The mathematics of knotted objects

Title

Abstract

How can mathematics be used to study knotted objects, like strings, loops, and molecules? In this talk I’ll discuss a variety of ways mathematicians quantify what it means for an object to be knotted and how knotted objects themselves (sometimes) act like numbers. I’ll highlight work I’ve done with Colby students in constructing a new class of knotted spatial graphs which are almost unknotted.

 

Sept. 17
Stephanie Eaneff
Talus Analytics
What does the Biological Weapons Convention have to do with statistics?
Case studies in data science and public policy

Title

Abstract

Policy makers tasked with developing processes, agreements, and regulations require relevant, accurate, and transparent information to inform their decisions. However, in many cases, decision makers do not have access to the data they need, when they need it, in formats that clearly communicate results. In some cases, for instance, during the early days of a rapidly unfolding infectious disease outbreak, data may simply not yet be available. In other cases, data may exist but have not yet been structured, analyzed, and visualized to support decision-making. This talk will explore three case studies in the use of data science to inform public health policy decisions, including prioritizing efforts to combat infectious diseases and tracking hospital capacity during a large-scale influenza outbreak. We will discuss considerations, challenges, and lessons learned in collecting, structuring, analyzing, and reporting on data to inform public policy.

 

Sept. 24
Colby Student Summer Research

Title

Abstract

Summer research assistants in the Math/Stats department will present short talks on their projects.

Shabab Ahmed ’19: Solvability of Polynomials

Simon Xu ’20 and Alice Gao ’20: Convex Neural Code

Charles Parham ’20 and Qidong He ’21: Knot Invariants

 

October 1
Meet our new faculty!

Title

Abstract

We are fortunate to have several new faculty in our department. Come meet them and find out something about their research and teaching.
Ariel Keller
Gabi Bontea
George Melvin
Jerzy Wieczorek

 

Oct. 8
Thiago Serra
Mitsubishi Electric Research Labs
Bounding and Counting Linear Regions of Deep Neural Networks

Title

Abstract

We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions on rectifier networks, which are exact for inputs of dimension one; (ii) a first upper bound for multi-layer maxout networks; and (iii) a first method to perform exact enumeration or counting of the number of regions by modeling the DNN with a mixed-integer linear formulation. These bounds come from leveraging the dimension of the space defining each linear region. The results also indicate that a deep rectifier network can only have more linear regions than any shallow counterpart with same number of neurons if that number exceeds the dimension of the input.

Joint work with Christian Tjandraatmadja (Carnegie Mellon University, now at Google) and Srikumar Ramalingam (The University of Utah), presented at the 35th International Conference on Machine Learning (ICML 2018).

 

Oct. 11 (Thurs.)
Danny Rorabaugh
University of Tennessee
Integer Sequences

Title

Abstract

The powers of 2: {1, 2, 4, 8, 16, 32, 64, …}. The maximum number of regions obtained when slicing a circle with n lines: {1, 2, 4, 7, 11, 16, 22, 29, …}. Integer sequences are found throughout mathematics, but especially in number theory and combinatorics. They might count a class of mathematical objects or just have fascinating numerical properties. What is the rule for constructing the following sequence: {1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, …}?

The number of neutrons in the most abundant isotope of each element on the periodic table: {0, 2, 4, 5, 6, 6, 7, 8, 10, 10, 12, …}. The year in which the population of earth reached n billion: {1804, 1927, 1959, 1974, 1987, 1999, 2011(, …?)}. Integer sequences are everywhere. Can you figure out what this sequence represents: {3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, …}?

In this talk, we share the joys of studying integer sequences and tools available for investigation. With sequences, you can practice programming and make connections between disciplines; they are the source of both silly puzzles and deep, unsolved mathematical questions.

 

Oct. 22
Helen Wong
Claremont McKenna
It’s not algebra, it’s knot algebra

Title

Abstract

Knots are an everyday part of life. They appear in shoelaces, computer cords, and fishing wire. But they also appear in less likely places; for example in bacterial DNA, in debunked atomic theories of Lord Kelvin, and in current schemes for creating a quantum computer by braiding anyons. Come to this talk to find out more about the mathematical theory of knots, and in particular, how mathematicians use techniques from algebra to understand them better!

 

Oct. 29
Chris Moore
Colby College (Biology)
TBA

 

Nov. 5
SPEAKERS
AFFILIATION
TBA

 

Nov. 12
SPEAKERS
AFFILIATION
TBA

 

Nov. 26
SPEAKERS
AFFILIATION
TBA

 

Dec. 3
Milja Poe
On S-unit Equations