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MSRI-UP 2019: Combinatorics and Discrete Mathematics

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Friday, June 21st, 2019

Speaker: Dr. Michael Young (Iowa State University)

"Polychromatic numbers of integers"

Given , an -coloring of is polychromatic if every translate of contains all colors. The polychromatic number of is the largest such that there exists a polychromatic -coloring of with respect to . In this talk, we prove that the polychromatic number of a set of size 4 is at least 3, which implies that has a codensity of at most 1/3, proving a conjecture of Newman.

Friday, June 28th, 2019

Speaker: Dr. Shannon Talbott (Moravian College)

"From an Idea to the Product of a Research Project (A Journey via Magic Labels)"

An x magic square is an array of the integers 1, 2, ..., (imagine, for instance, a 3 x 3 Sudoku) where the sum of elements of any column, or any row, or any diagonal, will equal the same constant , called the magic constant. A magic label extends the idea that using a specified addition (such as adding all elements in a column or row or diagonal) will always yield the same constant. In this talk, we will simultaneously explore the area of magic labels as well as the research process — from finding a problem to work on and collaborators to work with through to the end result of a research project.

Friday, July 12th, 2019

Speaker: Dr. April Harry (Rover.com)

"I finally know what I want to be when I grow up: My journey to Data Science"

It seems like some people are born knowing their destiny — I am not one of those people. In the first half of this talk I will describe my path from uncertain undergrad (and MSRI-UP 2009 participant) to my current career as a Data Scientist at Rover. In particular, I will highlight the coursework, skills, and hard lessons that have been the most valuable at each stop along the way. In the second half I will dive deeper into my current work at Rover, where I use statistical techniques to study customer lifetime value (CLV). We will walk through how a beta-geometric negative binomial model can be used to (1) estimate how many transactions a customer is expected to make, and (2) the probability that they will transact in the future.

Friday, July 19th, 2019

Speaker: Dr. Jose Rodriguez (University of Wisconsin - Madison)

"Numerical computation of Galois groups"

The Galois/monodromy group of a family of equations (or of a geometric problem) is a subtle invariant that encodes the structure of the solutions. In this talk, we will use numerical algebraic geometry to compute Galois groups. Our algorithm computes a witness set for the critical points of our family of equations. With this witness set, we use homotopy continuation to construct a generating set for the Galois group. Examples from optimization will be stated (maximum likelihood estimation and formation shape control). Joint work with Jonathan Hauenstein (University of Notre Dame) and Frank Sottile (Texas A&M). Reference: http://arxiv.org/abs/1605.07806