Student Colloquium Talk by Professor Allison Lewis, Lafayette College

**Abstract: **How can mathematical modeling assist in the development of treatment protocols for cancer? Recent technological advances make it possible to collect detailed information about tumors, and yet clinical assessments of treatment responses are typically based on extremely sparse datasets. We propose a workflow for choosing an appropriate model for tumor growth and treatment response, verifying parameter identifiability, and assessing the amount of data necessary to precisely calibrate model parameters in order to make accurate predictions of tumor size at future times. Throughout this talk, we will discuss ways in which we can bridge the gap between mathematical modelers and clinical physicians to better harness the power of both worlds to meet a common goal.

Student Colloquium Talk by Professor Kenny Barrese, Bucknell University

**Abstract**: Rook theory is a branch of mathematics which considers how many ways you can put rooks on a board so that no two are attacking each other. Here a “rook” is the usual chess piece, but the “board” that we are placing on probably is not an eight by eight square. One way to consider the numbers you obtain is as coefficients of a polynomial, the rook polynomial. It is a key result in rook theory that, if you define the rook polynomial correctly, it always factors completely! In fact, we will see that this factorization arises not by algebraic manipulation, but by counting things in a clever way.

**Abstract: ** Come learn what it takes to become fully certified and work as an actuary. Our presenter Gloria Asare, ACAS, MAAA will touch on various topics of interest related to the actuarial field. These include: how to become an actuary; the different types of actuaries that exist; the types of mathematical problems actuaries solve; what one’s journey to being an actuary could look like; and diversity in the actuarial profession.

**Anyone interested in the actuarial profession (even if you don’t know what it is) is welcome! A mathematical background is not required to attend. **

**Bio: **Gloria Asare is a Specialist Actuary in Pricing at AXA Insurance in Toronto, Canada. She is an Associate of the Casualty Actuarial Society (ACAS) and a member of the American Academy of Actuaries (MAAA). She has ten years of experience working as an actuary in the commercial property and casualty insurance industry supporting various lines of business. After graduating Cum Laude from the Wharton School – The University of Pennsylvania with Bachelor of Science in Economics with a Concentration in Actuarial Science, and a minor in African Studies, she started out her career in Exton, PA (about two hours away from Lewisburg) before relocating to lower Manhattan in New York City, and then to Toronto. Gloria is interested in helping people from all backgrounds get interested in and succeed in the actuarial profession, especially those from underrepresented backgrounds. Gloria is an active member of the CAS and the International Association of Black Actuaries (IABA). She has also served on the Scholarship committee of the Ontario Conference of Casualty Actuaries (OCCA – a regional affiliate of the CAS), on the Scholarship Committee of IABA, and last year founded the Toronto affiliate of IABA. She serves as mentor to a number of students and early career professionals in the field as well. Gloria is proudly African with roots in Nigeria, Kenya and Ghana. She is also a wife, and a mother to two spirited children.

Student Colloquium talk by Professor Chris Johnson, Bucknell University

**Abstract: ** The Prussian city of Königsberg once contained four land masses connected by a series of bridges, and citizens of the city would sometimes ponder the following simple puzzle: is it possible to walk through the city crossing each bridge exactly once? In analyzing this question, Leonhard Euler noted that the most important feature was how the bridges connected the land masses to one another. Understanding “connectedness” is one part of a branch of mathematics called topology, and in this talk I will give an overview of a few particular topological ideas. Beginning with Euler’s nearly 300 year old analysis of the bridges of Königsberg puzzle and ending with some recent developments concerning the shape of a data set, we will see that topological tools can have surprising applications.

**Speakers**:

Hannah Bokma ’20 – teaching intern, Breakthrough Houston

Elise Covert ’20 – data analytics, American Institute for Research

Mady Lawrence ’21 – data analytics, Highmark Health

Phil Thompson ’20 – financial sales and business development intern, IHS Market

**Abstract**: There are many exciting summer opportunities for students in the mathematical sciences! These range from internships in financial companies to research experiences at other universities to leadership development programs. In this week’s colloquium, a panel of your peers will tell you their experiences. What did they enjoy about their experiences? When did they apply? There will also be ample time for questions and answers. These varied opportunities, as well as being terrific fun, are also immensely valuable as you begin to think about your careers after Bucknell.

Student Colloquium talk by Professor Krishnan (Ravi) Shankar, University of Oklahoma

**Title: ** Archimedes’ Cattle Problem

**Abstract: ** Back in antiquity Archimedes devised a mathematical problem in the form of 22 elegiac couplets and delivered them to Eratosthenes of Cyrene (as a challenge of sorts). The problem is in three parts of increasing difficulty and the solution is rather astonishing, both for its complexity and for the problem’s ability to anticipate mathematics that didn’t come about for 2000 years (Pell’s equation). We will explore the problem and its solution (which was only completely solved in 1889 by Amthor) and ask ourselves the age old question: “What did Archimedes know?”

*Panelists:*

- Allison Gibson ‘13, Consultant, Boston Consulting Group; MBA Graduate 2019, Kellogg School of Management, Northwestern University
- Rachel Guen ‘19, Associate Analyst, Moody’s Investors Service
- Zach Moon, ASA ‘16, Actuarial Advisor, Cigna
- Jin On ’12, Manager, Data Science & Provider Analytics, Evariant
- Laura Papili ‘17, Forecast Analyst, Nielsen BASES

Moderated by Professor Linda Smolka, Mathematics

]]>Student Colloquium talk by Professor Kari Lock Morgan, Penn State University

**Title: **Understanding Statistical Significance

**Abstract: ** You may or may not have heard of results being “statistically significant,” and you may or may not know that results qualify as statistically significant if the p-value falls below a given threshold. Regardless of whether these phrases currently hold any meaning for you, the goal of this talk will be to shed light on the actual meaning of a p-value and statistical significance (beyond just “p < 0.05”). This will be accomplished by covering a modern and computationally intensive way of computing a p-value that will be illustrated both by hands-on and online activities (so bring a laptop or tablet if you want to play along!). This simulation-based approach will be both accessible to those who have never taken any statistics, and valuable to those who have taken statistics but want a deeper understanding or a more modern approach.

**Title: **Interacting with the Shadow of Data

**Abstract: ** In our first statistics class, we learn how to build a scatterplot to visualize two variables at once. But what happens when we have *many* variables? Projection methods such as Principal Component Analysis (PCA) can create 2D pictures of higher-dimensional data, much like how the sun projects our 3D body into a 2D shadow. However, exploring these high-dimensional datasets can be complicated. In this talk, we present a visual analytics model that allows the user to combine their personal knowledge with a projection method to find novel ways of exploring the data.

Yili Wang ’21, an applied mathematical sciences and computer science major from Sichuan, China, sees connections between the passions for music and mathematics that she’s pursuing at Bucknell.

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