Colloquium Series

Tuesday, April 22, 2025
Speaker: Jordan Ellenberg (University of Wisconsin-Madison)
Title:  Smyth’s conjecture and a non-deterministic Hasse principle
Abstract: The matrix

3     -3    4     -4    5     -5    0     0
4     -4    -3    3     0     0     5     -5
-5    5     0     0     -3    3     -4    4

has an interesting property.  Can you see what it is?

I will explain how to prove a conjecture of Smyth from 1986 about linear relations between Galois conjugates, and explain what this has to do with linear combinations of permutation matrices,  Brianchon’s theorem on ellipses inscribed in hexagons, weightings on the edges of directed hypergraphs, and the study of Diophantine equations where the equation is to be solved with probability distributions instead of with numbers.  This is joint work with Will Hardt.

Note from the organizers: Will Hardt is a 2018 Carleton alum. He was a student of Jordan Ellenberg at the University of Wisconsin-Madison, and graduated with a PhD in mathematics in 2023. 



Tuesday, January 28, 2025
Speaker: Louis Gaudet (University of Massachusetts Amherst)
Title:  Extension problems in arithmetic statistics
Abstract: Broadly speaking, arithmetic statistics is the study of enumerating number theoretic objects. Oftentimes there is an infinite set of objects we are interested in (e.g. primes, or quadratic number fields, or elliptic curves, …) and a notion of the size of these objects (e.g., respectively, absolute value, or discriminant, or conductor, …), and we are interested in counting how many of these objects have size less than some bound. I will discuss examples of such questions and introduce some of the techniques used to study them, hoping to convey why I find such questions so compelling. In particular, we will look at enumerative “extension problems” (related to my current work), where we are interested in counting extensions of number fields with a certain Galois group.  

Thursday, January 23, 2025
Speaker: Jaime Davila (St. Olaf College)
Title:  Unsupervised learning in mutational signatures elicits cancer diagnostic clues
Abstract: One of the hallmarks of cancer is the presence of somatic mutations, which are changes in the DNA of the tumor cell. The pattern in which such mutation occurs is called a mutational signature. Particular mutational signatures are caused by specific processes, for example, UV light causes CC to TT mutations, while tobacco smoking is characterized by the presence of C to A mutations. During this talk I will present my efforts in using mutational signatures to determine the tissue of origin in a clinical cohort with metastatic tumors of unknown primary. The approach I used leverages unsupervised learning, a branch from machine learning that aims to discover patterns in unlabeled data. In particular, I will describe my favorite unsupervised learning technique, non-negative matrix factorization, and describe how to use it on mutational signatures from clinical cancer cases to establish tissue of origin and provide diagnostic clues. 

Tuesday, November 12, 2024 (Week 9)
Speaker: Biyue Dai (University of Minnesota)
Title: Data coordinations and statistical analyses for clinical research in HIV-associated meningitis 
Abstract: HIV-associated meningitis/central nerve system (CNS) infections remain a public health challenge in sub-Saharan Africa. To improve the diagnosis, treatment and outcome of CNS infections, several clinical trials and observational studies have been conducted in Uganda, with a partnership between University of Minnesota and Makerere University. In the first part of this talk, I will introduce the data coordination activities that support this interdisciplinary clinical research team, as well as issues that must be considered and addressed in the data collection and data management process. In the second part of my talk, I will provide case studies of statistical analysis challenges that emerged from these clinical studies.

Tuesday, October 22, 2024
Speaker: Taylor Okonek (Macalester College)
Title:  A pseudo-likelihood approach to under-5 mortality estimation
Abstract: Estimates of under-5 mortality rates (U5MR) are an important indicator of the health of a country. In low- and middle-income countries (LMICs), estimates of U5MR primarily come from probability surveys as opposed to vital registration systems or censuses, and individual observations are subject to both interval- and right-censoring. These data challenges require the use of statistical methodology from both the survey and survival literature in order to produce unbiased estimates of U5MR, while utilizing the full amount of data available. We extend traditional methods from both of these literatures in a pseudo-likelihood approach to estimating U5MR that is more suitable for LMICs than existing demographic methods developed primarily for high-income countries.

Thursday, October 10, 2024
Speaker: Francis Su (Harvey Mudd College)
Title:  The Game of Cycles
Abstract: The Game of Cycles, introduced in my book Mathematics for Human Flourishing, is played on a connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source rule that gives the game a topological flavor. I first started playing this game with Christopher Jackson, an incarcerated man who is a featured contributor to my book. With Chris, several other mathematicians and undergraduate students, we’ve been learning a lot about this game, and I’ll share some of the things we discovered, including a surprising connection to a topological index theorem.

Tuesday, September 24, 2024
Speaker: Corrine Yap (Georgia Institute of Technology & ARC)
Title:  Evolution of Random Discrete Structures
Abstract: In grade school, we learn about phase transitions: at what temperature does solid turn to liquid and liquid turn to gas? The phenomenon of phase transitions occurs not only in nature but also in mathematics. Suppose we create a random network by flipping independent coins to determine if nodes are connected. If each coin is biased, what is the typical structure of the network? What amount of bias will result in the network being connected? In this talk, we’ll discover several notions of “thresholds,” including those defined by structural properties, by the existence of efficient sampling algorithms, and by the evolution rate of a dynamical process. Our examples will come from combinatorics, computer science, and statistical physics, but no background with these topics will be assumed!

Monday, April 15, 2024
Speaker: Moon Duchin (Tufts University)
Title:  Design for Democracy
Abstract: There is a classic, beautiful theory around fairness guarantees for electoral systems. But today, there’s a pressing need to contemplate a democracy reboot; this shifts the question from assessment to design, and counsels us to focus on tendencies rather than guarantees. In this talk I’ll briefly explain why many math modelers have warned that American democracy is in structural trouble, and I’ll overview some new research directions that bring math, CS, and economics into conversation with civil rights, geography, policy, and law.

Tuesday, April 30, 2024
Speaker: Pratima Hebbar (Grinnell) 
Title:  Long-time behavior of some birth-death models
Abstract: Birth-death processes are a classical model in probability to study evolution of biological populations. Francis Galton, the half-cousin of Charles Darwin, and the infamous originator of the eugenics movement in the Victorian era, first proposed a birth-death process to investigate the extinction of aristocratic family names in England. We will introduce Galton-Watson processes, discuss some long established results regarding survival vs. extinction. We then study some generalizations of this population model. The first generalization allows individuals that have differing traits. The second generalization allows individuals to undergo spatial displacement in addition to reproduction. This model is crucial in understanding how species spread across heterogeneous, fast changing landscapes, and is applicable to wildlife conservation in the context of climate change, urban planning, and the study of infectious diseases.

Tuesday, May 14, 2024
Speaker: Anne Grosse (‘16) and Yuriko Vaughan (‘16)
Title:  MAST Alumni Colloquium  – What can you do with a math or stat major?!
Abstract: What can you do with a math or stat major? Come and hear from Anne Grosse ’16 and Yuriko Vaughan ’16 about their career paths and words of advice to current students.

Tuesday, February 6th, 2024 (Week 6)
Speaker: Marissa Loving (UW Madison)
Title:  From dimension 2 to 3 and back again
Abstract:  In this talk I’ll begin by telling a little bit of Thurston’s beautiful story connecting the dynamics of finite-type surface homeomorphisms with the geometry of 3-manifolds. I will then share some more recent work of myself and others which connect the dynamics of infinite-type surface homeomorphisms with the geometry of 3-manifolds. My aim is for the talk to be accessible to a broad audience with many illustrations to help us build our intuition without getting too far into the technical weeds.

Tuesday, January 23rd, 2024
Speaker:Lianne Siegel (Assistant Professor of Biostatistics and Health Data Science, University of Minnesota)
Title:  Type I Error Control and Interim Monitoring for Co-Primary Hypotheses Involving a Subgroup
Abstract: The recent growth of immunoglobulin-based therapies has motivated clinical trials testing primary endpoints both in the overall cohort and in subgroups of patients, such as in patients without specific antibodies at baseline. Existing multiple correction methods in clinical trials often ignore the natural correlation between test statistics in such contexts, resulting in overly conservative type I error control. Motivated by OTAC, an ongoing Phase III trial evaluating the effect of a single infusion of anti-COVID-19 hyperimmune intravenous immunoglobulin (hIVIG), in outpatient adults with recently diagnosed SARS-CoV-2 infection, in both the overall cohort and in the subgroup of participants who had not received monoclonal antibodies or antiviral treatments, we propose a method to control the type I error at a predetermined rate while taking the estimated correlation into account, thus increasing efficiency. Extensive simulation studies indicate that the proposed method controls the type I error at the desired rate, improves power, and reduces the expected sample size compared to a Bonferroni correction. 

Tuesday, January 9, 2024
Speaker: Paula Mercurio  (St. Olaf)
Title:  A Network Science Approach to Fungal Networks and the “Wood Wide Web”
Abstract: As they grow, fungi naturally form underground networks from the growth of hyphae, fungal “roots” that divide and split off from each other, forming large interconnected networks over time. These networks serve a variety of functions, such as absorption and transport of nutrients, and can also interact with the roots of plants, creating the Wood Wide Web, an underground network connecting plants and trees. Network science and graph theory are useful for modeling relationships between interconnected or related items in many biological systems, particularly systems used for transportation or communication like these fungal networks. In this talk, I will discuss how we can use different tools from graph theory and network analysis techniques to investigate the relationships between plants and fungi

Tuesday, October 17, 2023
Speaker: Jasper Weinburd   (Hamline University)
Title:  Collective Behavior in Locust Swarms from Differential Equations to Data
Abstract: Locusts are devastating pests that infest and destroy crops. Locusts forage and migrate in large swarms which exhibit distinctive shapes that improve efficiency on the group level, a phenomenon known as collective behavior. One of the difficulties in understanding and preventing these collective behaviors has been a lack of biological data for individual interactions between locusts. In this talk, I’ll first describe mathematical models for these phenomena on both the collective and individual levels. I’ll then discuss a collaboration with undergraduate students that use field data derived from video footage of locust swarms. We digitized nearly 20,000 locust trajectories and revealed individual behaviors that depend on a locust’s motion and the relative position of its nearby neighbors. Finally, I will illustrate the challenges and potential benefits of incorporating these field observations into our models of locust swarms.

Tuesday, October 3, 2023
Speaker: Michelle Chu  (University of Minnesota)
Title:  Virtual properties of hyperbolic manifolds
Abstract: A virtual property of a manifold is a property satisfied by a finite cover of the manifold. In this talk I will introduce and motivate the study of virtual properties from
both the topological and algebraic perspectives while also discussing some interesting results at the intersection of topology, geometry, and group theory.

Tuesday, September 19, 2023
Speaker: Alex Sutherland   (Ohio State University)
Title: Solving Polynomials; An Ever-Evolving Discipline
Abstract: In this talk, we will look at how humanity’s approach to solving polynomials has evolved over time, with special attention paid to both mathematical and sociological developments. Mathematically, this story includes the classical approach of the Babylonians and their development of the quadratic formula, the beginning of modern formulations of the problem in the 19th century by Kronecker and Klein, and brand new theorems from within the past five years. Sociologically, this talk will highlight the reality that mathematicians are people and thus our humanity is an intrinsic part of mathematics; we will see examples of mathematics interacting with everything from language and how we communicate, to living through global events that we have no control over. If you have ever wondered about how mathematics develops on a societal level, this talk is for you!

Tuesday, May 30, 2023 (Special Alumni Colloquium featuring two mini-talks)

4-4:30pm Speaker: Marf Foster ‘16 (Senior Software Engineer, CrowdStrike)

Title: The Limits of Math: Amongst Adversaries and End Users

Abstract: TBA

4:30-5pm Speaker: Alice Agyiri ‘06 (Project Leader, The Boston Consulting Group)

Title: From Math Major to Business Consultant

Abstract: After graduating from Carleton with Math and Chemistry majors, I joined Citigroup’s Credit Portfolio Management team. I then went on to obtain my MBA from Harvard Business School and transitioned to management consulting with the Boston Consulting Group. If you are curious about careers in Finance and Business, come hear more about the “whys” and “hows” of my journey!

Tuesday, May 16, 2023

Speaker: Kelsey Grinde (Macalester College)

Title: Statistical methods for genetic studies in admixed populations

Abstract: Tools for analyzing genetic data and uncovering the genetic causes of human disease are at the heart of government-sponsored precision medicine initiatives, genetic testing routinely conducted at health clinics, and direct-to-consumer genetic and ancestry testing offered by companies like 23andMe and AncestryDNA. However, the vast majority of genetic studies to date have been conducted in populations of European ancestry. Not coincidentally, many of the statistical methods originally developed for genetics studies were designed for the context of studying populations with so-called “homogenous” ancestry. Populations with mixed, diverse ancestry (also known as admixed populations) have been particularly sorely underrepresented in genetic studies to date, and a number of open questions remain in terms of updating/developing statistical methods for genetic studies in these populations. In this talk, I will discuss work in developing statistical methods for two important tasks: inferring genetic ancestry and identifying genetic variants associated with complex traits and diseases. 

Tuesday, May 2, 2023

Speaker: Anna Haensch (Tufts University)

Title: OpArt: An Equity Based Recommender System for Optimal Art Curation

Abstract:  The placement of art in public spaces can have a significant impact on who feels a sense of belonging in a space. In cities, public art communicates whose interests and culture are being favored. On college campuses, which act like miniature cities, the same is true. In this joint work with Abiy Tasissa and Dina Deitsch, we explore a curatorial tool for selecting public art in a way that supports inclusive spaces. Drawing on Schelling’s model of segregation, we use an assignment derived from the graph matching algorithm and optimized using projected gradient descent to propose an allocation of artwork in a way that de-prioritizes “in-group” preferences, by satisfying minimum representation and exposure criteria. We attempt to bring notions of algorithmic fairness and equity based metrics into this allocation problem and we will discuss the potential pitfalls of this approach from both a curatorial and equity standpoint. 

Friday, April 28, 2023 (Special Colloquium featuring the 2023 Chesley Lecturer in Mathematics)

Speaker: Lillian Pierce (Duke University) 

Title: On Superorthogonality

Abstract:  How do we check if two vectors are orthogonal? We compute their dot product, which by definition takes two vectors as inputs. How do we check if two functions are orthogonal? We compute their inner product, which by definition takes two functions as inputs. Why only two? What would it mean for 4 functions to be “orthogonal”? Or 8 functions? Or 7 functions? Let’s call this superorthogonality. What can we deduce about collections of functions that are superorthogonal? We will explore how a wandering path through papers spanning 90 years led—completely by chance—to a systematic investigation of these questions, and a way to see that previously “unrelated” theorems share a very interesting structure deep under their surface.

Tuesday, April 18, 2023

Speaker: Michelle Mastrianni  (University of Minnesota)

Title: Discrepancy theory: approximating continuous objects by discrete distributions

Abstract: If I asked you to place N points evenly on a unit interval, you would likely be able to do so with no hesitation. Increase the dimension of the space, however, and the question of how to find a “most uniform” N-point set in such a space (e.g. the d-dimensional unit cube, or the surface of a sphere) becomes much more difficult. This talk will introduce the notion of the “discrepancy” of a finite point set, which is a measure of its irregularities of distribution. We will discuss examples of some elegant analytic techniques used in the study of discrepancy. More generally, we’ll survey some intriguing results and open problems in the field, which have connections to a variety of areas of mathematics such as approximation theory, discrete geometry, number theory, and probability.

Tuesday, February 7, 2023

Speaker: Michael Watson  (Northwestern University, co-founder of Opex Analytics)

Title: Two careers for people who like to use data and math to solve problems

Abstract:  Operations Research and Data Science are two exciting fields you should consider. This talk has some fun examples that show you the math behind kidney transplants, locating warehouses, inventory, and more.  I’ll also define the three different things people mean when they say AI (Artificial Intelligence).  AI is a fast-moving field and we’ll cover examples from self-driving cars to finding bad potato chips.  I’ve worked, hired, and taught in this field and will talk about the different ways you can get into it.  The job market is large for people who like data, math, programming, and solving challenging problems. 

Tuesday, January 24, 2023

Speaker: Alexandra Florea (University of California, Irvine)

Title: Moments of L-functions

Abstract: Prime numbers are fundamental objects in number theory, and many deep conjectures in the field concern properties of primes. I will explain how the primes are related, via analysis, to the study of zeros of a certain class of functions, called L-functions. I will discuss how understanding the analytic properties of the L-functions provides insight into the distribution of primes, and I will focus on studying moments (i.e., averages of powers of L-functions in certain families) and what these tell us about primes.

Tuesday, January 10, 2023

Speaker: Lisa Bramer (Pacific Northwest National Laboratory)

Title: Datasets Of Unusual Size and Other Interesting Problems at a National Laboratory

Abstract: The critical first step in analyzing or modeling data is visualization and exploration to assess data quality and the potential relationships between variables. The size and complexity of data are often the main factors that pose challenges to effective exploration. We will discuss a highly scalable framework for visualization of big data. In this talk, we discuss and demonstrate how it can be implemented on datasets from varied application areas such as multi-omics biological data, location tracking time series from sports data, and others.

Tuesday, November  15

Speaker: Lisa Bramer (Pacific Northwest National Laboratory)

Title: Datasets Of Unusual Size and Other Interesting Problems at a National Laboratory

Abstract: The critical first step in analyzing or modeling data is visualization and exploration to assess data quality and the potential relationships between variables. The size and complexity of data are often the main factors that pose challenges to effective exploration. We will discuss a highly scalable framework for visualization of big data. In this talk, we discuss and demonstrate how it can be implemented on datasets from varied application areas such as multi-omics biological data, location tracking time series from sports data, and others.

Tuesday, October 18

Speaker: Laura Boehme Vock (St. Olaf)

Title: Measuring volume change of Ecuador’s glaciers

Abstract: Though only a small fraction of the world’s glaciers, their high level of sensitivity makes the glaciers of the equatorial Andes important indicators of climate change. Though physical access to the glaciers is difficult, we take advantage of satellite imagery to study changes in the size and volume of the glacier in the 21st century. In this talk, I will discuss the ways I’ve used tools from data science, math, and statistics in an analysis of the glaciers in the Ecuadoran Andes. There are interesting parallels to image processing, applications of geometry, GIS tools in R, and statistical models for handling spatial correlation.

Tuesday, September 20

Speaker: Kevin Kwan (Columbia / University College London)

Title: Chebyshev and his Love of Prime NumbersAbstract: P. L. Chebyshev (1821-1894) was considered to be the father of the Russian school of mathematics and is known for his vast, foundational contributions to statistics and probability theory. Probably lesser known to people is his fascination with the distributions of prime numbers. Chebyshev bravely stepped foot in this area filled with plenty of conjectures and big mysteries. Despite the fact that he only wrote a couple of papers on primes, it is just remarkable how many spectacular results he obtained using simple and elegant ideas. His original ideas have opened up new frontiers and have continued to make an impact on modern-day number theory. This talk will be a tour of Chebyshev’s legacy in number theory.

Tuesday, May 17

Speaker: Adrienne Sands (MIT Lincoln Laboratory)

Tuesday, May 3

Speaker:  Jamie Davila (St. Olaf)

Tuesday, April 19

Speaker:  Ben Orlin (Math with Bad Drawings)

Title: Expected value is overrated 

Abstract: I resisted titling this talk “Expected value is stupid.” Expected value, i.e., the long-run average, is not stupid — but our reliance on it sometimes is. We invoke it even when the long run is unreachable, when the average is the wrong criterion, and even when “long-run average” is a contradiction in terms. Explored with bad drawings (and examples from sports, labor economics, and pub trivia).

Tuesday, April 5

Speaker:  Joe Benson (C.H. Robinson)

Title: A logistics data scientist navigates the supply chain

Abstract: Hearing about the supply chain in the news is never a good thing. As a data scientist for one of the world’s largest logistics platforms, news about supply chain disruptions echo loudly in my work. In this talk, I will introduce the complex domain of logistics that I work in, discuss my journey from differential geometry and liberal arts mathematics to data science, and describe an end-to-end project I’ve worked on in the past year, including the tools, skills, and technologies I picked up on the way. 

Tuesday, October 19

Speaker: Cory Colbert (Washington and Lee University)

Title: Complete Sequences

Abstract: A sequence of positive integers is said to be complete if every positive integer can be expressed as a sum of distinct terms from that sequence. We explore some examples of complete sequences and show a neat criterion due to J. L. Brown for detecting completeness. Time-permitting, we’ll make connections to Ostrowski decompositions and other topics. This talk is geared towards undergraduates with an introductory or developing background in mathematics.

Tuesday, October 5

Speaker: John Zobitz (Augsburg University)

Title: Mathematical models from soil to satellite: Fulbright adventures in Finland

Abstract: The Fulbright program supports students and faculty to engage in international exchanges and scholarship abroad.  Last year I was fortunate to travel abroad with my family (even during a pandemic!) to Finland on a project that developed mathematical models for soil carbon following forest fires.  This project involved an interesting mix of mathematics, data science, and some extra persistence and perseverance. This talk will describe some of the lessons learned from Finland, describe the project results, and provide perspectives on how ecological data informs mathematical models.

Tuesday, September 21

Speaker: Taryn Flock (Macalester College)

Title: The Kakeya Needle ProblemAbstract: How much space is required to rotate a needle so it points in every direction?  How do we talk about dimension, in a world without coordinates, or basis vectors? What do these two questions have to do with each other?  Come find out and learn about my favorite open problem in mathematics!

Tuesday, June 1 (Special Alumni Colloquium)

1st Speaker: Andy Hardt ‘13 (University of Minnesota)

Title: Solvable Lattice Models, Statistical Mechanics, & Symmetric Functions

Abstract: What makes a combinatorial object interesting? We might ask for three criteria: the object is simple to compute with; it has connections to many, potentially unexpected, mathematical phenomena; and the connections run deep, in the sense that the combinatorial object exhibits many important properties of the phenomena it represents.

      Lattice models are such an object. The type of model we’ll consider is a straightforward depiction of ice. Oxygen atoms lie at the vertices of a grid, while hydrogen atoms float between them. By giving each vertex a Boltzmann weight associated with its precise configuration, we can use local properties of the system to understand global properties like the system’s energy or the probability that it lies in a given state. Questions like these are the essence of statistical mechanics.

Remarkably, these concrete objects also have important uses in many areas of pure mathematics. One key use is to explore properties of certain special functions; combinatorial operations on the lattice model give us identities of the function it corresponds to. We will look in particular at a lattice model that corresponds to Schur polynomials, the most fundamental symmetric function, and we’ll see how the solvability of the model allows us to see many of the key identities of these polynomials.

2nd Speaker: Emily Kaegi ‘18 (Kraft Analytics Group)

Title: The Data Science Life Cycle with an Application in Sports Business

Abstract: Statistics is the foundation to all Data Science work. The goal of a data scientist is to take a larger problem and translate it into a question that can be answered with data or statistics. In this talk we will walk through the life cycle of a data science project and an application in the sports business industry.

Tuesday, May 4

Speaker: Anthony Várilly-Alvarado (Rice University)

Title: Perfect Cuboids and Magic Squares of Squares

Abstract: A perfect cuboid is a box such that the distance between any two corners is a positive integer.  A magic square is a grid filled with distinct positive integers, whose rows, columns, and diagonals add up to the same number.  To date, we don’t know if there exists a perfect cuboid, or a 3 x 3 magic square whose entries are distinct squares.  What do these problems have in common?  Secretly, they are both problems about rational points on algebraic surfaces of general type.  I believe there is no such thing as a perfect cuboid or a 3 x 3 magic square of squares, and I will try to convince you that geometry suggests this is so.  

Tuesday, April 6

Speaker: Brian Loe (Delta Airlines)

Title: Data Science at Delta Air Lines

Abstract: A data scientist is a person who translates a business problem into a data problem, solves the data problem, and then translates the data solution into a business solution. Airlines have a diverse set of business problems coming from all aspects of the business: maintenance, marketing, revenue management, and customer service to name a few. Many of these problems come with data, and data science makes a difference at the airline by improving the customer experience, reducing waste, or increasing revenue. This talk will present two examples of data science currently in use or under development at Delta Air Lines. One is a predictive, machine learning model, and the other is a descriptive problem in text analysis.

Tuesday, February 9

Speaker: Madeline Handschy (NextEra Analytics)

Title: Optimizing the performance of coupled renewable energy and energy storage resources

Abstract: Renewable energy sources – solar and wind – are inherently variable, and unlike a traditional power plant, energy generation can’t be ‘turned up’ or ‘turned down’ at will. In the past several years, the rapidly falling price of Lithium Ion batteries and related technology has made it more feasible than ever to build solar or wind farms coupled with energy storage capabilities to mitigate some of the variability of the renewable resource and provide more control over the energy output of the farm. In this talk, I will give an overview of working at NextEra Analytics and give examples of how we are applying math to operate energy storage projects as well as evaluate potential new renewable + energy storage hybrid projects.

Tuesday, January 26

Speaker: Mel Currie (NSA – retired)

Title:  A Little Magic with Combinatorics and Analysis

Abstract: We’ll take a look at how baking a nice bowl of combinatorics with a dash of analysis yields Brouwer’s Fixed Point Theorem in the two-dimensional case. We’ll leave with a sense of why it must hold in higher dimensions as well. Shades of algebraic topology!

Tuesday, January 12

Speaker: Pamela Harris (Williams College)

Title:  Kostant’s partition function and magic multiplex juggling sequences

Abstract: Kostant’s partition function is a vector partition function that counts the number of ways one can express a weight of a Lie algebra g as a nonnegative integral linear combination of the positive roots of g. Multiplex juggling sequences are generalizations of juggling sequences that specify an initial and terminal configuration of balls and allow for multiple balls at any particular discrete height. Magic multiplex juggling sequences generalize further to include magic balls, which cancel with standard balls when they meet at the same height. In this talk, we present a combinatorial equivalence between positive roots of a Lie algebra and throws during a juggling sequence. This provides a juggling framework to calculate Kostant’s partition functions, and a partition function framework to compute the number of juggling sequences. This is joint work with Carolina Benedetti, Christopher R. H. Hanusa, Alejandro Morales, and Anthony Simpson.

Tuesday, November 17

Speaker: Jessica Chapman (St. Lawrence University)

Title: The Statistics of Tree Rings with Application to Identifying Driftwood Origin

Abstract: In this talk, you will be introduced to some of the statistical modeling techniques used in the field of dendrochronology (the study of tree rings). Over the years, St. Lawrence University students have been involved in tree ring research from a variety of perspectives, from collecting data on driftwood from Native Alaskan villages to conducting simulation studies comparing the efficacy of the statistical models used to identify the origin of the driftwood. We will explore the findings from these various research projects.

Tuesday, October 20

Speaker: James Sellers (University of Minnesota Duluth)

Title: On Euler’s Partition Theorem Relating Odd-Part Partitions and Distinct-Part Partitions

Abstract: In the mid-18th century, Leonhard Euler single-handedly began the serious study of integer partitions and made fundamental contributions to the area for the next few decades. In particular, he proved a remarkable result which says that the number of partitions of the integer n into distinct parts equals the number of partitions of n into odd parts. My goal in this talk is to discuss Euler’s impressive work on partitions, including snapshots of historical (original) publications of Euler, and then to describe numerous 20th and 21st century results which spring from Euler’s original result. The talk will be self-contained and geared for both students and faculty alike.

Tuesday, October 6

Speaker: Audrey Malagon (Virginia Wesleyan University) 

Title: Votes of Confidence: Leveraging Mathematics to Ensure Election Security

Abstract: As we approach the November 2020 election, many Americans are asking “Will my vote count?” Concerns about foreign interference in our elections, unreliable voting technology, and last minute changes during a pandemic make this election one of the most challenging in recent history. In this talk, we’ll examine the key components of elections in America and how mathematicians are helping to ensure the integrity of our democratic process. 

Tuesday, September 22

Speaker: Edna Jones (Rutgers University)

Title:  Apollonian Circle Packings, Integers, and Higher-Dimensional Sphere Packings

Abstract: An Apollonian circle packing is a certain circle packing in which the circles do not intersect but may be tangent to each other. What do Apollonian circle packings have to do with integers? Under certain conditions, each circle in an Apollonian circle packing has a bend (1/radius) that is an integer! When all the bends are integral, which integers appear as bends? It turns out that this is a hard question to answer. However, it is easier to answer a similar question for analogous higher-dimensional sphere packings.