Claremont Center for the Mathematical Sciences

Silica-based glasses: Realizing process-structure-property connections through computational modeling
2019-11-20 16:15 - 17:15 (America/Los_Angeles) | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Silica-based glasses are increasingly becoming vital components in our current technology, from optical data transmission lines, to electronics, to optical lenses, to smartphone screens. These materials are inherently brittle and subject to failure under shock, non-equilibrium stress states, or corrosive environments. Identifying new compositions and processing conditions that result in improved fracture resistance (i.e. a higher fracture toughness) is achievable through materials design approaches. However, discovery primarily remains an empirically determined procedure. Atomistic molecular dynamics can be a powerful tool in this application, providing a capability to probe how glass breaks and what compositions or microstructural features result in better material performance. In this talk, a novel numerical method to determine the fracture toughness from atomistic material representations will be demonstrated on vitreous silica-based glass compositions. Process-structure-property connections will then be explored using this measure to highlight the relationships between processing conditions, chemical composition, microstructural content, and material performance. Finally, an overview of the collaboration between the 2019-20 CGU Math Clinic team and Sandia National Laboratories will be discussed, where project goals are focused on using machine learning to predict fracture nucleation in silica glass.
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Dynamics of a childhood disease model with isolation
2019-11-21 12:00 - 13:00 | Millikan 2141, Pomona College
Joan Ponce
Purdue University
Abstract: One of the main challenges of mathematical modeling is the balance between simplifying assumptions and incorporating sufficient complexity for the model to provide more accurate and reliable outcomes. For mathematical simplicity, many commonly used epidemiological models make restrictive modeling assumptions. Although models under such assumptions are capable of producing useful insights into the biological questions in many cases, they may generate discrepancies in model outcomes. One of the common assumptions in infectious disease models is that the duration for disease stages is exponentially distributed. This may result in discrepancies in model outcomes between such a model and models with more realistic stage distribution assumptions such as gamma distributions with the shape parameter greater than one (Feng et al., 2007). In this talk, I will present an ODE model with gamma-distributed infectious and isolated periods and compare it with a model with exponentially distributed stages. These models intend to show that, for childhood diseases, isolation of infected children may be a possible mechanism responsible for the observed oscillatory behavior in incidence. This is shown analytically by identifying a Hopf bifurcation with the isolation period as the bifurcation parameter.
An important result is that the threshold value for isolation to generate sustained oscillations from the model with gamma-distributed isolation period is much more realistic than the model assuming exponential distributions.
About the speaker: Joan Ponce is a graduate student from Purdue University

Applied Math Talk: Patterns deformed by spatial inhomogeneity give by Prof. Jasper Weinburd (HMC)
2019-11-25 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
At the turn of the twentieth century, physicist Henri Bénard heated a shallow plate of fluid from below. For temperatures above a critical value, the fluid’s evenly heated state became unstable as thermal convection took hold; heated fluid rose in localized areas while cooler fluid fell nearby. The rising and falling fluid created hexagonal convection cells, squares, and stripes.
Suppose that we modify Bénard’s experiment by heating only the left half plate. We expect the fluid on the right to remain stationary and only the the fluid on the left to form patterns. We confirm this intuition mathematically and, more surprisingly, find that the step-type inhomogeneity restricts the spatial period of the resulting patterns on the left. We examine this phenomenon using a universal partial differential equation model. The main difficulty arrises at the location of the discontinuous inhomogeneity because results on either side cannot be directly compared. We construct a transformation of variables that bridges this jump and allows a heteroclinic glueing argument from left to right. The explicit form of this transformation determines the widths of patterns that may occur in the inhomogeneous environment.

Exponential domination in grids (Michael Young, Iowa State University)
2019-11-26 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Domination in graphs has been an important and active topic in graph theory for over 40 years. It has immediate applications in visibility and controllability. In this talk we will discuss a generalization of domination called exponential domination. A vertex $v$ in an exponential dominating set assigns weight $2^{1−dist(v,u)}$ to vertex $u$. An exponential dominating set of a graph $G$ is a subset of $V(G)$ such that every vertex in $V(G)$ has been assigned a sum weight of at least 1. We will specifically look at grid graphs and graphs on the torus.

ANTC Seminar: Random Monomial Ideals (Lily Silverstein, CalPoly Pomona)
2019-12-02 12:15 - 13:10, 2019-12-03 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Probability is a now-classic tool in combinatorics, especially graph theory. Some applications of probabilistic techniques are: (1) describing the typical/expected properties of a class of objects, (2) uncovering phase transitions and sudden thresholds in the dependence of one property on another, and (3) producing examples of conjectured or unusual objects. (This last technique is sometimes called “the probabilistic method.”)
This talk will apply these techniques to commutative algebra, using monomial ideals as a bridge between combinatorics and algebra. I’ll introduce a family of random models for monomial ideals, and describe results of each type mentioned above, for instance: (1) typical projective dimension, (2) thresholds in Krull dimension as a function of number of monomial generators, and (3) how to generate unlimited examples of monomial ideals which aren’t generic (in the Bayer-Peeva-Sturmfels sense), but which nevertheless have minimal free resolutions that can be read from their Scarf complexes.
Joint work with subsets of: Jesús A. De Loera, Serkan Hoşten, Robert Krone, Sonja Petrović, Despina Stasi, Dane Wilburne, and Jay Yang.

Applied Math Seminar On Unlimited Sampling given by Prof. Felix Krahmer (Technische Universität München)
2019-12-02 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Shannons sampling theorem provides a link between the continuous and thediscrete realms stating that bandlimited signals are uniquely determined by itsvalues on a discrete set. This theorem is realized in practice using so called analog to digital converters (ADCs). Unlike Shannons sampling theorem, the ADCs are limited in dynamic range. Whenever a signal exceeds some preset threshold, the ADC saturates, resulting in aliasing due to clipping. In this talk,we analyze an alternative approach that does not suffer from these problems.Our work is based on recent developments in ADC design, which allow for ADCs that reset rather than to saturate, thus producing modulo samples. An open problem that remains is: Given such modulo samples of a bandlimited function as well as the dynamic range of the ADC, how can the original signal be recovered and what are the sufficient conditions that guarantee perfect recovery? In this paper, we prove such sufficiency conditions and complement them with a stable recovery algorithm. Our results not limited to certain amplitude ranges, in fact even the same circuit architecture allows for the recovery of arbitrary large amplitudes as long as some estimate of the signal norm is available whenrecovering.
This is joint work with Ayush Bhandari (Imperial College London) and Ramesh Raskar (MIT).
Bio:
Felix Krahmer received his PhD in Mathematics in 2009 from New York University under the supervision of Percy Deift and Sinan Güntürk. He was a Hausdorff postdoc in the group of Holger Rauhut at the University of Bonn, Germany from 2009-2012. In 2012 he joined the University of Göttingen as a an assistant professor for mathematical data analysis, where he has been awarded an Emmy Noether Junior Research Group. Since 2015 he has been tenure track assistant professor for optimization and data analysis in the department of mathematics at the Technical University of Munich.

Dan Douglas (USC)
2019-12-03 15:00 - 16:00 | Millikan 2099, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract TBA

A geospatial modeling analysis of travel-time, bicycles, and HIV elimination in sub-Saharan Africa: the case of Malawi
2019-12-04 16:15 - 17:15 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
UNAIDS has proposed an ambitious strategy for ending the HIV pandemic. Their strategy depends upon achieving a treatment coverage goal of 90% by 2030. However, distance to healthcare and lack of transportation are major barriers to accessing HIV treatment in SSA. I will use data-based geospatial modeling to determine their potential impact as barriers to elimination in Malawi. I will address two specific questions: How much time would people living with HIV (PLHIV) need to spend travelling to access treatment in order for Malawi to achieve UNAIDS’ goal of 90% coverage? Could providing bicycles to rural communities help eliminate HIV?
Our results show that it will only be possible to achieve UNAIDS’ 90% coverage goal in Malawi if many of the PLHIV (who have yet to initiate treatment) are willing, and able, to spend a great deal of time travelling to access treatment. Additionally, they show that making bicycles available to PLHIV in rural areas has the potential to make the 90% target goal more attainable, and hence to help eliminate HIV in Malawi.

"Remember Maryam Mirzakhani"
2019-12-04 17:30 - 18:00 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
The Pomona College Student AWM chapter
warmly invites you to an event honoring Maryam Mirzakhani

“Remember Maryam Mirzakhani”
Curator, Thaís Jordão
Designer, Rafael Meireles Barroso
You are cordially invited to hear recollections of Maryam Mirzakhani

Wednesday
Dec. 4
5:30pm
Argue Auditorium

The memorial exhibit (commissioned by the
International Mathematical Union’s Committee for Women in Mathematics)
will be on display in the Math Foyer upstairs.
Light refreshments to enhance your experience

GEMS Workshop: Working Together without a Leader with Professor Jasper Weinburd of Harvey Mudd College
2019-12-07 10:00 - 12:00 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
TOPIC: Working Together without a Leader
Bees all work together by communicating and obeying the orders of the Queen. Other animals gather in swarms, flocks, or schools and move in complicated ways without any leader at all. In a school of fish, each one is identical and they all follow the same simple rules. Yet they still manage to form tight bait balls and make sharp turns in unison. So a school of fish is more than just a group of fish; it is greater than the sum of its parts. In this workshop, we’ll investigate this deep mathematical idea by thinking about groups of animals.
Also, it may be fun to check out this video that illustrates some of the ideas we will be looking at:

WHAT IS GEMS:

The Gateway to Exploring Mathematics program (GEMS) is a series of workshops that helps excite the interests and curiosity of young students in mathematics and science.

GEMS meets once a month on a Saturday morning from 10:00 AM to 12:00 PM.

GEMS is designed to reach 8th, 9th and 10th grade students who have an interest in mathematics and science.

Participants interact with excellent and award winning faculty, staff, students and alumni from each of the seven Claremont Colleges.

FALL 2019 DATES:

October 5, 2019

November 2, 2019

December 7, 2019

REGISTRATION:

To register for our next event on November 2nd, please click on the following link:

https://forms.gle/6LQbpRWVdGDvc97Q9

ANY QUESTIONS:

Please contact our 2019-2020 GEMS coordinator, Josh Kiernan at joshua.kiernan@cgu.edu

Applied Math Talk: Set your parasites low (or high) given by Professor Maryann Hohn (Pomona College)
2019-12-09 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Individuals may choose to create social groups where their individual fitness and success is influenced by those around them. A group may increase an individual’s success in finding food, shelter, and safety; however, if the group fails, so does the individual. In this talk, we will explore how choices of individuals influence group dynamics using both agent-based modeling and partial differential equations. In particular, we will examine individuals who live in close, collaborate groups who are susceptible to infectious diseases such as pathogens and parasites through their social network.

Computational bounds for doing harmonic analysis on permutation modules of finite groups (Mike Orrison, HMC)
2019-12-10 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
In this talk, I will describe an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express the resulting computational bounds. I will then conclude by showing that these bounds are surprisingly small when dealing with certain permutation modules arising from the action of the symmetric group on tabloids. This is joint work with Michael Hansen, Masanori Koyama, Matthew McDermott, and Sarah Wolff.

Ryan Blair (Cal State Long Beach)
2019-12-10 15:00 - 16:00 | Millikan 2099, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States

Epidemiological models for Ebola exploring different dynamics
2019-12-11 16:15 - 17:15 | Argue Auditorium, Pomona College, 610 N. College Ave., Claremont, CA, 91711, United States
In today’s environment of universal connection and media updates, we are constantly informed about infectious diseases and the ramifications. We can combat infectious diseases using mathematics to gain insight into diseases dynamics and outbreaks. I will focus primarily on Ebola Virus Disease, exploring different models focused on capturing various dynamics.
First, I will present a model whose goal is to illustrate role of education in limiting a potential future Ebola outbreaks in Sudan using data and modeling. Then, I will introduce a model which captures superspreader dynamics and compare the model for Ebola and Middle Eastern Respiratory Syndrome (MERS). In addition to these models I will explain about how I became interested in Mathematical Epidemiology and some of the great programs which have led to my research collaborations.

CCMS Field Committee Meeting
2020-01-22 16:15 - 17:15 | Shanahan B460, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
The Field Committee Meeting is our chance to socialize with our colleagues and coordinate our course offerings for the coming academic year (2020-2021).

Please come to discuss course offerings and other synergistic items.

Refreshments starting at 3:15, meeting at 4:15.

Dragging the roots of a polynomial to the unit circle (Sinai Robins, University of Sao Paulo)
2020-01-23 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Several conditions are known for a self-inversive polynomial that ascertain the location of its roots, and we present a framework for comparison of those conditions. We associate a parametric family of polynomials p_α(x) to each such polynomial p, and define cn(p), il(p) to be the sharp threshold values of α that guarantee that, for all larger values of the parameter, p_α(x) has, respectively, all roots in the unit circle and all roots interlacing the roots of unity of the same degree. Interlacing implies circle rootedness, hence il(p) ≥ cn(p), and this inequality is often used for showing circle rootedness. Both il(p) and cn(p) turn out to be semi-algebraic functions of the coefficients of p, and some useful bounds are also presented, entailing several known results about roots in the circle. The study of il(p) leads to a rich classification of real self-inversive polynomials of each degree, organizing them into a complete polyhedral fan. We have a close look at the class of polynomials for which il(p) = cn(p), whereas in general the quotient il(p)/cn(p) is shown to be unbounded as the degree grows. Several examples and open questions are presented. This is joint work with Arnaldo Mandel.

Applied Math Talk: Statistical Mechanics of Molecular Evolution and its Role in the SELEX Protocol given by Prof. Bhaven Mistry (CMC)
2020-01-27 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Antibodies are the standard biomolecule for marking molecular structures and delivering drugs due to their specific binding capabilities. However, they are expensive to produce and their relatively large size prevents their easy traversal of bi-lipid membranes. Over the past 30 years, molecular recognition has also been achieved through the use of aptamers, short oligonucleotide sequences that fold in conformations that allow them to specifically bind to targets. These aptamers are produced rapidly and efficiently through a process known as Systematic Evolution of Ligands by EXponential enrichment (SELEX) whereby a molecular selection mechanism based on competitive binding enriches the population of given strands and removes unwanted sequences, yielding high target specificity and affinity. Current SELEX mathematical models are formulated in the mass action limit, which assumes large aptamer/target concentrations. Low number effects, such as the extinction probability of the best binding aptamer, however, require a full stochastic model currently lacking in the literature. We derive such a statistical mechanics model verifying that in the large aptamer/target concentration limit, the mass action results are recovered. Our stochastic model also allows us to calculate the extinction probability and efficiency of selection, and to propose a method of optimizing the SELEX protocol.

Castelnuovo-Mumford regularity of edge ideals of graphs (Siamak Yassemi, University of Tehran)
2020-01-28 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Let K be a field and S = K[x_1,…,x_n] be the polynomial ring in n variables over K. For a graded S-module M with minimal free resolution the Castelnuovo-Mumford regularity is defined. We survey a number of recent studies of the Castelnuovo-Mumford regularity of the ideals related to a graph and their (symbolic) powers. Our focus is on the bounds and exact values for the regularity in terms of combinatorial data from associated graphs. This research program has produced many exciting results and, at the same time, opened many further interesting questions and conjectures.

Stefano Vidussi (UCRiverside)
2020-01-28 15:00 - 16:00
Title: The BNS invariant of the fundamental group of a surface bundle over a surface.
Abstract: We will discuss some new results on the Bieri-Neumann-Strebel invariant of these groups, showing in particular that (with obvious exceptions) they algebraically fiber. As a corollary, we show that for “most” bundles these groups are not coherent.

A Tauberian theorem and some of its applications
2020-01-29 16:15 - 17:15 | Freeberg Forum, LC 62, Kravis Center, CMC
In general terms, a Tauberian theorem deals with the relationship between the properties of one transform of a measure with those of another transform. We will introduce the notion of a Tauberian theorm, and present our own recent theorem in this direction. Our theorem provides a uniform theory for the construction of certain localized kernels in a very general context. These in turn play a fundamental role in many different applications in numerical analysis, signal processing, and machine learning. We will discuss a few applications, for example, the construction of a theory inspired neural network for the solution of Burgers equation, inversion of Laplace transform of point masses, and an alternative theory for function approximation in the setting of diffusion geometry in machine learning without the need for any eigen-decomposition of a large matrix.

GEMS Workshop: Superheroes vs. Supercomputers with Professor Jeho Park of Claremont McKenna College
2020-02-01 10:00 - 12:00 | Shanahan 1480, Harvey Mudd College, 301 Platt Blvd., Claremont, CA, 91711, United States
TOPIC: Superheroes vs. Supercomputers
Superheroes like Wonder Woman, Black Panther, Superman, and Captain Marvel, just to name a few, all have “super” power and they save the world from “super”-villains. Well, just one catch–they are not real. In our real world, there are computers built for super power to save the (real) world. In this talk, you will be introduced to “super”computers built to defeat “super”villains (i.e., super difficult problems). To understand supercomputing, you will learn some (or all) of the following exciting terms and theories (which are not commonly discussed in high school classrooms): cluster, GPU, parallel processing, decomposition, shared memory, distributed memory, Amdahl’s law, big data, artificial intelligence, deep learning, machine learning, and data science.
WHAT IS GEMS:
The Gateway to Exploring Mathematics program (GEMS) is a series of workshops that helps excite the interests and curiosity of young students in mathematics and science
GEMS meets once a month on a Saturday morning from 10:00 AM to 12:00 PM
GEMS is designed to reach 8th, 9th and 10th grade students who have an interest in mathematics and science
Participants interact with excellent and award winning faculty, staff, students and alumni from each of the seven Claremont Colleges
SPRING 2020 DATES:
February 1, 2020
March 7, 2020
April 18, 2020
REGISTRATION:
To register for our next event on February 1, please click on the following link:
https://forms.gle/14wMcsV5iUGN5mqNA
ANY QUESTIONS:
Please contact our 2019-2020 GEMS coordinator, Josh Kiernan at joshua.kiernan@cgu.edu

Covering point-sets with parallel hyperplanes and sparse signal recovery (Lenny Fukshansky, CMC)
2020-02-04 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Let S be a set of k > n points in n-dimensional Euclidean space. How many parallel hyperplanes are needed to cover it? In fact, it is easy to prove that every such set can be covered by k-n+1 parallel hyperplanes, but do there exist sets that cannot be covered by fewer parallel hyperplanes? We construct a family of examples of such extremal sets. We then use it, along with a result on girth of bipartite graphs, to construct a family of n x d integer matrices with bounded sup-norm and the property that no m column vectors are linearly dependent, m < n. If m < (log n)^{1-e} for any e > 0, then d/n tends to infinity as n tends to infinity. This is a deterministic construction of a family of sensing matrices, which are used for sparse signal recovery in compressed sensing. Joint work with Alex Hsu.

Tommaso Cremaschi (USC)
2020-02-04 15:00 - 16:00
Title: Volumes and filling collections of multicurves

Abstract: In this talk we will be concerned with links L in a Seifert-Fibered space N such that their projection to the base surface is a collection of curves G in minimal position. After stating a hyperbolization result, for the complement of L, in terms of G we will study the volume of their complement and give combinatorial asymptotics. We will be particularly interested in the case where N is the projective tangent bundle of a hyperbolic surface. This is joint work with J.A. Rodrigues-Migueles and A. Yarmola.

Kernel approaches in global statistical distances, local measure detection, and active learning
2020-02-05 16:15 - 17:15 | Freeberg Forum, LC 62, Kravis Center, CMC
In this talk, we’ll discuss the problem of constructing meaningful distances between probability distributions given only finite samples from each distribution. We approach this through the use of data-adaptive and localized kernels, and in a variety of contexts. First, we construct locally adaptive kernels to define fast pairwise distances between distributions, with applications to unsupervised clustering. Then, we construct localized kernels to determine a statistical framework for determining where two distributions differ, with applications to measure detection for generative models. Finally, we’ll begin to address the question of measure detection without a priori known labels of which distribution a point came from. This is addressed through active learning, in which one can choose a small number of points at which to query a label. This is ongoing work with Xiuyuan Cheng (Duke) and Hrushikesh Mhaskar (CGU), among others.

Applied Math Talk: Robust Estimators for Monte Carlo data given by Prof. Mark Huber (CMC)
2020-02-10 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Data coming from Monte Carlo experiments is often analyzed in the same way as data from more traditional sources. The unique nature of Monte Carlo data, where it is easy to take a random number of samples, allows for estimators where the user can control the relative error of the estimate much more precisely than with classical approaches. In this talk I will discuss three such estimators useful in different problems. The first is a user-specified-relative-error (USRE) estimate for the mean of a Bernoulli random variable. This allows us to obtain exact error results while using slightly fewer samples than the CLT approximation. The second is more general, applying to any random variable where a bound on the relative error is known. For this problem we give exact error bounds using a number of samples that is the same (to first order) as the CLT approximation requires. In other words, the new algorithm is the equivalent of always actually having normal data. Finally, we look at the problem of data with unknown variance and develop an algorithm that runs very close to the minimum number of samples established by results of Wald.

Quandle module quivers (Sam Nelson, CMC)
2020-02-11 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
Quandle coloring quivers categorify the quandle counting invariant. In this talk we enhance the quandle coloring quiver invariant with quandle modules, generalizing both the quiver invariant and the quandle module polynomial invariant. This is joint work with Karma Istanbouli (Scripps College).

Applications of Markov Chains to Swarm Robotics and Political Redistricting
2020-02-12 16:15 - 17:15 | Freeberg Forum, LC 62, Kravis Center, CMC
What do swarm robotics and political redistricting have in common? One answer is Markov chains, which have recently been used in very different ways to address problems in both these areas. To get a large swarm to exhibit a desired behavior, one solution is to make each individual in the swarm fairly intelligent; another is to make the individuals simple, but to let the desired behavior emerge as a result of their interactions. My collaborators and I recently used Markov chains and ideas from statistical physics to develop distributed algorithms that follow this second paradigm. We also worked with physicists to create a physical robot system where each individual cannot compute anything, but the system as a whole can still accomplish complex tasks. For political redistricting, the main mathematical technique developed in the last few years for detecting gerrymandering is to compare a proposed plan to the space of all possible alternative plans; if the proposed plan is an outlier, that’s an indicator it might be gerrymandered. However, the space of all possible districting plans is far too large to ever be studied in its entirety. Instead, Markov chains are used to generate random samples of alternative plans, where the hope is that the sampled plans are reasonably representative of all possible plans. This approach has already been used successfully in court cases around the country, though questions still remain about what mathematical guarantees we can give about the randomly sampled districting plans.

Applied Math Talk: Information Theory, Archetypal Analysis and MT Flu given by Professor Emily Stone (University of Montana-Missoula)
2020-02-17 16:15 - 17:15 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
In this talk I will discuss a rather unique collection of tools and how they have been used to understand the spread of Influenza virus in the State of Montana. With flu counts from each county over a 10 year period some patterns emerge, which explain some vectors of the disease spread. Archetypal analysis then creates reduced dimension sets, and the dynamics of the flu spread can be understood by parameterizing SIR models with the reduced data.

On badly approximable numbers (Nikolai Moshchevitin, Moscow State University)
2020-02-18 12:15 - 13:10 | Emmy Noether Room, Millikan 1021, Pomona College, 610 N. College Ave., Claremont, California, 91711
It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful paper by Ngoc Ai Van Nguyen, Anthony Poels and Damien Roy (where the authors give a simple alternative solution of Schmidt-Summerer’s problem) we found an unusual generalization of this criterion for badly approximable d-dimensional vectors.
