# Past Events

## September 2018

### Applied math organizational meeting

We will have an organizational meeting for the applied math seminar today. Anyone who is interested in suggesting speakers and/or organizing applied math seminar is welcome to come.

Find out more »### Diffusion, Social Networks, and Logic (Pavel Naumov, CMC)

Once a new commercial product, technology, political opinion, or social norm is adopted by a few people, these few often put peer pressure on others to consider adopting it as well. Those who adopt next put even more pressure on the rest of the population. This cascading “epidemic” effect is often called diffusion in social networks. There are many natural questions that can be asked about diffusion. Which initial group of people should get “infected” by a new product to…

Find out more »## October 2018

### Agent-Based and Continuous Models of Locust Hopper Bands: The Role of Intermittent Motion, Alignment, Attraction and Repulsion (Andrew J. Bernoff, HMC)

Locust swarms pose a major threat to agriculture, notably in northern Africa and the Middle East. In the early stages of aggregation, locusts form hopper bands. These are coordinated groups that march in columnar structures that are often kilometers long and may contain millions of individuals. We propose a model for the formation of locust hopper bands that incorporates intermittent motion, alignment with neighbors, and social attraction, all behaviors that have been validated in experiments. Using a particle-in-cell computational method,…

Find out more »### Minimal Gaussian Partitions, Clustering Hardness and Voting (Steven Heilman, USC)

A single soap bubble has a spherical shape since it minimizes its surface area subject to a fixed enclosed volume of air. When two soap bubbles collide, they form a "double-bubble" composed of three spherical caps. The double-bubble minimizes total surface area among all sets enclosing two fixed volumes. This was proven mathematically in a landmark result by Hutchings-Morgan-Ritore-Ros and Reichardt using the calculus of variations in the early 2000s. The analogous case of three or more Euclidean sets is…

Find out more »## November 2018

### CFTP: the algorithm ERGM deserves, but not the one it needs right now (Matt Moores, University of Wollongong)

The exchange algorithm enables Bayesian posterior inference for models with intractable likelihoods, such as Ising, Potts, or exponential random graph models (ERGM). Crucially, this algorithm relies on an auxiliary Markov chain to obtain an unbiased sample from the generative distribution of the model. It was originally proposed to use coupling from the past (CFTP) for this purpose, but this requires the Markov chain to be uniformly ergodic. In the case of the Ising model, coupling time increases super-exponentially for parameter…

Find out more »### Digital sequences for frequency hopping CDMA systems (Lenny Fukshansky, CMC)

Frequency hopping is a method of transmitting signals by rapidly switching between many frequency channels, following some sequence of frequencies known to the transmitter and the receiver. This technique is used in the CDMA (code division multiple access) systems, and has many civilian and military applications. For successful transmission minimizing signal interference, we want to use sets of digital frequency sequences with minimal Hamming cross-correlation, which measures frequency overlaps with time shifts between two different sequences. We discuss a construction of a…

Find out more »### Turing mechanism for homeostatic control of synaptic density during C. elegans growth (Heather Zinn Brooks, UCLA)

It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism for Turing pattern formation that provides a possible explanation for the regular spacing of synapses along the ventral cord of C. elegans during development. The model consists of two interacting chemical species, where one is passively diffusing and the other is actively trafficked by molecular motors; we identify the former…

Find out more »### A renormalization approach to existence of the blow-up solutions of the Navier-Stokes equations (Denis Gaidashev, Uppsala University, Sweden)

The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics. Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example to existence. In this approach, existence of a blow-up solution (a solution whose energy becomes infinite in finite time) is equivalent to existence of fixed point of an appropriate operator in some functional space. We will explain a computer assited technique which can be conjecturally used to prove existence of…

Find out more »## December 2018

### A Martingale Approach to the Question of Fiscal Stimulus (Michael Imerman, CGU)

Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending is wasteful, discourages investment, and so increases unemployment. These arguments cannot both be correct, but both arguments seem meritorious. We address this economic question of…

Find out more »### Transfinite $\zeta$-metrics (Zair Ibragimov, CMC)

I will discuss the concept of transfinite ζ-metrics. In some details I will discuss transfinite Apollonian metric in the settings of semi-metric spaces. I will discuss specific examples of domains where the transfinite Apollonian metric can be computed explicitly. This is a preliminary work.

Find out more »## January 2019

### Applied Math Seminar Organizational Meeting

We will have an organizational meeting for the applied math seminar at 4:15pm in Emmy Noether Rm, Millikan 1021, Pomona on 1/28 (Monday). Anyone who in interested in suggesting speakers and/or organizing applied math seminar is welcome to come.

Find out more »## February 2019

### Estimating the physical location of Twitter users with the von Mises-Fisher distribution (Mike Izbicki, UC Riverside)

Approximately 500 million tweets are sent everyday. Scientists monitor these tweets to predict the spread of disease, better allocate social welfare services, help first responders during natural disasters, and many other important tasks. A key step in each of these tasks is estimating the location the tweet was sent from. In this talk, I discuss how to combine machine learning and the von Mises-Fisher distribution to estimate this location. The von Mises-Fisher distribution is the spherical analog of the Gaussian distribution, and this distribution lets us exploit…

Find out more »### Community structure in networks: the effect of communities on a preferential attachment model and epidemic spreading (Emily Fischer, Cornell)

Online social networks and other networks of interest are known to exhibit community structure, where a community is defined to be a highly interconnected group of nodes with possibly shared traits or features. However, classic network models, such as the preferential attachment model, do not account for community structure. In this talk, I will present the Community-Aware Preferential Attachment Model (CAPAM), which allows the user to specify community structure via edge probabilities. I will show that CAPAM retains desirable properties…

Find out more »### Applied Math Seminar: Measurement Error Modeling using Empirical Phase Functions (Prof. Cornelis Potgieter, Southern Methodist University)

Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the instrumentation may not be properly calibrated and the reading is subject to error. When completing an online Harry Potter Sorting Hat quiz, you may accidentally click the wrong option for a specific question and find yourself in House Slytherin!. The effect of measurement error is sometimes insignificant, but there are…

Find out more »### Applied Math Seminar: Eulerian Approaches based on the Level Set Method for Visualizing Continuous Dynamical Systems (Shingyu Leung, Department of Mathematics, HKUST)

One very important concept in understanding a dynamical system is coherent structure. Such structure segments the domain into different regions with similar behavior according to a quantity. When we try to partition space-time into regions according to a Lagrangian quantity advected along with passive tracers, such class of coherent structure is called the Lagrangian coherent structures (LCSs). Among many, a simple definition of an LCS uses the finite-time Lyapunov exponent (FTLE). It measures the rate of separation between adjacent particles…

Find out more »## March 2019

### Applied Math Seminar: Fluid mechanics at the microscale (Prof. Amy Buchmann, University of San Diego)

I will present mathematical and computational methods used to model interactions between a viscous fluid and elastic structures in biological processes. For example, microfluidic devices carry very small volumes of liquid through channels and may be used to gain insight into many biological applications including drug delivery and development, but mixing and pumping at this scale is difficult. Experimental work suggests that the flagella of bacteria may be used as motors in microfluidic devices, and mathematical modeling can be used…

Find out more »### Applied Math Talk: Cluster analysis on covariance stationary ergodic processes and locally asymptotically self-similar processes (Nan Rao, CGU)

We study the problems of clustering covariance stationary ergodic processes and locally asymptotically self-similar stochastic processes, when the true number of clusters is priorly known. A new covariance-based dissimilarity measure is introduced, from which efficient consistent clustering algorithms are obtained. As examples of application, clustering fractional Brownian motions and clustering multifractional Brownian motions are respectively performed to illustrate the asymptotic consistency of the proposed algorithms.

Find out more »## April 2019

### Applied Math Talk: Repurposing FDA-approved drugs as host-oriented therapies against infectious diseases (Prof. Mikhail Martchenko, KGI)

The traditional method of treating most human diseases is to direct a therapy against targets in the host patient, whereas conventional therapies against infectious diseases are directed against the pathogen. Unfortunately, the efficacy of pathogen-oriented therapies and their ability to combat emerging threats such as genetically engineered and non-traditional pathogens and toxins have been limited by the occurrence of mutations that render pathogen targets resistant to countermeasures. Our work shows that host proteins that are exploited by pathogens (Host Proteins…

Find out more »### Models of Biological Tissue Electrostatics and Molecular Transport (Jim Sterling, KGI)

In this presentation, some fundamentals of electrostatics in biology will be discussed with focus on the fact that most biological macromolecules including nucleic acids, carbohydrates, and proteins are negatively-charged. Electroneutrality requires cations to move toward the macromolecules where they both screen and bind to the negatively-charged groups. An important class of mathematical models of species-flux and electrostatics are known as the Poisson-Nernst-Planck, or PNP equations. These are partial differential equations describing some important biophysical consequences.

Find out more »### Applied Math Talk: Solving Complex Public Health Problems—Cancer, Obesity and Aging (Jessica Dehart, CGU)

Abstract: Remember smoking? What’s the new public health problem? In the US, we are currently entangled within three converging and intertwined complex problems: Cancer, Obesity, Aging. There are over 16 million cancer survivors living in the US as we speak. Over 50% of our society is overweight and/obese. Our society is aging and the age distribution is much older than a few years back. Cancer, obesity and aging share several risk factors, biological mechanisms and patterns. Given the multidimensionality and…

Find out more »### Applied Math Talk: Nonlocal problems for linear evolution equations (Prof. Smith David Andrew, Yale-NUS College, Singapore)

Linear evolution equations, such as the heat equation, are commonly studied on finite spatial domains via initial-boundary value problems. In place of the boundary conditions, we consider “multipoint conditions”, where one specifies some linear combination of the solution and its derivative evaluated at internal points of the spatial domain, and “nonlocal” specification of the integral over space of the solution against some continuous weight.

Find out more »### Applied Math Seminar: The Kaczmarz Algorithm and its Applications to Data Science (Anna Ma, UCSD)

Data is exploding at a faster rate than computer architectures can handle. For that reason, mathematical techniques to analyze large-scale data need be developed. Stochastic iterative algorithms have gained interest due to their low memory footprint and adaptability for large-scale data. In this talk, we will study the Randomized Kaczmarz algorithm for solving extremely large linear systems of the form Ax=y. In the spirit of large-scale data, this talk will proceed under the assumption that the entire data matrix A…

Find out more »## May 2019

### Applied math seminar: Topological descriptions of protein folding (Helen Wong, CMC)

Knotting in proteins was once considered exceedingly rare. However, systematic analyses of solved protein structures over the last two decades have demonstrated the existence of many deeply knotted proteins, and researchers now hypothesize that the knotting presents some functional or evolutionary advantage for those proteins. Unfortunately, there is very little known (whether experimentally, through computer simulations, or theoretically) about how proteins fold into knotted configurations. In this talk, we will discuss some of the theorized pathways from a topological point…

Find out more »## September 2019

### Frobenius problem over number fields (Lenny Fukshansky, CMC)

The classical Frobenius problem asks for the largest integer not representable as a non-negative integer linear combination of a relatively prime integer n-tuple. This problem and its various generalizations have been studied extensively in combinatorics, number theory, algebra, theoretical computer science and probability theory. In this talk, we will consider a reformulation of this problem in the context of number fields, which leads to some arithmetic questions about semigroups of algebraic integers and height functions. This is joint work with…

Find out more »### Applied Math Seminar: A hybrid inverse problem in the fluorescence ultrasound modulated optical tomography given by Yimin Zhong (UCI)

We investigate a hybrid inverse problem in fluorescence ultrasound modulated optical tomography (fUMOT) in the diffusive regime. We prove that the boundary measurement of the photon currents allows unique and stable reconstructions of the absorption coefficient of the fluorophores at the excitation frequency and the quantum efficiency coefficient simultaneously, provided that some background medium parameters are known. Reconstruction algorithms are proposed and numerically implemented as well.

Find out more »### Introduction to theory of Euclid graphs (Sin-Min Lee, SJSU)

In Euclidean geometry, the sum of two sides of any triangle is greater than the third side. We introduce this idea to labeling of graphs. A (p,q)-graph G=(V,E) is said to be in Euclid(0) if there exists a bijection f: V(G) --> {1,…,p} such that for each induced C3 subgraph with vertices {v1,v2,v3} with f(v1)<f(v2)<f(v3) we have f(v1)+f(v2)>f(v3) . For k > 1, G is in Euclid(k) class of graphs if there exits smallest k such that G U Nk in Euclid(0), where…

Find out more »### Adinkras: Snapshots of Supersymmetry (Jordan Kostiuk, Brown University)

An “Adinkra” is a graphical tool to describe a branch of particle physics known as supersymmetry. Understanding the mathematics of Adinkras shines a light on the underlying physics, as well as helps to explore new areas of mathematics. After describing the basic structure of Adinkras, I will discuss some of these interesting interactions between mathematics and physics.This talk is intended for a general mathematics audience; undergraduate students are welcome.

Find out more »## October 2019

### Combinatorics and representation theory of Temperley-Lieb algebras (Zajj Daugherty, CUNY)

The classical, one-boundary, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as "diagram algebras", meaning that they have basis elements depicted as certain kinds of graphs, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk, we will explore these algebras and their representation theory, as well as their relationship to other important diagram algebras in combinatorial representation theory.

Find out more »### Regime transitions of liquid films flowing down a fiber (Applied Math Talk given by Prof. Claudia Falcon, UCLA)

Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. Determining the regime transitions from absolute (Rayleigh- Plateau) instability is useful in the design of heat and mass exchangers for applications that include cooling systems and desalination. We present a detailed analysis using a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and a film stabilization term. This study brings to focus…

Find out more »### Applied Math Seminar: Mathematical model of Hematopoietic cell differentiation from single-cell gene sequencing data (Prof. Heyrim Cho ,UCR)

Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk, I will discuss different approaches to develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data, dimension reduction techniques are applied to find the trajectories of cell states in the reduced differentiation space. Then, we develop PDE models that describe the cell differentiation as directed and random movement on the abstracted graph or…

Find out more »### Matroids: a unified theory of independence (Mauricio Gomez Lopez, University of Oregon)

In this talk, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions of this theory, I will discuss several examples of matroids and explain some connections with optimization. Also, in this talk, I will introduce matroid polytopes, which provide a geometric framework for studying matroids. If time permits, I will discuss some new proofs to known results that I developed with one…

Find out more »### Applied Math Talk: A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1 given by Zhengji Guo (CGU)

We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with $\beta=1$) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the…

Find out more »### Sporadic points on modular curves (Ozlem Ejder, Colorado State University)

A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure. In particular, $X_1(n)$ classifies the elliptic curves with a point of order of $n$. Motivated by…

Find out more »### Faster point counting for curves over prime power rings (Maurice Rojas, Texas A&M)

Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings, e.g., the integers modulo a prime power. However, the theory behind the latter kind of point counting began more recently and there are numerous gaps in our algorithmic knowledge. We give a simple combinatorial construction that reduces point counting over prime power point…

Find out more »## November 2019

### Markov Chains and Emergent Behavior in Programmable Matter given by Prof. Sarah Canon (CMC)

Markov chains are widely used throughout mathematics, statistics, and the sciences, often for modelling purposes or for generating random samples. In this talk I’ll discuss a different, more recent application of Markov chains, to developing distributed algorithms for programmable matter systems. Programmable matter is a material or substance that has the ability to change its features in a programmable, distributed way; examples are diverse and include robot swarms and smart materials. We study an abstraction of programmable matter where particles…

Find out more »### Differential spectra of power permutations (Daniel Katz, CSUN)

If $F$ is a finite field and $d$ is a positive integer relatively prime to $|F^\times|$, then the power map $x \mapsto x^d$ is a permutation of $F$, and so is called a power permutation of $F$. For any function $f: F \to F$, and $a, b \in F$, we define the differential multiplicity of $f$ with respect to $a$ and $b$, written $\delta_f(a,b)$, to be the number of pairs $(x,y) \in F^2$ with $x-y=a$ and $f(x)-f(y)=b$. We usually insist that $a\not=0$, since it is immediate that…

Find out more »### Applied Math Talk: Stochastic similarity matrices and data clustering given by Prof. Denis Gaidashev (Uppsala University)

Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices, and an algorithm in which a collection of image elements is treated as a dynamical system. Efficient clustering in this framework is achieved if the dynamical system admits a spectral gap. We expand upon recent results in spectral analysis for Gaussian mixture distributions, and in particular, provide conditions for the existence of a spectral gap between…

Find out more »### Counting stuff with quantum Airy structures (Vincent Bouchard, University of Alberta)

Mathematicians like to count things. Often in very complicated and fancy ways. In this talk I will explain how we can use quantum Airy structures -- an abstract formalism recently proposed by Kontsevich and Soibelman, underlying the Eynard-Orantin topological recursion -- to count various interesting geometric structures. Quantum Airy structures can be seen as a wide generalization of the famous Witten conjecture, connecting enumerative geometry, integrable systems, representation theory and mathematical physics. It is a great example of "physical mathematics"…

Find out more »### Recent developments biquandle brackets (Sam Nelson, CMC)

We review some recent developments in the study of biquandle brackets and other quantum enhancements.

Find out more »### Applied Math Talk: Patterns deformed by spatial inhomogeneity give by Prof. Jasper Weinburd (HMC)

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…

Find out more »### Exponential domination in grids (Michael Young, Iowa State University)

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…

Find out more »## December 2019

### ANTC Seminar: Random Monomial Ideals (Lily Silverstein, CalPoly Pomona)

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…

Find out more »### Applied Math Seminar On Unlimited Sampling given by Prof. Felix Krahmer (Technische Universität München)

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…

Find out more »### ANTC Seminar: Random Monomial Ideals (Lily Silverstein, CalPoly Pomona)

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…

Find out more »### Applied Math Talk: Set your parasites low (or high) given by Professor Maryann Hohn (Pomona College)

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…

Find out more »### Computational bounds for doing harmonic analysis on permutation modules of finite groups (Mike Orrison, HMC)

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…

Find out more »## January 2020

### Dragging the roots of a polynomial to the unit circle (Sinai Robins, University of Sao Paulo)

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…

Find out more »### Applied Math Talk: Statistical Mechanics of Molecular Evolution and its Role in the SELEX Protocol given by Prof. Bhaven Mistry (CMC)

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…

Find out more »### Castelnuovo-Mumford regularity of edge ideals of graphs (Siamak Yassemi, University of Tehran)

Let K be a field and S = K 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…

Find out more »## February 2020

### Covering point-sets with parallel hyperplanes and sparse signal recovery (Lenny Fukshansky, CMC)

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…

Find out more »### Applied Math Talk: Robust Estimators for Monte Carlo data given by Prof. Mark Huber (CMC)

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…

Find out more »### Quandle module quivers (Sam Nelson, CMC)

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).

Find out more »### Applied Math Talk: Information Theory, Archetypal Analysis and MT Flu given by Professor Emily Stone (University of Montana-Missoula)

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.

Find out more »### On badly approximable numbers (Nikolai Moshchevitin, Moscow State University)

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.

Find out more »## March 2020

### Applied Math Talk: Approaches to modeling dispersal and swarm behavior at multiple scales given by Prof. Christopher Strickland ( The University of Tennessee, Knoxville)

Biological invasions often have outsized consequences for the invaded ecosystem and represent an interesting challenge to model mathematically. Landscape heterogeneity, non-local or time-dependent spreading mechanisms, coarse data, and air or water flow transport are but a few of the complications that can greatly affect our understanding of small organism movement – a critical component of both invasion success and the ability of native organisms to persist at a location. In this talk, I will look at dispersal and swarm behavior…

Find out more »### Graph coloring reconfiguration systems (Prateek Bhakta, University of Richmond)

For k >= 2, the k-coloring graph C(G) of a base graph G has a vertex set consisting of the proper k-colorings of G with edges connecting two vertices corresponding to two different colorings of G if those two colorings differ in the color assigned to a single vertex of G. A base graph whose k-coloring graph is connected is called k-mixing; here it is possible to reconfigure a particular k-coloring of G to any other k-coloring of G by…

Find out more »### (Cancelled!!) Applied Math Talk: Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems given by Prof. Paul Carter (University of Minnesota)

In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms representing the downhill flow of water. We focus on one such model in the 'large-advection' limit, and we prove the existence of traveling planar stripe…

Find out more »### Finding bases of new infinite dimensional representations of $\mathfrak{osp}(1|2n)$ ( Dwight Williams, UT Arlington)

The orthosymplectic Lie superalgebra $\mathfrak{osp}(1|2n)$ is rich in representation theory: while the finite dimensional $\mathfrak{osp}(1|2n)$-module category is semisimple, the study of infinite dimensional representations of $\mathfrak{osp}(1|2n)$ is wide open. In this talk, we will define the orthosymplectic Lie superalgebras, realize $\mathfrak{osp}(1|2n)$ as differential operators on complex polynomials, and describe the space of polynomials in commuting and anti-commuting variables as a representation space for $\mathfrak{osp}(1|2n)$. Moreover, we will present operators---and perhaps generalized versions of these operators---which help give explicit bases for…

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