BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:https://colleges.claremont.edu/ccms X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/Los_Angeles BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20200308T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20201101T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20210314T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20211107T090000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0800 TZOFFSETTO:-0700 TZNAME:PDT DTSTART:20220313T100000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0700 TZOFFSETTO:-0800 TZNAME:PST DTSTART:20221106T090000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210208T150000 DTEND;TZID=America/Los_Angeles:20210208T160000 DTSTAMP:20260405T111904 CREATED:20210126T021149Z LAST-MODIFIED:20210201T225414Z UID:2147-1612796400-1612800000@colleges.claremont.edu SUMMARY:Applied Math. Talk: Complex Fluids in the Immersed Boundary Method: From Viscoelasticity to Blood Clots by Aaron Barrett\, Department of Mathematics\, University of Utah DESCRIPTION:The immersed boundary method was first developed in the 1970s to model the motion of heart valves and has since been utilized to study many different biological systems. While the IB method has seen countless modifications and advancements from the perspective of fluid-structure interaction\, the use of a Newtonian fluid model remains a fundamental component of many implementations. However\, many biological fluids exhibit non-Newtonian responses to stresses\, and as such\, a Newtonian fluid model falls short to fully describe the system. In this talk\, we will discuss models of two different systems: polymeric fluids and blood clotting\, and we will address the numerical challenges associated with each system. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-aaron-barrett-department-of-mathematics-university-of-utah/ LOCATION:CA CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210210T161500 DTEND;TZID=America/Los_Angeles:20210210T171500 DTSTAMP:20260405T111904 CREATED:20210116T020409Z LAST-MODIFIED:20210116T020409Z UID:2136-1612973700-1612977300@colleges.claremont.edu SUMMARY:Prof. Henry Schellhorn DESCRIPTION:Title: No-arbitrage pricing in a market for position on a multilane freeway\, with an application to lane changing \nAbstract: We introduce a trading mechanism allowing cars to change position in a multilane congested freeway by doing peer-to-peer transactions. For the car initiating the operation\, or incoming car\, the goal can be to increase speed\, to have less speed variability\, to join a platoon\, or to join an exit lane that is slower but full. We focus in this paper on the maneuver where the incoming car changes lanes by asking an adjacent car on a busy target lane (to the left or right) to slow down\, but we also consider the case where the incoming car asks the car in front of it to change lanes\, so that the incoming car takes its position but stays on the same lane. In both cases\, the incoming car pays a transaction fee.\nWe solve the microscopic problem of determining these transaction fees by (i) embedding the problem in a macroscopic model and (ii) determining lane prices by the no arbitrage condition. This no-arbitrage condition states that no future trajectory will always be better than all others in terms of both speed and money exchanged to change lanes. The terms “always better” has to be understood in a probabilistic sense: we analyze a stochastic model\, in order to include uncertainty in both the speed model and the driver decision. We highlight the advantages of no-arbitrage theory over a traditional expected utility maximization approach. First\, no-arbitrage pricing does not require any individual data\, whether on the driver’s risk-aversion\, preference of speed over money or increased safety\, or final destination. Second\, the macroscopic model that we use considers endogeneously the global impact of any individual priced transaction\, as opposed to local models that require extraneous assumptions on the road conditions after the transaction.\nWe implemented a simple case of our lane change model. After simulating it extensively\, we implemented it in real-time\, with 2 cars trading position on a freeway using macroscopic speed information to determine the transaction fee. \nProf. Schellhorn is Professor of Mathematics and Academic Director of the Financial Engineering Program at Claremont Graduate University. URL:https://colleges.claremont.edu/ccms/event/prof-henry-schellhorn/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210215T150000 DTEND;TZID=America/Los_Angeles:20210215T160000 DTSTAMP:20260405T111904 CREATED:20210114T013414Z LAST-MODIFIED:20210127T210557Z UID:2120-1613401200-1613404800@colleges.claremont.edu SUMMARY:Applied Math. Talk: Modeling and Simulation of Ultrasound-mediated Drug Delivery to the Brain by Peter Hinow\, University of Wisconsin\, Milwaukee DESCRIPTION:We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound. Thereupon\, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier. We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the blood plasma and at the blood-brain barrier. We apply this model to the delivery of L-dopa\, (used to treat Parkinson’s disease) and doxorubicin (an anticancer agent). The goal is to optimize the delivery of drug while at the same time minimizing possible side effects of the ultrasound. In a second project\, we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-peter-hinow-university-of-wisconsin-milwaukee/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210217T161500 DTEND;TZID=America/Los_Angeles:20210217T171500 DTSTAMP:20260405T111904 CREATED:20210116T021143Z LAST-MODIFIED:20210204T000155Z UID:2140-1613578500-1613582100@colleges.claremont.edu SUMMARY:Dr. Homan Igehy DESCRIPTION:Title: Quantitative Investment and Modern Portfolio Theory \nAbstract:\nInvestment strategies come in many flavors. Quantitative strategies incorporate or fully direct investment based on mathematical models. One of the cornerstones of investment is portfolio management\, and modern portfolio theory can serve as a basis for quantitative portfolio management. In this talk\, we will discuss quantitative investing and how modern portfolio theory can be incorporated into it. We’ll take an intuitive approach toward understanding modern portfolio theory and discuss how it can (at times\, spectacularly) go wrong. \nHoman Igehy is a managing director of D. E. Shaw & Co.\, L.P. and a member of the D. E. Shaw group’s Systematic Futures trading unit. In that capacity\, Dr. Igehy contributes to the research and development of forecast models and the technical infrastructure supporting the unit’s research efforts. He joined the D. E. Shaw group in 2003. Dr. Igehy received a B.S. and Ph.D.\, each in computer science\, from Stanford University. URL:https://colleges.claremont.edu/ccms/event/dr-homan-igehy/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210222T150000 DTEND;TZID=America/Los_Angeles:20210222T160000 DTSTAMP:20260405T111904 CREATED:20210112T175752Z LAST-MODIFIED:20210213T053831Z UID:2102-1614006000-1614009600@colleges.claremont.edu SUMMARY:Applied math. talk: Heatmap centrality: a new measure to identify super-spreader nodes in scale-free networks by Christina Duron\, the University of Arizona DESCRIPTION:Abstract: The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the “shortest path” between two nodes\, this talk will explore the properties of the recently proposed measure\, the heatmap centrality\, by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free\, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the new “shortest path” based measure with regards to its CPU run time and ranking of influential nodes. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-heatmap-centrality-a-new-measure-to-identify-super-spreader-nodes-in-scale-free-networks-by-christina-duron-the-university-of-arizona/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210224T161500 DTEND;TZID=America/Los_Angeles:20210224T173000 DTSTAMP:20260405T111904 CREATED:20210116T021257Z LAST-MODIFIED:20210209T220719Z UID:2142-1614183300-1614187800@colleges.claremont.edu SUMMARY:Prof. Lori Ziegelmeier DESCRIPTION:Title: Using Topology to Measure Shape in Data \nAbstract: Data of various kinds is being collected at an enormous rate\, and in many different forms. Often\, the data are equipped with a notion of distance that reflects similarity in some sense. Using this similarity measure\, certain topological features–e.g. the number of connected components\, loops\, and trapped volumes–can be ascertained and can provide insight into the structure of these complex data sets. In this talk\, I will introduce topology and a fundamental tool of topological data analysis\, persistent homology. Then\, we will see how these tools can be used for clustering\, with machine learning\, and to explain features in data. In particular\, we will discuss (1) using persistence to explore the relationship between country development and geography\, (2) vectorizing persistence information via a persistence image to analyze the discrete dynamical system of the linked twist map\, and (3) explore notions of minimal generators to extract geometric meaning from homological features. \nDr. Ziegelmeier is an Associate Professor at Macalester College. URL:https://colleges.claremont.edu/ccms/event/prof-lori-ziegelmeier/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210301T150000 DTEND;TZID=America/Los_Angeles:20210301T160000 DTSTAMP:20260405T111904 CREATED:20210112T180006Z LAST-MODIFIED:20210210T190755Z UID:2104-1614610800-1614614400@colleges.claremont.edu SUMMARY:Applied math. talk: Blowup rate estimates of a singular potential in the Landau-de Gennes theory for liquid crystals by Xiang Xu\, Old Dominion University. DESCRIPTION:Abstract: The Landau-de Gennes theory is a type of continuum theory that\ndescribes nematic liquid crystal configurations in the framework of the\nQ-tensor order parameter. In the free energy\, there is a singular bulk\npotential which is considered as a natural enforcement of a physical\nconstraint on the eigenvalues of symmetric\, traceless Q-tensors. In this\ntalk we shall discuss some analytic properties related to this singular\npotential. More specifically\, we provide precise estimates of both this\nsingular potential\nand its gradient as the Q-tensor approaches its physical boundary. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-xiang-xu-old-dominion-university/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210303T161500 DTEND;TZID=America/Los_Angeles:20210303T173000 DTSTAMP:20260405T111904 CREATED:20210204T003334Z LAST-MODIFIED:20210221T214207Z UID:2166-1614788100-1614792600@colleges.claremont.edu SUMMARY:Ioana Dumitriu DESCRIPTION:Title: Spectral gap in random regular graphs and hypergraphs \nAbstract: Random graphs and hypergraphs have been used for decades to model large-scale networks\, from biological\, to electrical\, and to social. Various random graphs (and their not-so-random properties) have been connected to algorithms solving problems from community detection to matrix completion\, coding theory\, and various other statistics / machine learning fundamental questions; in the past decade\, this research area has expanded to include random hypergraphs. One of these special properties is the spectral gap for graph-associated matrices; roughly speaking\, it means that the main eigenvalue(s) are well-separated from the bulk and it guarantees strong connectivity properties. This talk will take a look at the spectra of adjacency / Laplacian matrices for some random regular models\, explain how we know that the spectral gap is there\, and connect spectral properties to the aforementioned applications. It will cover joint work with Gerandy Brito\, Kameron Decker Harris\, and Yizhe Zhu. \nIoana Dumitriu is a Professor of Mathematics at The University of California\, San Diego. URL:https://colleges.claremont.edu/ccms/event/ioana-dumitru/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210308T150000 DTEND;TZID=America/Los_Angeles:20210308T160000 DTSTAMP:20260405T111904 CREATED:20210112T180325Z LAST-MODIFIED:20210223T174630Z UID:2106-1615215600-1615219200@colleges.claremont.edu SUMMARY:Applied math. talk: Optimal control of the SIR model in the presence of transmission and treatment uncertainty by Henry Schellhorn\, CGU DESCRIPTION:Abstract \nThe COVID-19 pandemic illustrates the importance of treatment-related decision making in populations. This article considers the case where the transmission rate of the disease as well as the efficiency of treatments is subject to uncertainty. We consider two different regimes\, or submodels\, of the stochastic SIR model\, where the population consists of three groups: susceptible\, infected and recovered. In the first regime the proportion of infected is very low\, and the proportion of susceptible is very close to 100%.  This corresponds to a disease with few deaths and where recovered individuals do not acquire immunity. In a second regime\, the proportion of infected is moderate\, but not negligible. We show that the first regime corresponds almost exactly to a well-known problem in finance\, the problem of portfolio and consumption decisions under mean-reverting returns (Wachter\, JFQA 2002)\, for which the optimal control has an analytical solution. We develop a perturbative solution for the second problem. To our knowledge\, this paper represents one of the first attempts to develop analytical/perturbative solutions\, as opposed to numerical solutions to stochastic SIR models. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-optimal-control-of-the-sir-model-in-the-presence-of-transmission-and-treatment-uncertainty-by-henry-schellhorn-cgu/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210315T150000 DTEND;TZID=America/Los_Angeles:20210315T160000 DTSTAMP:20260405T111904 CREATED:20210114T012637Z LAST-MODIFIED:20210114T012637Z UID:2118-1615820400-1615824000@colleges.claremont.edu SUMMARY:Applied Math. Talk: by a guest University of UTAH DESCRIPTION:TBA URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-a-guest-university-of-utah/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210317T161500 DTEND;TZID=America/Los_Angeles:20210317T173000 DTSTAMP:20260405T111904 CREATED:20210204T003526Z LAST-MODIFIED:20210312T000508Z UID:2168-1615997700-1616002200@colleges.claremont.edu SUMMARY:Finding soap films in non-Euclidean geometry (Prof. David Bachman) DESCRIPTION:Title: Finding soap films in non-Euclidean geometry \nAbstract: In many computer graphics applications we approximate a smooth surface with one made up of tiny triangles. A common problem is to determine which way to move the vertices (the corners of the triangles)\, so that the total surface area decreases. If the boundary of the surface remains fixed\, this allows us to find the soap film surface spanned by that boundary curve. In Euclidean geometry this leads to the famous “cotan-Laplace formula.” After reviewing this formula we will introduce spherical and hyperbolic space\, and discuss a solution to the same problem in those geometries. \nDr. Bachman is Professor of Mathematics at Pitzer College and Director of the Claremont Center for the Mathematical Sciences. URL:https://colleges.claremont.edu/ccms/event/david-bachman/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210322T150000 DTEND;TZID=America/Los_Angeles:20210322T160000 DTSTAMP:20260405T111904 CREATED:20210112T180523Z LAST-MODIFIED:20210317T211201Z UID:2108-1616425200-1616428800@colleges.claremont.edu SUMMARY:Applied math. talk: Periodic travelling waves in nonlinear wave equations: modulation instability and rogue waves by Dmitry Pelinovsky\, McMaster University\, Canada DESCRIPTION:Abstract:     I will overview the following different wave phenomena in\nintegrable nonlinear wave equations: \n(1) universal patterns in the dynamics of fluxon condensates in the\nsemi-classical limit;\n(2) modulational instability of periodic travelling waves;\n(3) rogue waves on the background of periodic and double-periodic waves. \nMain examples include the sine-Gordon equation\, the nonlinear\nSchroedinger equation\, and the derivative nonlinear Schroedinger\nequation. For the latter equation\, in collaboration with Jinbing Chen\n(South East University\, China) and Jeremy Upsal (University of\nWashington\, USA)\, we adapted the method of nonlinearization of the Lax\nsystem in order to characterize the existence and modulation stability\nof periodic travelling waves. We give precise information on the\nlocation of Lax and stability spectra\, with assistance of numerical\npackage based on the so-called Hill’s method. Particularly interesting\noutcome is the explicit relation between the onset of modulation\ninstability and the existence of a rogue wave (localized solution in\nspace and time) on the background of periodic travelling waves. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-periodic-travelling-waves-in-nonlinear-wave-equations-modulation-instability-and-rogue-waves-by-dmitry-pelinovsky-mcmaster-university-canada/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210324T161500 DTEND;TZID=America/Los_Angeles:20210324T173000 DTSTAMP:20260405T111904 CREATED:20210204T004055Z LAST-MODIFIED:20210312T000436Z UID:2170-1616602500-1616607000@colleges.claremont.edu SUMMARY:Our muscles aren't one-dimensional fibres (Prof. Nilima Nigam) DESCRIPTION:Title: Our muscles aren’t one-dimensional fibres. \nAbstract: Skeletal muscles possess rather amazing mechanical properties. They possess an intricate structure\, and behave nonlinearly in response to mechanical stresses. In the 1910s\, A.V. Hill observed muscles heat when they contract\, but not when they relax. Based on experiments on frogs he posited a mathematical description of skeletal muscles which approximated muscle as a 1-dimensional nonlinear and massless spring. This has been a remarkably successful model\, and remains in wide use. Recently\, we’ve realized that skeletal muscle is three dimensional\, has mass\, and fairly complicated structure. I’ll present some work on a mathematical model which captures some of this complexity. \nDr. Nilima Nigam is Professor at Simon Fraser University. URL:https://colleges.claremont.edu/ccms/event/nilima-nigam/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210329T150000 DTEND;TZID=America/Los_Angeles:20210329T160000 DTSTAMP:20260405T111904 CREATED:20210113T011843Z LAST-MODIFIED:20210325T164523Z UID:2115-1617030000-1617033600@colleges.claremont.edu SUMMARY:Applied math. talk: Hyperbolicity-Preserving Stochastic Galerkin Method for Shallow Water Equations by Dihan Dai\, Department of Mathematics\, University of Utah DESCRIPTION:Abstract: The system of shallow water equations and related models are\nwidely used in oceanography to model hazardous phenomena such as tsunamis\nand storm surges. Unfortunately\, the inherent uncertainties in the system\nwill inevitably damage the credibility of decision-making based on the\ndeterministic model. The stochastic Galerkin (SG) method seeks a solution\nby applying the Galerkin method to the stochastic domain of the equations\nwith uncertainty. However\, the resulting system may fail to preserve the\nhyperbolicity of the original model. In this talk\, we will discuss a\nstrategy to preserve the hyperbolicity of the stochastic systems. We will\nalso discuss a well-balanced hyperbolicity-preserving central-upwind\nscheme for the random shallow water equations and illustrate the\neffectiveness of our schemes on some challenging numerical tests. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-dihan-dai-department-of-mathematics-university-of-utah/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210331T161500 DTEND;TZID=America/Los_Angeles:20210331T173000 DTSTAMP:20260405T111904 CREATED:20210204T004224Z LAST-MODIFIED:20210312T000546Z UID:2172-1617207300-1617211800@colleges.claremont.edu SUMMARY:An ideal convergence: an example in noncommutative metric geometry (Prof. Konrad Aguilar) DESCRIPTION:Title: An ideal convergence: an example in noncommutative metric geometry \nAbstract: \nThe ability to calculate the distance between sets (rather than just distance between points) has found applications in geometry and group theory as well as various branches of applied mathematics. The Hausdorff distance and the Gromov-Hausdorff distance are standard distances used in these applications. Moreover\, a certain generalization of the Gromov-Hausdorff distance called the quantum Gromov-Hausdorff distance was built by M. A. Rieffel to answer some questions from physics about operator algebras\, which are generalizations of algebras of complex-valued square matrices. In another direction\, J.M.G. Fell introduced a notion of convergence of ideals of a given operator algebra. Can the quantum Gromov-Hausdorff distance also be used to establish convergence of the associated quotient algebras? We discuss this for certain operator algebras called approximately finite-dimensional (AF) C*-algebras\, which can be represented by infinite graphs called Bratteli diagrams where the ideals and quotients are represented by subgraphs. It is the movement of the quotient graphs with respect to the ideal graphs that motivates our question and its answer. The main example we discuss will be given by graph representations of irrational numbers built by their associated continued fractions. (This talk contains joint work with Samantha Brooker\, Frédéric Latrémolière\, and Alejandra López). \nProfessor Konrad Aguilar is Assistant Professor at Pomona College. URL:https://colleges.claremont.edu/ccms/event/konrad-aguilar/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210407T161500 DTEND;TZID=America/Los_Angeles:20210407T173000 DTSTAMP:20260405T111904 CREATED:20210204T004426Z LAST-MODIFIED:20210324T171332Z UID:2174-1617812100-1617816600@colleges.claremont.edu SUMMARY:Alexandria Volkening DESCRIPTION:Title:\nHow do zebrafish get their stripes — or spots? \nAbstract:\nMany natural and social systems involve individual agents coming together to create group dynamics\, whether the agents are drivers in a traffic jam\, voters in an election\, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology\, though\, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in fish. Because they are surprisingly similar to humans genetically\, we will investigate zebrafish\, which are named for their dark and light stripes. Mutant zebrafish\, on the other hand\, feature variable skin patterns\, including spots and labyrinth curves. All these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. This leads to the question: how do mutations change cell behavior to create spotted zebrafish? In this talk\, we will combine different modeling approaches (including agent-based and continuum) and topological data analysis to help shed light on this question. More broadly\, we will explore how a combination of biological and mathematical approaches are being used to better understand how genes\, cell behavior\, and visible animal characteristics are related in fish. \nDr. Volkening is an NSF-Simons Fellow at the NSF-Simons Center for Quantitative Biology at Northwestern University URL:https://colleges.claremont.edu/ccms/event/alexandria-volkening/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210412T150000 DTEND;TZID=America/Los_Angeles:20210412T160000 DTSTAMP:20260405T111904 CREATED:20210112T180713Z LAST-MODIFIED:20210406T193121Z UID:2110-1618239600-1618243200@colleges.claremont.edu SUMMARY:Applied math. talk: Large Eddy Simulation Reduced Order Models by Traian Iliescu\, Virginia Tech DESCRIPTION:In this talk\, we present reduced order models (ROMs) for turbulent flows\,\nwhich are constructed by using ideas from large eddy simulation (LES) and\nvariational multiscale (VMS) methods.  First\, we give a\ngeneral introduction to reduced order modeling and emphasize the\nconnection to classical Galerkin methods (e.g.\, the finite element method)\nand the central role played by data.  Then\, we describe the closure\nproblem\, which represents one of the main obstacles in the development of\nROMs for realistic\, turbulent flows.  To tackle the ROM closure problem\,\nwe use ROM spatial filters (e.g.\, the ROM projection and the ROM\ndifferential filter) and build new LES-ROMs that capture the large scale\nROM features and model the interaction between these large scales and the\nsmall scale ROM features. Finally\, we present results for these LES-ROMs\nin the numerical simulation of\nunder-resolved engineering flows (e.g.\, flow past a cylinder and\nturbulent channel flow) and the quasi-geostrophic equations (which model\nthe large scale ocean circulation). URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-traian-iliescu-virginia-tech/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210414T161500 DTEND;TZID=America/Los_Angeles:20210414T173000 DTSTAMP:20260405T111904 CREATED:20210204T004536Z LAST-MODIFIED:20210326T180738Z UID:2176-1618416900-1618421400@colleges.claremont.edu SUMMARY:Jennifer Taback DESCRIPTION:Title: Groups\, Graphs and Trees \nAbstract: What do we mean by the geometry of a group? Groups seem like very abstract objects when we first study them\, and it’s natural to ask whether we can visualize them in some way. Given a group with a finite set of generators and relators\, I will describe a canonical way to construct a geometric model of that group\, called a Cayley graph. We will see many examples — both standard and unusual — and I will discuss some fundamental questions from the field of geometric group theory\, including whether this geometric model is well defined. One goal of this field of mathematics is to use the geometry of a group to provide insight into its algebraic structure\, and to use the algebraic properties of a group to draw conclusions about its geometry. This will be a very visual talk\, involving many examples of groups\, graphs\, and trees. \nDr. Jennifer Taback is Isaac Henry Wing Professor and Chair of the Mathematics Department at Bowdoin College. URL:https://colleges.claremont.edu/ccms/event/jennifer-taback/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210419T150000 DTEND;TZID=America/Los_Angeles:20210419T160000 DTSTAMP:20260405T111904 CREATED:20210112T180844Z LAST-MODIFIED:20210417T022158Z UID:2112-1618844400-1618848000@colleges.claremont.edu SUMMARY:Applied math. talk: Adversarially robust classification via geometric flows\, by Ryan Murray\, North Caroline State University DESCRIPTION:Abstract: Classification is a fundamental task in data science and machine learning\, and in the past ten years there have been significant improvements on classification tasks (e.g. via deep learning). However\, recently there have been a number of works demonstrating that these improved algorithms can be “fooled” using specially constructed adversarial examples. In turn\, there has been increased attention given to creating machine learning algorithms which are more robust against adversarial attacks. In this talk I will describe a recently proposed framework for optimal adversarial robustness which is related to optimal transportation. I will then discuss some recent work\, with Nicolas Garcia Trillos\, which characterizes solutions of the optimal adversarial robust classification problem by using a geometric evolution equation. Surprisingly\, this geometric evolution equation asymptotically takes the form of a weighted mean curvature flow\, which suggests new analytical and computational approaches to the problem. I will also discuss a number of related open questions. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-ryan-murray-north-caroline-state-university/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210421T161500 DTEND;TZID=America/Los_Angeles:20210421T173000 DTSTAMP:20260405T111904 CREATED:20210204T004641Z LAST-MODIFIED:20210418T004801Z UID:2178-1619021700-1619026200@colleges.claremont.edu SUMMARY:Haydee Lindo DESCRIPTION:Title: Trace Ideals and Endomorphism Rings \nAbstract: In many branches of mathematics\, the full set of “functions” between two objects exhibits remarkable structure; it often forms a group and in some special cases it forms a ring. In this talk\, we will discuss this phenomenon in Commutative Algebra. In particular\, we will talk about the endomorphism ring formed by the homomorphisms from a module to itself by first looking at commuting square matrices. I’ll also introduce the trace ideal and explain its role in the question “What properties of a module does its endomorphism ring detect?” \nDr. Lindo is Assistant Professor at Harvey Mudd College. URL:https://colleges.claremont.edu/ccms/event/haydee-lindo/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210426T150000 DTEND;TZID=America/Los_Angeles:20210426T160000 DTSTAMP:20260405T111904 CREATED:20210128T180721Z LAST-MODIFIED:20210426T165641Z UID:2155-1619449200-1619452800@colleges.claremont.edu SUMMARY:Applied Math. Talk: Balancing Geometry and Density: Path Distances on High-Dimensional Data by Anna Little\, University of Utah DESCRIPTION: Abstract: This talk discusses multiple methods for clustering\nhigh-dimensional data\, and explores the delicate balance between utilizing\ndata density and data geometry. I will first present path-based spectral\nclustering\, a novel approach which combines a density-based metric with\ngraph-based clustering. This density-based path metric allows for fast\nalgorithms and strong theoretical guarantees when clusters concentrate\naround low-dimensional sets. However\, the method suffers from a loss of\ngeometric information\, information which is preserved by simple linear\ndimension reduction methods such as classic multidimensional scaling\n(CMDS). The second part of the talk will explore when CMDS followed by a\nsimple clustering algorithm can exactly recover all cluster labels with\nhigh probability. However\, scaling conditions become increasingly\nrestrictive as the ambient dimension increases\, and the method will fail\nfor irregularly shaped clusters. Finally\, I will discuss how a more\ngeneral family of path metrics\, when combined with CMDS\, give\nlow-dimensional embeddings which respect both data density and data\ngeometry. This new method exhibits promising performance on single cell\nRNA sequence data and can be computed efficiently by restriction to a\nsparse graph. URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-by-anna-little-university-of-utah/ LOCATION:Zoom meeting\, United States CATEGORIES:Applied Math Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210428T161500 DTEND;TZID=America/Los_Angeles:20210428T173000 DTSTAMP:20260405T111904 CREATED:20210204T004751Z LAST-MODIFIED:20210406T011522Z UID:2180-1619626500-1619631000@colleges.claremont.edu SUMMARY:Jennifer Franko Vasquez DESCRIPTION:Title: Puzzling Permutations \nAbstract: Permutations are one of the most fundamental notions in mathematics. In this talk\, we will discuss a visual representation of permutations and introduce some games one can play to help “see” different properties. These puzzling games can be used to provide insight into deeper mathematical content as well. Time permitting\, we will explore connections to topology and biology. This talk is based on joint work with Steven Dougherty and Michael Allocca. \nDr. Vasquez is a Professor of Mathematics at the University of Scranton. URL:https://colleges.claremont.edu/ccms/event/jennifer-franko-vasquez/ LOCATION:Zoom CATEGORIES:Colloquium ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210831T123000 DTEND;TZID=America/Los_Angeles:20210831T132000 DTSTAMP:20260405T111904 CREATED:20210823T222615Z LAST-MODIFIED:20210829T182033Z UID:2216-1630413000-1630416000@colleges.claremont.edu SUMMARY:Representing integers by multilinear polynomials (Lenny Fukshansky\, CMC) DESCRIPTION:Given a homogeneous multilinear polynomial F(x) in n variables with integer coefficients\, we obtain some sufficient conditions for it to represent all the integers. Further\, we derive effective results\, establishing bounds on the size of a solution x to the equation F(x) = b\, where b is any integer. For a special class of polynomials coming from determinants of rectangular matrices we are able to obtain necessary and sufficient conditions for such an effective representation problem. This result naturally connects to the problem of extending a collection of primitive vectors to a basis in a lattice\, where we present counting estimates on the number of such extensions. Equivalently\, this can be described as the number of ways a rectangular integer matrix can be extended to a matrix in GL_n(Z)\, when such extensions are possible. The talk is based on joint works with A. Boettcher and with M. Forst. URL:https://colleges.claremont.edu/ccms/event/representing-integers-by-multilinear-polynomials-lenny-fukshansky-cmc/ LOCATION:On Zoom CATEGORIES:Algebra / Number Theory / Combinatorics Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210907T123000 DTEND;TZID=America/Los_Angeles:20210907T132000 DTSTAMP:20260405T111904 CREATED:20210823T221435Z LAST-MODIFIED:20210830T213551Z UID:2214-1631017800-1631020800@colleges.claremont.edu SUMMARY:Region colorings in knot theory (Sam Nelson\, CMC) DESCRIPTION:In this talk we will survey recent developments in the use of ternary algebraic structures known as Niebrzydowski Tribrackets in defining invariants of knots\, with some perhaps surprising applications. URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc/ LOCATION:On Zoom CATEGORIES:Algebra / Number Theory / Combinatorics Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210914T123000 DTEND;TZID=America/Los_Angeles:20210914T132000 DTSTAMP:20260405T111904 CREATED:20210822T191624Z LAST-MODIFIED:20210829T182323Z UID:2208-1631622600-1631625600@colleges.claremont.edu SUMMARY:On Hermite's problem\, Jacobi-Perron type algorithms\, and Dirichlet groups (Oleg Karpenkov\, Liverpool) DESCRIPTION:In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the totally-real case to the question of algebraic periodicity for cubic irrationalities posed in 1848 by Ch.Hermite. \nWe will briefly discuss a new approach which is based on geometry of numbers. In addition we point out one important application of Jacobi-Perron type algorithms to the computation of independent elements in the maximal groups of commuting matrices of algebraic irrationalities. URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pavel-guerzhoy-university-of-hawaii/ LOCATION:On Zoom CATEGORIES:Algebra / Number Theory / Combinatorics Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210915T163000 DTEND;TZID=America/Los_Angeles:20210915T174500 DTSTAMP:20260405T111904 CREATED:20210831T233907Z LAST-MODIFIED:20210907T223233Z UID:2274-1631723400-1631727900@colleges.claremont.edu SUMMARY:Topic Models\, Methods\, and Medicine (Prof. Jamie Haddock) DESCRIPTION:Title: Topic Models\, Methods\, and Medicine \nSpeaker: Prof. Jamie Haddock (Harvey Mudd College) \nAbstract: There is currently an unprecedented demand for efficient\, quantitative\, and interpretable methods to study large-scale (often multi-modal) data. One key area of interest is that of topic modeling\, which seeks to automatically learn latent trends or topics of complex data sets\, providing practitioners a view of what is “going on” inside their data. This talk will survey several new tools for topic modeling on matrix and tensor data which allow for use of various forms of supervision and which learn hierarchical structure amongst topics.  These tools are of interest across the many fields and industries producing\, capturing\, and analyzing big data\, but are of particular interest in applications where expert supervision is available and often essential (e.g.\, medicine).  We will describe two applications of these methods to medical data; an application to a large-scale patient survey database and an ongoing application to cardiovascular imaging data. \n  \nProf. Jamie Haddock is an Assistant Professor in the Mathematics Department at Harvey Mudd College URL:https://colleges.claremont.edu/ccms/event/jamie-haddock-harvey-mudd-college/ LOCATION:Zoom meeting\, United States CATEGORIES:Colloquium ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210920T161500 DTEND;TZID=America/Los_Angeles:20210920T171500 DTSTAMP:20260405T111904 CREATED:20210903T174347Z LAST-MODIFIED:20210919T211719Z UID:2290-1632154500-1632158100@colleges.claremont.edu SUMMARY:Applied Math Seminar -- Phil Chodrow (UCLA) DESCRIPTION:Title: Eigenvector Methods for Community Detection in Hypergraphs \nAbstract: \n\n\nHypergraphs are generalizations of graphs in which edges are allowed to contain arbitrary numbers of nodes. Hypergraphs are well-suited for modeling complex data sets with multi-body interactions. Familiar examples include email threads with multiple participants\, projects with multiple collaborators\, and forum posts with multiple tags. \nThe hypergraph community detection problem asks us to find groups of related or similar entities in hypergraph data. While there are many approaches to this problem\, I’ll focus on methods that rely on matrix eigenvectors. I’ll give a quick illustration of how eigenvector methods work in the graph case\, and explain the roadblocks to extending these standard methods for hypergraphs. I’ll then describe the Hashimoto operator\, a matrix that smoothly generalizes for hypergraphs. I’ll present a theorem for speeding up eigenvector calculations with this matrix\, and discuss detection algorithms that use these eigenvectors. I’ll touch on the relationship between the Hashimoto operator and belief-propagation for statistical inference\, using this relationship to obtain a performant hypergraph community detection algorithm. I’ll discuss the phase transition separating success from failure for this detection algorithm. I’ll close by posing some conjectures on the fundamental limits of community detection in hypergraphs. URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-phil-chodrow-ucla/ LOCATION:Emmy Noether Room\, Estella 1021\, Pomona College\,\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States CATEGORIES:Applied Math Seminar ORGANIZER;CN="Heather Zinn Brooks":MAILTO:hzinnbrooks@g.hmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210921T123000 DTEND;TZID=America/Los_Angeles:20210921T131000 DTSTAMP:20260405T111904 CREATED:20210831T205637Z LAST-MODIFIED:20210906T215314Z UID:2272-1632227400-1632229800@colleges.claremont.edu SUMMARY:The magic of the number three: three explanatory proofs in abstract algebra (Gizem Karaali\, Pomona) DESCRIPTION:When first learning how to write mathematical proofs\, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. Explanatory proofs\, in the sense of Steiner\, transform what might initially seem mysterious or even magical into lucid mathematics. In this talk we explore three specific statements from abstract algebra that involve the number three\, whose proofs are explanatory. This is joint work with Samuel Yih PO’18. URL:https://colleges.claremont.edu/ccms/event/antc-seminar-gizem-karaali-pomona/ LOCATION:On Zoom CATEGORIES:Algebra / Number Theory / Combinatorics Seminar END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210921T150000 DTEND;TZID=America/Los_Angeles:20210921T160000 DTSTAMP:20260405T111904 CREATED:20210914T225152Z LAST-MODIFIED:20210914T225937Z UID:2338-1632236400-1632240000@colleges.claremont.edu SUMMARY:Topology Seminar -- Sam Nelson DESCRIPTION:Sam Nelson will wow us with his maths. URL:https://colleges.claremont.edu/ccms/event/topology-seminar/ LOCATION:Zoom meeting\, United States CATEGORIES:Topology Seminar ORGANIZER;CN="Helen Wong":MAILTO:hwong@cmc.edu END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Los_Angeles:20210922T163000 DTEND;TZID=America/Los_Angeles:20210922T174500 DTSTAMP:20260405T111904 CREATED:20210817T140933Z LAST-MODIFIED:20210817T141610Z UID:2198-1632328200-1632332700@colleges.claremont.edu SUMMARY:Quantitative Approaches to Social Justice (Prof. Chad Topaz) DESCRIPTION:Title: Quantitative Approaches to Social Justice \nProf. Chad Topaz (he/him/his)\nCo-Founder and Executive Director of Research\, QSIDE Institute\nProfessor of Mathematics\, Williams College \nAbstract: Civil rights leader\, educator\, and investigative journalist Ida B. Wells said that “the way to right wrongs is to shine the light of truth upon them.” This talk will demonstrate how quantitative and computational approaches can shine a light on social injustices and help build solutions to remedy them. We will present quantitative social justice projects on topics ranging from diversity in art museums to equity in criminal sentencing to affirmative action\, health care access\, and other fields. The tools engaged include crowdsourcing\, data cleaning\, clustering\, hypothesis testing\, statistical modeling\, Markov chains\, data visualization\, and much more. I hope that this talk leaves you informed about the breadth of social justice applications that one can tackle using mathematical and data science tools in careful collaboration with other scholars and activists. \nProf. Chad Topaz (he/him/his) is the co-Founder and Executive Director of Research at the QSIDE Institute which promote the quantitative study of inclusion\, diversity\, and equity. He is also a Professor of Mathematics\, Williams College. \nThis colloquium will be virtual and a Zoom link will be distributed via the CCMS Email list. URL:https://colleges.claremont.edu/ccms/event/prof-chad-topaz/ LOCATION:Zoom meeting\, United States CATEGORIES:Colloquium ORGANIZER;CN="Andrew Bernoff":MAILTO:ajb@hmc.edu END:VEVENT END:VCALENDAR