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Lisa Fauci, Tulane University, Confined helical swimmers and coupled oscillators: two studies in elastohydrodynamics
SAS 1102Through the actuation of elastic filaments, microorganisms can move through a viscous fluid or generate a flow within a complex environment. In this talk, we will focus on simple models of two such systems. First, as a step towards understanding the chemotactic behavior of bacteria within micropores, we consider a single elastic helical flagellum confined…
NCSU’s 7th Annual Sonia Kovalevsky Day
SAS Hall LobbyAny 7th or 8th grade girl interested in math Saturday, April 7, 2018 | 10:00am – 3:00pm SAS Hall at NCSU RSVP: Space is limited! Please reserve your spot by April 2nd by emailing graduate student Katherine Harris at keharri4@ncsu.edu. Please include any dietary allergies/restrictions in your email. PDF
Pierre-Emmanuel Jabin, University of Maryland, College Park, Quantitative estimates of propagation of chaos for many-particle systems with bounded stream functions
SAS 4201We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our…
Katherine Raoux, Michigan State University, τ-invariants for knots in rational homology spheres
SAS 4201Using the knot filtration on the Heegaard Floer chain complex, Ozsváth and Szabó defined an invariant of knots in the three sphere called τ(K) and showed that it is a lower bound for the 4-ball genus. Generalizing their construction, I will show that for a (not necessarily null-homologous) knot, K, in a rational homology sphere, Y, we obtain…
Tom Witelski, Duke University, Dynamics of non-conservative fluid thin films
SAS 4201The behavior of thin layers of viscous fluids coating solid surfaces is of importance in many industrial and natural applications. Interfacial instabilities and pattern formation can occur in films on water-repellent (also called hydrophobic or partially wetting) surfaces. Lubrication models asymptotically reduce the governing equations for the free-surface flow to a fourth-order nonlinear parabolic partial differential equation for the evolution…
Chetak Hossain, NC State, Enumerative and Algebraic Combinatorics of OEIS A071356
We will talk about bijections between various families of combinatorial objects counted by OEIS A071356. These include certain underdiagonal lattice paths, pattern avoiding permutations, pattern avoiding inversion sequences, and posets. Connections will be made to combinatorial Hopf algebras using some lattice theory. OEIS A071356 is closely related to the Catalan numbers.
Sharon Lubkin, NC State, Surprises from modeling lung development
Tissues grow, change shape, and differentiate, function normally or abnormally, get diseased or injured, repair themselves, and sometimes atrophy. This complex suite of behaviors is governed by a complex suite of controls. Nonetheless, we can identify some general principles at work in the dynamics of tissues. Our goal is to understand how a tissues mechanics and biology regulate each…
Sergi Elizalde, Dartmouth College, Cyclic descents of standard Young tableaux
SAS 4201Cyclic descents of a permutation were defined by Cellini, by allowing the permutation to wrap around as if the last entry was followed by the first. A natural question is whether a similar, well-behaved notion of cyclic descents exists for standard Young tableaux (SYT). We conjectured that such a notion exists for SYT of any…
Daniel B. Szyld, Temple University, Asynchronous Optimized Schwarz Methods for the solution of PDEs
SAS 4201Asynchronous methods refer to parallel iterative procedures where each process performs its task without waiting for other processes to be completed, i.e., with whatever information it has locally available and with no synchronizations with other processes. In this talk, an asynchronous version of the optimized Schwarz method is presented for the solution of differential equations on a parallel computational environment. Convergence is…
John Harlim, Penn State University, Data-driven methods for estimating operator and parameters of dynamical systems
SAS 4201I will discuss a nonparametric modeling approach for forecasting stochastic dynamical systems on smooth manifolds embedded in Euclidean space. This approach allows one to evolve the probability distribution of non-trivial dynamical systems with an equation-free modeling. In the second part of this talk, I will discuss a nonparametric estimation of likelihood functions using data-driven basis functions and the…
Kwangil Koh Series Reception
SAS Hall LobbyAndrew Belmonte, Pennsylvania State U, Koh Lecture on Mathematics in Our Time: Games, Decisions, Evolution, and Chance
SAS 2203Humans play games. Sometimes we roll the dice, or buy lottery tickets - sometimes we play chess, or mind games of manipulation. History gives us two examples of the development of new mathematical ideas and directions from our playful habits: games of chance, which led to the formulation of Probability Theory, and games of strategy,…
Andrew Belmonte, Pennsylvania State University, Careers in Mathematics: Be Nonlinear
1911 Building Room 124Students are often given the impression that there is one way to have an academic career, the right way. Reality is much more complicated, but this can also be empowering. We will discuss such things informally, while drawing some examples from my own path: from particle physics at Fermilab and CERN to cancer research at…
Tea and Cookies
SAS 4104Andew Belmonte, Pennsylvania State U, Do Your Fair Share! Evolutionary Games and the Tragedy of the Commons
SAS 1102Public goods games involve interactions between players or organisms who produce a commonly available good (cooperators) and those who consume it without producing (cheaters, defectors, freeloaders) - several instances are known to occur in nature and economics. The solution that freeloading is a better individual choice is known as the “tragedy of the commons” -…
Ying Zhou, Brandeis University, Tame Hereditary Algebras have finitely many m-Maximal Green Sequences
SAS 4201Keller introduced the concept of maximal green sequences. Brustle-Dupont-Perotin proved that tame quivers have finitely many maximal green sequences. We have generalized the result to m-maximal green sequences. This talk will include a gentle introduction to tame path algebras, their indecomposable modules, silting objects and their mutations, the Auslander-Reiten quiver of bounded derived categories of tame path algebras and the outline…
Caprice Stanley, Suzanne Crifo, NC State
SAS 1102Speaker 1: Caprice Stanley Title: Markov Chain Mixing Time Abstract: Informally a Markov chain is a memoryless stochastic process and its mixing time is the time required for the chain to be near its stationary distribution. Depending on the context, analysis of mixing time can be of great importance. For example, random walk-based algorithms for…
Mario Ricchiuto, INRIA Bordeaux, On dispersive-like effects in channels with banks
SAS 4201The study of the propagation of undular bores in channels is relevant to many applications which go from the propagation of tsunami waves, to that of tidal bores/waves, to the propagation of strong waves in manmade channels due to hazards (e.g. dam breaking). In absence of banks, the flow exhibits a transition across which undulating waves start breaking and transform…