June 23, 2024

There are no events currently scheduled for June 23rd.

June 24, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work / Writing Time

  Group Work - Assigned Group Work Space

• 1:00 - 1:30 pm EDT

  Welcome

  11th Floor Lecture Hall
• 1:30 - 2:15 pm EDT

  From Dynamics to Algorithms for Optimization and Sampling

  11th Floor Lecture Hall

  • Speaker
  • Andre Wibisono, Yale University

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  Optimization and sampling are fundamental algorithmic tasks in machine learning and in many applications. In this talk, we will survey recent results in the design and analysis of algorithms for optimization and sampling via a continuous-time perspective, and via the perspective of sampling as optimization in the space of distributions. Many algorithms in discrete time can be derived as discretization of continuous-time dynamics; for example, gradient descent is a discretization of gradient flow, and momentum method is a discretization of accelerated gradient flow. This perspective provides a systematic way to design algorithms via discretizing continuous-time dynamics, and to derive convergence guarantees via translating the continuous-time properties. In sampling, many random walks or Markov chain methods can be viewed as optimization algorithms in the space of probability distributions; for example, the Langevin dynamics is implementing the gradient flow for minimizing relative entropy. This perspective provides a systematic way to analyze the mixing times of Markov chains via translating the optimization techniques, and to design new sampling algorithms via translating the optimization principles to the space of distributions.

  • Video Available Soon
• 2:30 - 2:45 pm EDT

  Computing Barycenters and Applications in Data Science

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Stephan Patterson, Louisiana State University in Shreveport

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  A barycenter is, informally, a weighted average of a set of probability measures. Finding barycenters is of interest in a variety of fields; however, the barycenter problem has recently been shown to be NP-hard. Barycenters can be computed using linear programming, but designing practical exact and approximate algorithms remains an active area of research. In this talk, I will describe the linear programming models that form the basis of the computations and highlight their uses in data science, such as image and natural language processing.
• 2:45 - 3:00 pm EDT

  Strong Data Processing Inequalities and Langevin Dynamics

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Siddharth Mitra, Yale University

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  The data processing inequality is a fundamental concept in information theory that states that relative entropy, mutual information, and other important quantities are non-increasing along Markov chains. Strong data processing inequalities check if these quantities are strictly decreasing, and if so, quantify the decrease. In this talk, we will review these information theoretic concepts and present a way to show strong data processing inequalities for some important Markov chains, such as the Langevin dynamics. As an application, by studying the strong data processing inequality in mutual information, we’ll be able to quantify the rate at which we get independent samples along these Markov chains.
• 3:00 - 3:15 pm EDT

  Using projected multi-reference alignment to study challenges in cryo-EM

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Tait Weicht, University of California, Davis

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  Cryogenic electron microscopy (cryo-EM) is one particular imaging technique used to determine the structure of a molecule. One goal has been to develop an algorithm based on the method of moments that can recover such structure. We will explain some of the advantages of such an approach; however, an efficient and robust algebraic algorithm that can determine multiple molecular structures from cryogenic electron micrographs remains elusive. Time permitting we, will explore a toy model, projected multi-reference alignment, developed to capture some of the fundamental challenges in developing such an algorithm. We will present a method to recursively decompose the problem into sub-problems and the larger implications for solving these types of problems.
• 3:15 - 3:30 pm EDT

  Vertex clustering in diverse dynamic networks

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Devavrat Dabke, Princeton University

  • Session Chair
  • Rustum Choksi, McGill University
• 3:30 - 3:45 pm EDT

  Multiscale perspectives on the self-assembly of bicontinuous networks from computational geometry

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Michael Dimitriyev, Texas A&M University

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  Under conditions of thermodynamic equilibrium, amphiphilic molecules often arrange into a variety of nanoscale structures, including complex "bicontinuous network" phases, consisting of pairs of intercatenated domains that can span large, well-ordered domains. Despite the complex morphologies of these network phases, they possess robust formation pathways in biological systems and synthetic versions, mainly formed from block copolymers, have attracted interest for use in emerging technologies. However, theoretical and computational efforts to understand network phases have long struggled due to the large number of molecules involved in the assembly of a single repeat unit under strong space-filling constraints. We found that the geometry of so-called "terminal boundaries" play a previously-unrecognized role in determining the stability of these phases, resolving a long-standing question about the asymptotic stability of these phases. Our approach relies on the medial axis transform of computational geometry to generate close approximations to these terminal boundaries, in the process yielding space-filling tessellations that serve as coarse-grained molecular environments that are consistent with packing constraints. The result is a multiscale picture of network phases that bridges molecular details with interface and domain geometry, pointing towards a way to relate large-scale structure and structural changes to alterations in molecular packing.
• 3:45 - 4:00 pm EDT

  The Winning Pursuit-Evasion Strategies in Dynamic Systems

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Mehdi Salimi, Kwantlen Polytechnic University

  • Session Chair
  • Rustum Choksi, McGill University

  Abstract

  This research focuses on a pursuit-evasion differential game set in a two-dimensional space, incorporating a hybrid system of dynamics. The game involves a pursuer with non-inertial characteristics and an evader with inertial properties, with both players' controls constrained integrally. The duration of the game, denoted as T, remains constant, and the evader's position at time T adheres to a phase constraint. We delineate the attainability domains for both players and devise a winning strategy for the pursuer, ensuring the capture of the evader. Additionally, we demonstrate the validity of our devised strategy.
• 4:00 - 5:00 pm EDT

  Working Groups

  Group Work - 11th Floor Collaborative Space

June 26, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break - Assigned Group Work Space
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  10th Floor Collaborative Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work/ Writing Time

  Group Work - Assigned Group Work Space

• 9:00 - 9:45 am EDT

  Discrete statistics of permutations and their generalizations

  11th Floor Lecture Hall

  • Speaker
  • Pamela E. Harris, University of Wisconsin Milwaukee

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  The study of discrete statistics has a long history and many connections to numerous areas of mathematics. In this talk, we introduce discrete statistics such as descents, ascents, peaks, and pinnacles of permutations and provide a sample of known results. We then focus on a superset of permutations called parking functions, give a summary of what is known about their discrete statistics, and provide open problems for us to explore.
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 10:45 am EDT

  Probabilistic Computing? Bet on Dice.

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • J. Darby Smith, Sandia National Laboratories

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Operations in biological brains are probabilistic and hence stochasticity has become intertwined with brain-inspired hardware, algorithms, and devices. Within this sea of stochasticity, we find a growing trend of new probabilistic computing devices for generating true random numbers. The ability to quickly and efficiently generate true random numbers at a device level suggests a future where stochastic elements are ubiquitous in computing. That same trend of new computing devices is focused largely on binary or two-state devices, i.e. coin flips. However, we find that there are inherent benefits to multi-state random draws, i.e. dice rolls. In this talk, we will revisit classic distribution results for distributions induced by Bernoulli random variables and extend them to the multi-state dice roll case, providing a proof of a ‘folk theorem.’ We analyze the benefits of dice compared to coins through simulation of a sampling neural network. Additionally, we showcase benefits from a real two-state stochastic tunnel diode device interpreted as a die roll.
• 10:45 - 11:00 am EDT

  Adaptive optimized Schwarz methods

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Conor McCoid, Université Laval

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Optimized Schwarz methods use Fourier analysis or similar to find transmission conditions between subdomains that provide faster convergence over standard Schwarz methods. However, this requires significant upfront analysis of the operator, and may not be straightforward for all problems. This work presents black box methods for adaptively optimizing the transmission conditions, which is equivalent to a Krylov subspace method.
• 11:00 - 11:15 am EDT

  Row-aware Randomized SVD with applications

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Davide Palitta, Alma Mater Studiorum, Universita' di Bologna

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  After briefly recalling state-of-the-art procedures, either deterministic or randomized, for computing an SVD-type approximation of a tall matrix A, I will introduce a novel randomization-based algorithm that improves the standard Randomized Singular Value Decomposition (RSVD). Most significantly, this new approach, the Row-aware RSVD (R-RSVD), explicitly constructs information from the row space of A. This leads to better approximations to Range(A) while maintaining the same computational cost of RSVD. The efficacy of the R-RSVD scheme is supported by both robust theoretical results and extensive numerical experiments. Furthermore, I present an alternative algorithm inspired by R-RSVD, capable of achieving comparable accuracy despite utilizing only a subsample of the rows of A, resulting in a significantly reduced computational cost. This method, named the Subsample Row-aware RSVD (Rsub-RSVD), is supported by a weaker error bound compared to the ones derived for R-RSVD, but still meaningful as it ensures that the error remains under control. Additionally, numerous experiments demonstrate that the Rsub-RSVD trend is akin to the one attained by RSVD when the subsampling parameter is on the order of n, for a m×n A, with m >> n. Finally, I will consider the application of these schemes in the computation of DEIM-induced CUR decompositions. This talk is based on a joint work with Sascha Portaro (University of Bologna).
• 11:15 - 11:30 am EDT

  Graph ‘texture’ features, using image analysis methods to derive new summary statistics for complex graphs.

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Rowan Barker-Clarke, Cleveland Clinic Lerner Institute

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Image texture features, such as those derived by Haralick et al, are widely used for image classification across fields including cancer research. We demonstrate how analogous texture features can be derived for graphs and networks. We also illustrate how these new metrics summarize graph-structured data and may aid comparative graph studies including evaluating dysregulation in gene expression networks. Node weight co-occurrence matrices for graphs are generated by summing frequencies of pairs of neighboring nodes in the graph. These texture features form novel second-order summary features for networks or graphs with ordered node labels. Our novel graph 'texture' features are shown to correspond to different graph structure and node label distributions. Just like equivalent image textures, the metrics are sensitive to discretization parameters and noise in node labels. In the complex cancer informatics setting, evolutionary analyses and drug response prediction are two examples where new network science approaches like this may prove fruitful.
• 11:30 - 11:45 am EDT

  Quantum state transfer on graphs

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Hermie Monterde, University of Manitoba

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Quantum states carry information, and in order to construct an operational quantum computer, it is important to understand how quantum states travel across a network. In this talk, we survey old and new results in the study of quantum state transfer that are of interest to both physicists and mathematicians. Our focus is to highlight the role of spectral and algebraic graph theory in this study. We also discuss some open problems.
• 11:45 am - 12:00 pm EDT

  Guiding Stress : From Pentamodes to Cable Webs to Masonry Structures

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Graeme Milton, University of Utah

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Pentamode materials are a class of materials that are useful for guiding stress. In particular, they have been proposed for acoustic cloaking by guiding stress around objects, and have been physically constructed. A key feature of pentamode materials is that each vertex in the material is the junction of 4 double cone elements. Thus the tension in one element determines the tension in the other elements, and by extension uniquely determines the stress in the entire metamaterial. Here we show how this key feature can be extended to discrete wire networks, supporting forces at the terminal nodes and which may have internal nodes where no forces are applied. In usual wire or cable networks, such as in a bridge or bicycle wheel, one distributes the forces by adjusting the tension in the wires. Here our discrete networks provide an alternative way of distributing the forces through the geometry of the network. In particular the network can be chosen so it is uniloadable, i.e. supports only one set of forces at the terminal nodes. Such uniloadable networks provide the natural generalization of pentamode materials to discrete networks. We extend such a problem to compression-only 'strut nets' subjected to fixed and variable nodal loads. These systems provide discrete element models of masonry bodies, which lie inside the polygon/polyhedron with vertices at the points of application of the given forces ('underlying masonry structures'). In particular, we solve the two-dimensional problem where one wants the strut net to avoid a given set of obstacles, and also allow some of the forces to be reactive ones. This is joint work with Ada Amendola, Guy Bouchitt{\'e}, Andrej Cherkaev, Antonio Fortunato, Fernando Fraternali, Ornella Mattei, and Pierre Seppecher.
• 12:00 - 1:30 pm EDT

  EDI Theme

  Working Lunch - 11th Floor Collaborative Space
• 1:30 - 2:30 pm EDT

  Working Groups

  Group Work - 11th Floor Collaborative Space
• 2:30 - 3:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space
• 3:00 - 5:00 pm EDT

  EDI Panel

  Panel Discussion - 11th Floor Lecture Hall

  • Session Chair
  • Colton Sawyer, Regis University

June 27, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 9:00 - 9:30 am EDT

  Check in with TAs

  - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  10th Floor Collaborative Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work / Writing Time

  Group Work - Assigned Group Work Space
• 8:00 - 10:00 pm EDT

  Movie Night

  - 11th Floor Lecture Hall

• 9:00 - 9:45 am EDT

  Key Factors and Parameter Ranges for Immune Control of Equine Infectious Anemia Virus Infection

  11th Floor Lecture Hall

  • Speaker
  • Stacey Smith?, University of Ottowa

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  Equine Infectious Anemia Virus (EIAV) is an important infection in equids, and its similarity to HIV creates hope for a potential vaccine. We analyze a within-host model of EIAV infection with antibody and cytotoxic T lymphocyte (CTL) responses. In this model, the stability of the biologically relevant endemic equilibrium, characterized by the coexistence of long-term antibody and CTL levels, relies upon a balance between CTL and antibody growth rates, which is needed to ensure persistent CTL levels. We determine the model parameter ranges at which CTL and antibody proliferation rates are simultaneously most influential in leading the system towards coexistence and can be used to derive a mathematical relationship between CTL and antibody production rates to explore the bifurcation curve that leads to coexistence. We employ Latin hypercube sampling and least squares to find the parameter ranges that equally divide the endemic and boundary equilibria. We then examine this relationship numerically via a local sensitivity analysis of the parameters. Our analysis is consistent with previous results showing that an intervention (such as a vaccine) intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. Finally, we show that the CTL production rate can entirely determine the long-term outcome, regardless of the effect of other parameters, and we provide the conditions for this result in terms of the identified ranges for all model parameters.
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 - 10:45 am EDT

  A first-principles geometric model for dynamics of motor-driven centrosomal asters

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Yuan Young, New Jersey institute of technology

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  The centrosomal aster is a mobile and adaptable cellular organelle that exerts and transmits forces necessary for tasks such as nuclear migration and spindle positioning. Recent experimental and theoretical studies of nematode and human cells demonstrate that pulling forces on asters by cortically anchored force generators are dominant during such processes. Here we present a comprehensive investigation of a first-principles model of aster dynamics, the S-model (S for stoichiometry), based solely on such forces. The model evolves the astral centrosome position, a probability field of cell-surface motor occupancy by centrosomal microtubules (under an assumption of stoichiometric binding), and free boundaries of unattached, growing microtubules. We show how cell shape affects the stability of centering of the aster, and its transition to oscillations with increasing motor number. Seeking to understand observations in single-cell embryos, we use highly accurate simulations to examine the nonlinear structure of the bifurcations, and demonstrate the importance of binding domain overlap to interpreting genetic perturbation experiments. More generally, we find a rich dynamical landscape, dependent upon cell shape, including internal aster orbits that arise as traveling waves. Finally, we explore the interactions of multiple asters, unveiling novel phenomena such as centrosome relaxation to the vertices of platonic solids. Our findings align with experimental observations, providing insights into the mechanisms governing spindle positioning and cell division dynamics.
• 10:45 - 11:00 am EDT

  Using evolutionary methods to bridge data science and clinical research to describe and subvert cancer progression and therapeutic resistance.

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • NIc Fisk, University of Rhode Island

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  Cancer is a complex family of diseases with high stakes and is on track to overtake heart disease as the leading cause of death in the United States in the next decade. The majority of these moralities are due to metastatic progression and spread of tumors which are often resistant to first-line therapy. Due to the complexity and urgency for better understanding and subverting this evolving scourge, researchers have approached the study of cancer origination, progression, and acquisition of resistance using myriad techniques developed across the diverse biological, medical, and physical sciences alongside advancement in mathematical, informatic, and computational methods to make sense of the results of these experiments. However, like all tools of research, these informatics tools must be fit-for-purpose to maximize their utility in the shared endeavor of understanding and undermining cancer progression. In this work, we demonstrate that explicit inclusion of evolutionary theory in informatics approaches to the study of cancer improves the predictive power of models, generates more interpretable and actionable findings, and—due to the fundamental nature of the theory of evolution to biology—can be used pan-cancer, across scales (i.e., individual to catchment), and especially thru time. We further demonstrate the translational utility of bridging cancer biology and informatics by identifying orthogonal immunotherapuetic targets.
• 11:00 - 11:15 am EDT

  Uniform Boundedness and Long-time Behavior of Solutions to SI Models with Intermittent Treatment

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Haseeb Ansari, University of Houston

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  We study a dynamic SI (Susceptible-Infected) model with an intermittent treatment term. Results are given for the cases when no components diffuse, and all components diffuse. In each case, we prove uniform boundedness of solutions and investigate their long-time behavior.
• 11:15 - 11:30 am EDT

  Analytical Predictions of Epidemic Dynamics on Sparse Locally Tree-Like Networks

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Juniper Cocomello, Brown University

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  Formulating and analyzing tractable models of infectious disease spreading is a public health priority, with applications that extend to a variety of phenomena characterized by the spreading of information, such as the propagation of blackouts, computer viruses and rumors. We study compartmental models of epidemics with non-fading immunity, such as the SIR and SEIR models, with possibly time-varying rates, on a class of networks that are locally tree-like, which includes sparse Erdős-Rènyi random graphs, random regular graphs, and other configuration models. We identify tractable systems of ODEs that exactly describe the dynamics of such process in a suitable asymptotic regime in which the population size goes to infinity. We characterize the outbreak size of the SIR and SEIR models as the unique zero of an explicit functional. We also demonstrate via simulations the efficacy of our approximations for populations of moderate size.
• 11:30 - 11:45 am EDT

  Magnetic skyrmions under confinement

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Theresa Simon, University of Münster

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  In extremely thin ferromagnetic films, an additional interaction, the so-called Dzyaloshinskii-Moriya interaction (DMI), arises in the micromagnetic energy. In such materials, topoligically nontrivial, point-like configurations of the magnetization called magnetic skyrmions are observed, which are of great interest in the physics community due to possible applications in high-density data storage. We characterize skyrmions as minimizers of a micromagnetic energy augmented by DMI on bounded domains with Dirichlet data and describe their asymptotics in the regime of dominating exchange (or Dirichlet) energy. As in this limit skyrmions collapse into a point, we rely on a quantitative rigidity result for degree 1 harmonic maps into the two-dimensional sphere.
• 11:45 am - 12:00 pm EDT

  A Geometric Perspective on Computational Mechanics

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • Eitan Grinspun, University of Toronto

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  The connection between geometry and mechanics has been explored for centuries. How this connection shapes computation is a question we are just beginning to explore. If computers can predict how materials move and deform, they can help us to understand, predict, and manipulate the physical world. Our group develops models and algorithms that capture the characteristic behavior of a mechanical system. We focus on the geometry behind the physics. We build a discrete geometric picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting. The result is a readily computable model that preserves invariants and conservation laws. With applications spanning flagellar propulsion to robotics, we are learning that this geometric approach can impact consumer product design, medical research, engineering design and basic scientific research.
• 12:00 - 12:15 pm EDT

  Active nematic fluids on arbitrary manifolds

  Contributed Talk - 11th Floor Lecture Hall

  • Speaker
  • David Saintillan, UC San Diego

  • Session Chair
  • Michael Robert, Virginia Tech

  Abstract

  The dynamics of biological surfaces often involves the coupling of internal active processes with in-plane orientational order and hydrodynamic flows. Such active surfaces play a key role in various biological processes, from cytokinesis to tissue morphogenesis. In this talk, we present a novel computational approach for the simulation of active nematic fluids confined to Riemannian manifolds. The fluid velocity and nematic order parameter are represented as the sections of the complex line bundle of a two-manifold. Using a geometric approach based on the Levi-Civita connection, we introduce a coordinate-free discretization method that preserves the continuous local-to-global theorems in differential geometry. Furthermore, we establish a nematic Laplacian on complex functions that can accommodate fractional topological charges through the covariant derivative on the complex nematic representation. Advection of the nematic field is formulated based on the Lie derivative, resulting in a stable geometric semi-Lagrangian discretization scheme for transport by the flow. The proposed surface-based method offers an efficient and stable means to investigate the influence of local curvature and topology on the hydrodynamics of active nematic systems, and we illustrate its capabilities by simulating active flows on a range of surfaces of increasing complexity.
• 12:15 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 2:15 pm EDT

  Storm Surge Modeling with Compound Flood Effects

  11th Floor Lecture Hall

  • Speaker
  • Clint Dawson, University of Texas at Austin

  • Session Chair
  • Becca Thomases, Smith College

  Abstract

  In this talk we will describe mathematics, software, and applications of coastal ocean models to hurricane storm surge and compound flooding. Applications include validation studies, forecasting, and futurecasting. Recent research on compound flood modeling will be highlighted.
• 2:30 - 3:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space
• 3:00 - 5:00 pm EDT

  Working Groups

  Group Work - 11th Floor Lecture Hall

June 28, 2024

• 8:30 - 9:00 am EDT

  Arrival Time / Sign In

  Arrival Time / Sign In - 11th Floor Collaborative Space
• 8:30 - 9:00 am EDT

  Check in with TAs

  Check in with TAs - 10th Floor Collaborative Space
• 9:30 - 10:30 am EDT

  Group Work

  Assigned Group Work Space
• 10:30 - 11:00 am EDT

  Break

  Coffee Break
• 11:00 - 11:15 am EDT

  Question of the Day

  - 10th Floor Collaborative Space
• 11:15 am - 12:00 pm EDT

  Group Work

  Assigned Group Work Space
• 12:00 - 1:30 pm EDT

  Lunch/Free Time
• 1:30 - 3:00 pm EDT

  Group Work

  Assigned Group Work Space
• 3:00 - 3:30 pm EDT

  Coffee Break

  10th Floor Collaborative Space
• 3:30 - 4:30 pm EDT

  Group Work/ Writing Time

  Group Work - Assigned Group Work Space

• 9:00 - 9:45 am EDT

  Shape optimization and shapeshifting in soft matter

  11th Floor Lecture Hall

  • Speaker
  • Timothy Atherton, Tufts University

  • Session Chair
  • Alexander Hoover, Cleveland State University

  Abstract

  Soft materials are ubiquitous in biology and are ideal candidates for advanced engineering applications including soft, biomimetic robots, self-building machines, shape-shifters, artificial muscles, and chemical delivery packages. In many of these, the material must make a dramatic change in shape with an accompanying re-ordering of the material; in others changes in the ordering can be used to drive or even interrupt shape change. To optimize the materials and structures, it is necessary to have a detailed understanding of how the microstructure and macroscopic shape co-evolve. In this talk, I will present my group's mathematical modelling work on shape shifting in emulsions, liquid crystals and other soft materials. To develop the description, we draw upon differential geometry, topology, optimization theory and computer simulations. I will also describe a second research direction: Elucidating the climate for LGBTQ+ people in Physics & Astronomy, and present ideas and opportunities for the Applied Math community to better support queer people.
• 10:00 - 10:30 am EDT

  Coffee Break

  11th Floor Collaborative Space
• 10:30 am - 12:00 pm EDT

  Town Hall

  - 11th Floor Lecture Hall

  • Session Chair
  • Alexander Hoover, Cleveland State University
• 12:00 - 1:30 pm EDT

  Networking Lunch

  Working Lunch - 11th Floor Collaborative Space
• 1:30 - 2:30 pm EDT

  Working Groups

  Group Work - 11th Floor Collaborative Space
• 2:30 - 3:00 pm EDT

  Coffee Break

  11th Floor Collaborative Space
• 3:00 - 4:30 pm EDT

  Working Groups

  Group Work - 11th Floor Lecture Hall

June 29, 2024

There are no events currently scheduled for June 29th.