Embedded Files
Jan 7, 2025: Chadi Saad-Roy, UC Berkeley
Location: EXED 110 at 4pm
Jan 7, 2025: Chadi Saad-Roy, UC Berkeley
Location: EXED 110 at 4pm
Title: Mathematical models to untangle infectious disease dynamics across scales
Abstract: Infectious diseases are complex systems across many scales. In this talk, I will use mathematical models to investigate a range of cross-scale questions in infectious disease dynamics, from immuno-epidemiology, to pathogen evolution, and to behavioral-epidemiology. I will begin by examining potential future SARS-CoV-2 transmission dynamics, landscapes of immunity, and the effects of vaccination. I will then use mathematical models to examine pathogen evolutionary dynamics, and to study individual decision-making and its effect on epidemiological dynamics (and vice-versa). Overall, I will provide a broad overview to highlight the use of mathematical models in infectious disease epidemiology.
Jan 14 , 2025: Jorge Garza-Vargas, Caltech
Jan 14 , 2025: Jorge Garza-Vargas, Caltech
Location and time: EXED 110 at 4pm
Title: Proving rapid global convergence for the shifted QR algorithm
Abstract: The design of efficient and reliable algorithms for computing the eigenvalues and eigenvectors of a matrix (i.e. solving the eigenvalue problem) is critically important in both science and engineering. Despite significant advancements in various practical aspects, fundamental theoretical questions about the eigenvalue problem remain poorly understood.
In this talk, I will present joint work with Jess Banks and Nikhil Srivastava, in which we provide nearly optimal rigorous guarantees, on all inputs, for the most widely used diagonalization algorithm: the shifted QR algorithm. Similar results were established by Wilkinson in 1968 and Dekker and Traub in 1971 for Hermitian matrices; however, despite sustained interest and several attempts, the non-Hermitian case remained elusive for the last five decades.
Jan 16, 2025: Krutika Tawri, UC Berkeley
Jan 16, 2025: Krutika Tawri, UC Berkeley
Location and time: EXED 110 at 4pm
Title: Stochastic and deterministic moving boundary problems
Abstract: In this talk we will discuss recent results concerning stochastic (and deter ministic) moving boundary problems, particularly arising in fluid-structure interaction (FSI), where the motion of the boundary is not known a priori. Fluid-structure interaction refers to physical systems whose behavior is dictated by the interaction of an elastic body and a fluid mass and it appears in various applications, ranging from aerodynamics to structural engi neering. Our work is motivated by FSI models arising in biofluidic applications that describe the interactions between a viscous fluid, such as human blood, and an elastic structure, such as a human artery. To account for the unavoidable numerical and physical uncertainties in applications we analyze these PDEs under the influence of external stochastic (random) forces.
We will consider nonlinearly coupled fluid-structure interaction (FSI) problems involving a viscous fluid in a 2D/3D domain, where part of the fluid domain boundary consists of an elastic deformable structure, and where the system is perturbed by stochastic effects. The fluid flow is described by the Navier-Stokes equations while the elastodynamics of the thin structure are modeled by shell equations. The fluid and the structure are coupled via two sets of coupling conditions imposed at the fluid-structure interface. We will consider the case where the structure is allowed to have unrestricted deformations and explore different kinematic coupling conditions (no-slip and Navier slip) imposed at the randomly moving fluid-structure interface, the displacement of which is not known a priori. We will present our results on the existence of (martingale) weak solutions to the (stochastic) FSI models. This is the first body of work that analyzes solutions of stochastic PDEs posed on random and time-dependent domains and a first step in the field toward further research on control problems, singular perturbation problems etc. We will further discuss our findings, which reveal a novel hidden regularity in the structure’s displacement. This result has allowed us to address previously open problems in the 3D (deterministic) case involving large vec torial deformations of the structure. We will discuss both the cases of compressible and incompressible fluid.
Jan 23, 2025: Mari Kawakatsu, UPenn
Jan 23, 2025: Mari Kawakatsu, UPenn
Location: EXED 110 at 4pm
Title: Mathematical models of reputation, polarization, and cooperation
Abstract: Addressing contemporary problems of collective action—from pandemic management to climate change—requires that we understand the dynamic interplay between information and behavior. In this talk, I will discuss two models of cooperative behavior coupled with dynamics of information spread. In the first model, we will consider cooperation driven by the spread of social reputations. Using methods from evolutionary game theory and dynamical systems, we develop a mathematical model of cooperation that integrates a mechanistic description of how reputations spread through peer-to-peer gossip. We show that sufficiently long periods of gossip can stabilize cooperation by facilitating consensus about reputations. In the second model, we will examine the dynamics of prosociality under political polarization. We develop a stochastic model of game-theoretic opinion dynamics in a multi-dimensional space of political interests. We show that while increasing the diversity of interests can improve both cooperation and social cohesion, strong partisan bias reduces the effective dimensionality of the opinion space via self-sorting along party lines, yielding greater in-group cooperation at the cost of increasing polarization. Taken together, these studies contribute to our understanding of when and how communication and opinion contagion facilitate cooperation.
Feb 3, 2025: Pratik Patil, UC Berkeley
Feb 3, 2025: Pratik Patil, UC Berkeley
Location: EXED 110 at 4pm
Title: Facets of regularization in overparameterized machine learning
Abstract: Modern machine learning often operates in an overparameterized regime in which the number of parameters far exceeds the number of observations. In this regime, models can exhibit surprising generalization behaviors: (1) Models can overfit with zero training error yet still generalize well (benign overfitting); furthermore, in some cases, even adding and tuning explicit regularization can favor no regularization at all (obligatory overfitting). (2) The generalization error can vary non-monotonically with the model or sample size (double/multiple descent). These behaviors challenge classical notions of overfitting and the role of explicit regularization.
In this talk, I will present theoretical and methodological results related to these behaviors, primarily focusing on the concrete case of ridge regularization. First, I will identify conditions under which the optimal ridge penalty is zero (or even negative) and show that standard techniques such as leave-one-out and generalized cross-validation, when analytically continued, remain uniformly consistent for the generalization error and thus yield the optimal penalty, whether positive, negative, or zero. Second, I will introduce a general framework to mitigate double/multiple descent in the sample size based on subsampling and ensembling and show its intriguing connection to ridge regularization. As an implication of this connection, I will show that the generalization error of optimally tuned ridge regression is monotonic in the sample size (under mild data assumptions) and mitigates double/multiple descent. Key to both parts is the role of implicit regularization, either self-induced by the overparameterized data or externally induced by subsampling and ensembling. Finally, I will briefly mention some extensions and variants beyond ridge regularization.
The talk will feature joint work with the following collaborators (in alphabetical order): Pierre Bellec, Jin-Hong Du, Takuya Koriyama, Arun Kumar Kuchibhotla, Alessandro Rinaldo, Kai Tan, Ryan Tibshirani, Yuting Wei. The corresponding papers (in talk-chronological order) are: optimal ridge landscape (https://pratikpatil.io/papers/ridge-ood.pdf), ridge cross-validation (https://pratikpatil.io/papers/functionals-combined.pdf), risk monotonization (https://pratikpatil.io/papers/risk-monotonization.pdf), ridge equivalences (https://pratikpatil.io/papers/generalized-equivalences.pdf), and extensions and variants (https://pratikpatil.io/papers/cgcv.pdf, https://pratikpatil.io/papers/subagging-asymptotics.pdf).
Feb 6, 2025: Florian Schaefer, Georgia Tech
Feb 6, 2025: Florian Schaefer, Georgia Tech
Location: EXED 110 at 4pm
Title: Toward Information Geometric Mechanics
Abstract: Shock waves in high-speed gas dynamics cause severe numerical challenges for classical and learning-based solvers. This talk begins with the observation that shock formation arises from the flow map reaching the boundary of the manifold of diffeomorphisms. We modify its geometry such that geodesics approach but never reach the boundary. The resulting information geometric regularization (IGR) has smooth solutions while avoiding the excessive dissipation of viscous regularizations, accelerating and simplifying the simulation of flows with shocks. We prove the existence of global strong IGR solutions in the unidimensional pressureless case and illustrate its practical utility on multidimensional examples with complex shock interactions.
The modified geometry of the diffeomorphism manifold is the information geometry of the mass density. The last part of the talk explains how this observation motivates information geometric mechanics that views the solutions of continuum mechanical PDEs as parameters of probability distributions originating from statistical physics. Replacing the Euclidean geometry of individual particles with the information geometry of statistical families promises performant numerical methods that readily integrate with learning-based approaches.
Feb 20, 2025: Morgan Craig, University of Montreal
Feb 20, 2025: Morgan Craig, University of Montreal
Location: EXED 110 at 4pm
Title: Identifying treatment and vaccine targets using mechanistic mathematical models
Abstract: Immunological heterogeneity heavily influences treatment and vaccine successes and failures. Many factors contribute to disparate outcomes in cancer therapies and immunizations, including age, sex, and the microenvironment. In this talk, I will discuss how we use mechanistic mathematical models and computational immunology to dissect the influence of heterogeneity on immune responses with the goal of identifying new treatment and vaccine strategies tailored to key characteristics driving outcomes.
Feb 27, 2025: Roy Choudhury, UCF
Feb 27, 2025: Roy Choudhury, UCF
Location: EXED 110 at 4pm
Title: Extensions of the General Solution Families for the Inverse Problem of the Calculus of Variations for Sixth- and Eighth-order Ordinary Differential Equations
Abstract: New third- and fourth-order Lagrangian hierarchies are derived in this study. The free coefficients in the leading terms satisfy the most general differential geometric criteria currently known for the existence of a variational formulation, as derived by solution of the full inverse problem of the Calculus of Variations for scalar sixth- and eighth-order ordinary differential equations (ODEs). The Lagrangians obtained here have greater freedom since they require conditions only on individual coefficients. In particular, they contain four arbitrary functions, so that some investigations based on the existing general criteria for a variational representation are particular cases of our families of models. The variational equations resulting from our generalized Lagrangians may also represent traveling waves of various nonlinear evolution equations, some of which recover known physical models. For a typical member of our generalized variational ODEs, families of regular and embedded solitary waves are also derived in appropriate parameter regimes. As usual, the embedded solitons are found to occur only on isolated curves in the part of parameter space where they exist.
Mar 4, 2025: Anthony Bloch, University of Michigan
Mar 4, 2025: Anthony Bloch, University of Michigan
Location: EXED 110 at 4pm
Title: Integrable Hamiltonian and gradient flows and total positivity
Abstract: In this talk I will discuss various connections between the dynamics of integrable (solvable) Hamiltonian flows, gradient flows, and geometry. A key example will be the Toda lattice flow which describes the dynamics of interacting particles on the line. I will show how versions of this can also be viewed as gradient flows and relate the flow to the geometry of convex polytopes as well as to the theory of total positivity. The latter theory has its origins in linear algebra and matrices all of whose minors are positive. This simple idea has fascinating generalizations to representation theory and applications in combinatorics, small vibrations and high energy physics. The type of dynamics discussed here turns out to be able to prove interesting results in the general theory of total positivity. I will also discuss links to general dissipative dynamics and to deep learning.
Mar 6 , 2025: Arie Israel, UT Austin
Mar 6 , 2025: Arie Israel, UT Austin
Location: EXED 110 at 4pm
Title: TBA
Abstract: TBA
Mar 13, 2025: Boeing Colloquium, Michael Weinstein, Columbia
Mar 13, 2025: Boeing Colloquium, Michael Weinstein, Columbia
Location: EXED 110 at 4pm
Title: TBA
Abstract: TBA
Page updated
Report abuse