2019
Marina Ferreira (University of Helsinki)
Mass localization in multicomponent coagulation systems
Riccardo Cristoferi (Heriot-Watt University)
Epitaxial crystal growth with adatoms
Theodore Drivas (Princeton University)
Anomalous dissipation for passive scalars
Robert P. Lipton (Louisiana State University)
Non-local Brittle Fracture Modeling
Sean McCurdy (Carnegie Mellon University)
A two-phase free boundary problem for harmonic measure
Russell Schwab (Michigan State University)
Analyzing a special case of the Hele-Shaw flow using integro-differential operators
KiHyun Yun (Hankuk University of Foreign Studies)
High stresses occurring in fiber-reinforced composites
Boris Springborn (TU Berlin)
Ideal Hyperbolic Polyhedra and Discrete Uniformization
Pedro Aceves Sanchez (North Carolina State University)
Fractional diffusion limit of a linear kinetic transport equation in a bounded domain
Tarek Elgindi (UCSD)
Singularity formation for classical solutions to the 3D Euler equation
Hau-Tieng Wu (Duke University)
Single channel blind source separation and its clinical applications
Adrian Tudorascu (West Virginia University)
Mean Field Games and Hamilton-Jacobi equations in spaces of probability measures
Tran Minh Binh (Southern Methodist University)
On the energy cascade of acoustic wave turbulence: Beyond Kolmogorov-Zakharov solutions
Hui Yu (Columbia University)
Regularity of optimal transport between planar convex domains
Lei Li (Shanghai Jiao Tong University)
Some algorithms and analysis for first order interacting particle systems
Elisa Davoli (University of Vienna)
Two-well rigidity and multidimensional sharp-interface limits for solid-solid phase transitions
Rita Ferreira (KAUST)
Existence of weak solutions to first-order stationary mean-field games: a general framework, the case of Dirichlet conditions, and the congestion problem
2018
Raghavendra Venkatraman (CMU)
Defects and Phase Transitions in Highly Anisotropic Nematic Liquid Crystals
Michael Siegel (New Jersey Institute of Technology)
Accurate and efficient boundary integral computations for interfacial flow with surfactant
Yulong Lu (Duke University)
Rényi entropy and gradient flow in classical and quantum dynamics
Shawn Walker (Louisiana State University)
A Numerical Scheme for the Generalized Ericksen Model of Liquid Crystals With Applications to Virus DNA Packing
Peter Palffy Muhoray (Kent State)
Repulsive and Attractive Interactions in Nematic Liquid Crystals
Shankar Venkataramani (University of Arizona)
Existence and regularity for solutions to Hyperbolic Monge-Ampere equations with applications to Non-euclidean elasticity
Jack Xin (UC Irvine)
Blended Coarse Gradient Descent for Full Quantization of Deep Neural Networks
Smita Sahu (University of Durham)
An efficient filtered scheme for some first order time-dependent Hamilton-Jacobi equations
Marco Morandotti (Technical University of Munich)
Structured deformations of continua: theory and applications
Massimiliano Morini (U. Parma)
A Variational Approach to Nonlocal Geometric Flows and Crystalline Mean Curvature
Nicola Fusco (U. Naples)
Asymptotic Stability of the Gradient of Flow of Nonlocal Energies
Chris Henderson (University of Chicago)
The influence of non-local interactions on front propagation
Carlos Mora Corral (Universidad Autonoma de Madrid)
Nonlocal variational problems and applications to peridynamics
Roberto Camassa (University of North Carolina)
Tailoring the tails in Taylor dispersion
Xiaoqin Guo (UW Madison)
Quantitative homogenization and Harnack inequality for a non-elliptic balanced random environment
Luis Silvestre (University of Chicago)
Regularity and structure of scalar conservation laws
Franca Hoffmann (Caltech)
Equilibria for nonlinear diffusion and nonlocal interaction
Mike Shelley (Courant Institute)
The Dynamics of Microtubule/Motor-Protein Assemblies
Peter Sternberg (Indiana University)
A Ginzburg-Landau type problem for highly anisotropic nematic liquid crystals
Francesco De Anna (Penn State)
Global well-posedness for dynamical models of nematic liquid crystals
Dmitriy Drusvyatskiy (University of Washington)
Slope and geometry in variational mathematics
2017
Athanasios Tzavaras (KAUST)
The problem of shear band formation: a study of a parabolic regularization of an elliptic initial-value problem
Jeffrey Case (Penn State)
Some results on a fully nonlinear boundary value problem from conformal geometry
Alethea Barbaro (Case Western Reserve University)
Phase transition in a kinetic flocking models
Martin Kruzik (Institute of Information Theory and Automation, Czech Republic)
Weak lower semicontinuity for signed integral functionals on BV and applications
Alexis Drouot (Columbia University)
Resonances for highly oscillatory and stochastic Schrodinger operators
Augusto Visintin (Universita' degli Studi di Trento)
Compactness and Structural Stability of Nonlinear Flows
Stephan Wojtowytsch (Carnegie Mellon University)
Diffuse Interfaces and Topology: A Phase-Field Model for Willmore's Energy
Nicolas Garcia Trillos (Brown University)
Graph-based Bayesian learning: continuum limits and scalability of sampling algorithms
Monica Torres (Purdue University)
Characterizations of measures in the dual of $BV$ and related isometric isomorphisms
Petronela Radu (University of Nebraska-Lincoln)
Double nonlocality in continuum mechanics models
Katy Craig (University of California, Santa Barbara)
From slow diffusion to a hard height constraint: characterizing congested aggregation
Maria Giovanna Mora (Universita degli Studi di Pavia)
The equilibrium measure for a nonlocal dislocation energy
Christopher Larsen (Worcester Polytechnic Institute)
An overview of mathematical issues in dynamic fracture
Michel Chipot (University of Zurich)
Minimal Solutions To Some Variational Inequalities
Carlos Mora-Corral (Universidad Autonoma de Madrid)
Local invertibility in Sobolev spaces
Daniel Tenbrinck (University of Muenster)
Graph Methods for Manifold-Valued Data
Walter Craig (McMaster University)
On the size of the Navier - Stokes singular set
Edriss Titi (Texas A & M and The Weizmann Institute of Science)
Analysis of Certain Geophysical Models: Global Regularity and Finite-time Blowup Results
2016
Ihsan Topaloglu (Virginia Commonwealth University)
Droplet phase in a nonlocal isoperimetric problem under confinement
Janusz Ginster (Carnegie Melllon University)
Plasticity as the Gamma-Limit of a Nonlinear Dislocation Energy with Mixed Growth
Ari Stern (Washington University)
Recent advances in finite element exterior calculus
Peter Gladbach (Carnegie Melllon University)
The phase-field model of dislocations: Interaction between parallel slip planes
Abigail Hunter (Los Alamos National Lab)
Phase field dislocation dynamics (PFDD) for nanoscale fcc metals
Gianluca Crippa (University of Basel)
Exponential self-similar mixing by incompressible flows
Zack Bradshaw (University of Virginia)
Self-similar and discretely self-similar solutions to the Navier-Stokes equations
Yao Yao (Georgia Tech)
Long time behavior of solutions to the 2D Keller-Segel equation with degenerate diffusion
Benjamin Seibold (Temple University)
Nonlinear waves in traffic flow, and the future of traffic modeling
Xiaoqian Xu (Carnegie Melllon University)
Suppression of chemotactic explosion by mixing
Cheng Yu (UT Austin)
Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations
Max Fathi (University of California, Berkeley)
Gradient flows and scaling limits for interacting particle systems
Antoine Mellet (University of Maryland)
Anomalous diffusion phenomena: A kinetic approach
Mikaela Iacobelli (University of Rome, Sapienza)
A gradient flow approach to quantization of measures
Jeff Calder (UC Berkeley)
Partial differential equation continuum limits for discrete sorting problems
Marian Bocea (Loyola University Chicago)
Duality for the L∞ Optimal Transport Problem
Martin Glicksman (Florida Institute of Technology)
Thermodynamics of Autogenous Pattern Formation
Ricardo Nochetto (University of Maryland)
Bilayer Plates: Model Reduction, Discretization and Gradient Flow
Ming Chen (University of Pittsburgh)
Existence of large-amplitude solitary stratified water waves
Panagiotis Souganidis (University of Chicago)
Scalar conservation laws with rough time dependence
Daniel Tenbrinck (Muenster University)
Partial Difference Operators on Weighted Graphs for Point Cloud Processing - From 3D Surfaces to Machine Learning
Robin Neumayer (University of Texas at Austin)
A strong form of the quantitative Wulff inequality
2015
Stanley Snelson (University of Chicago)
Weak harmonic map flows with singular targets
Timo Seppalainen (University of Wisconsin)
Kardar-Parisi-Zhang universality and the exactly solvable log-gamma polymer
Daniel Spirn (University of Minnesota)
Hydrodynamic limits in Ginzburg-Landau theory
Tarek Elgindi (Princeton University)
Well/ill-posedness issues for equations modelling incompressible fluid flow
Marco Caroccia (Carnegie Melllon University)
On the asymptotic behavior of isoperimetric planar partitions
Michael Kowalczyk (University of Chile)
Kink dynamics in the $ phi^4$ model: asymptotic stability for odd perturbations in the energy space
Albert Cohen (Michigan State University)
Bond and CDS Pricing with Stochastic Recovery
Lei Wu (Carnegie Melllon University)
Geometric correction for diffusive expansion in neutron transport equation
Laurent Dietrich (Carnegie Melllon University)
Enhancement of propagation in reaction-diffusion equations by a line of fast diffusion
Snejana Abarji (Carnegie Melllon University)
Scale coupling in Richtmyer-Meshkov flows
Alberto Bressan (Pennsylvania State University)
Lipschitz Metrics for Nonlinear Wave Equations
Saleh Tanveer (Ohio State University)
Quasi-solution approach towards nonlinear problems
Charis Tsikkou (West Virginia University)
Analysis of 2+1 Diffusive-Dispersive PDE Arising in River Braiding
Toan Nguyen (Pennsylvania State University)
On the stability of Prandtl boundary layer expansions of Navier-Stokes in the inviscid limit
Nam Le (Indiana University)
Second inner variations of Allen-Cahn type energies and applications to local minimizers
Chanwoo Kim (University of Wisconsin)
Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
Massimilano Morini (Universita' di Parma)
Motion of elastic films by anisotropic surface diffusion
Nicola Fusco (Universita' di Napoli)
Stability of the isoperimetric inequality on the sphere
2014
Wujun Zhang (University of Maryland)
A finite element method for nematic liquid crystals with variable degree of orientation
Jacob Bedrossian (University of Maryland)
Mixing and enhanced dissipation in the inviscid limit of the Navier-Stokes equations near the 2D Couette flow
Josh Ballew (Carnegie Melllon University)
Relative Entropy and the Navier-Stokes-Smoluchowski System for Compressible Fluids
Changhui Tan (University of Maryland)
Flocking dynamics in different scales
Elaine Cozzi (Oregon State University)
Solutions to the 2D Euler equations with velocity unbounded at infinity
Michel Chipot (University of Zurich)
Limits of the Stokes and Navier-Stokes equations in a punctured periodic domain
Luca Deseri (Mechanics, Materials and Computing Center, CEE & ME-CIT, Carnegie Mellon University)
Modeling membrane-receptors interplay due to ligand binding to GPCRs and cell response
Scott Armstrong (CEREMADE Universite' Paris Dauphine)
Quantitative stochastic homogenization of convex energy functionals
Elvira Zappale (Universita' di Salerno)
Existence of minimizers for non-level convex supremal functionals
Bo Li (Case Western Reserve University)
Predictive modeling and simulation of High Energy Density (HED) dynamic response of materials
Misha Neklyudov (University of Sydney)
Dynamics of nanomagnetic particle systems
Laszlo Szekelyhidi (University of Leipzig)
The h-principle for the Euler equations
John Ball (Oxford University)
Bounded domains, good boundary directions and topology
Camillo De Lellis (University of Zurich)
Regularity and singularity of area-minimizing currents
Pierre-Emmanuel Jabin (University of Maryland)
Regularity estimates for transport equations through "dual norms"
Nicola Fusco (Universita' di Napoli)
On the stability of Almgren's isoperimetric inequality
Michael Falk (Johns Hopkins University)
The Atomistic Origins of Plasticity, Localization and Failure in Amorphous Solids
2013
Marshall Slemrod (University of Wisconsin-Madison)
A Korteweg approach to thermal transpiration and Sone's ghost effect
Leonid Koralov (University of Maryland)
Polymer measures and branching diffusions
Paolo Podio Guidugli (Universita' di Roma Tor Vergata)
On the validation of theories of thin elastic structure
Gilles Francfort (Universite' Paris 13)
Periodic homogenization in Elasto-plasticity
Ihsan Topaloglu (McGill University)
Minimization of an Energy Defined via an Attractive-Repulsive Interaction Potential
Amy Novick-Cohen (Technion, Haifa)
Mobility measurements for grain growth: the grim reaper solution
Yao Yao (University of Wisconsin)
Quasi-static evolution and congested crowd motion
Eliot Fried (McGill University)
Stability and bifurcation of a soap film spanning an elastic loop
Christophe Lacave (Universite' Paris-Diderot)
Well-posedness for Euler 2D in non-smooth domains
Richard Ellis (University of Massachusetts, Amherst)
From Large Deviations to Statistical Mechanics: What Is the Most Likely Way for an Unlikely Event To Happen?
Jose Carrillo (Imperial College, London)
Stable stationary states for repulsive-attractive potentials
Ralph Showalter (Oregon State)
General Porous Medium Equation as a multi-phase methane-hydrate Model
Benoit Pausader (Universite' de Paris XIII)
Global existence for the Euler-Maxwell 2 fluid system
Stephen Watson (University of Glasgow)
G-Covariant Theory of Phase-Ordering Kinetics via the Emergent Symmetry Group G
Robert Jensen (Loyola University Chicago)
Convexity of solutions to nonlinear PDEs
Massimiliano Morini (Universita' di Parma)
Variational nonlocal curvature flows
Robert Jerrard (University of Toronto)
On the stability of filament flows and Schroedinger maps
Frank Merle (Universite' de Cergy-Pontoise)
Blowup for the Generalized Korteweg-de-Vries Equation
Charles Smart (Massachusetts Institute of Technology)
Optimal regularity of Lipschitz extensions
Michel Chipot (University of Zurich)
Elliptic Variational inequalities in unbounded domains
2012
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 18
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 17
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 16
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 15
Matthew Elsey (Courant Institute, New York University)
Simulations of Polycrystalline Grain Growth with Unequal Surface Energies
Isaac Chenchiah (University of Bristol)
Quasi-Static Brittle Damage Evolution with Multiple Damaged Elastic States
Dorian Goldman (Courant Institute)
The Gamma limit of the Ohta-Kawasaki energy: Droplet density and the Renormalized Energy
Marcus Wunsch (ETH, Zurich)
The Hunter-Saxton System and geodesics on (pseudo-) spheres
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 14
Jose' Miguel Urbano (CMUC - University of Coimbra)
Local Holder continuity for doubly nonlinear parabolic equations
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 13
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 12
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 11
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 10
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 9
Tao Huang (University of Kentucky)
Some new results on the uniqueness of heat flow of harmonic maps and nematic liquid crystal flows
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 8
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 7
Misha Neklyudov (University of Tubingen)
The role of noise in ensembles of nanomagnetic particles
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 6
Xin Yang Lu (CNA)
Evolution schemes related to the average distance functional
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 5
Paolo Marcellini (Universita' di Firenze)
Nonlinear elliptic systems with general growth
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 4
Leonard Monsaingeon (Carnegie Melllon University)
Existence of travelling waves for a degenerate non-linear advection-diffusion equation
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 3
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 2
Hao Wu (Fudan University)
Well-posedness and long-time behavior of the Hele-Shaw-Cahn-Hilliard system
Irene Fonseca (Carnegie Mellon University)
Course 21-820: Modern Methods in the Calculus of Variations in Sobolev Spaces
Lecture 1
Paolo Podio Guidugli (Universita' di Roma Tor Vergata)
Dissipative Entropy Makes The Heat Equation Hyperbolic
Robert Pego (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 27
Michael Goldman (Ecole Polytechnique)
Plane-like minimizers, calibrations and differentiability of the stable norm
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 26
Robert Pego (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 25
Marco Morandotti (Carnegie Mellon University)
Self-propulsion in viscous fluids through shape deformation
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 24
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 23
Peter Monk (University of Delaware)
Analysis of Hybridizable Discontinuous Galerkin Methods Applied to the Wave Equation
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 22
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 21
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 20
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 19
Jim Kelliher (UC Riverside)
Bounded vorticity, bounded velocity (Serfati) solutions to 2D Euler equations in an external domain
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 18
Maria Emilianenko (George Mason University)
Course 21-820: Perspectives on Microstructure
Lecture 16
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 16
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 15
Shu-Ming Sun (Virginia Polytechnic Institute)
Existence of Gravity-Capillary Waves on Water of Finite Depth
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 14
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 13
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 12
Dan Blazevski (University of Texas and Georgia Tech)
Classical scattering theory and applications to computing invariant manifolds in chemistry
Katayun Barmak (Columbia University)
Course 21-820: Perspectives on Microstructure
Lecture 11
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 10
Nicola Fusco (Universita' di Napoli)
The sharp quantitative isoperimetric inequality and related inequalities in quantitative form
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 9
Massimiliano Morini (Universita' di Parma)
Motion of elastic thin films by anisotropic surface diffusion with curvature regularization
Shlomo Ta'asan (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 8
A. D. Rollett (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 7
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 6
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 5
Henry Shum (Rudolf Peierls Centre for Theoretical Physics, University of Oxford)
Hydrodynamics and elastodynamics of flagellated bacteria
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 4
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 3
David Kinderlehrer (Carnegie Mellon University)
Course 21-820: Perspectives on Microstructure
Lecture 2
2011
Chris Evans (University of Missouri)
A Strong Maximum Principle for Reaction Diffusion Systems
Michael Shearer (North Carolina State University)
Two Phase Flow in Porous Media: the Saffman-Taylor Instability Revisited
Konstantinos Zygalakis (Oxford)
Qualitative behaviour of numerical methods for SDEs and application to homogenization
Richard Kollar (Comenius University, Bratislava, Slovakia)
Coagulation-fragmentation dynamics in telomeres
Dmitry Vorotnikov (University of Coimbra)
Global dissipative solutions of a coupled problem for image restoration
Greg Hayrapetyan (Carnegie Mellon University)
Geometric evolution of interfaces in the functionalized Cahn-Hilliard equation
David Owen (Carnegie Melllon University)
Moving interfaces that separate loose and compact phases of elastic aggregates
Bernard Dacorogna (EPFL, Lausanne)
On the pullback equation for differential forms
Jose Matias (Instituto Superior Tecnico Lisbon)
Coupled second order singular perturbations for phase transitions
Thomas Laurent (University of California, Riverside)
Aggregation Patches (with movies!)
Matteo Focardi (Universita' degli Studi, Firenze)
An Intrinsic Approach to Manifold Constrained Variational Problems
Pierre Cardaliaguet (University of Paris, Dauphine)
On the homogenization of an equation arising in flame propagation problems
Adrian Tudorascu (West Virginia University)
Weak Lagrangian solutions for the Semi-Geostrophic system in physical space
Charles Smart (Courant Institute, NYU)
Partial regularity for fully nonlinear uniformly elliptic equations
Jeff Ovall (University of Kentucky)
A Framework for Constructing and Analyzing Hierarchical-Type Error Estimators
Yasemin Sengul (University of Coimbra)
Well-posedness of dynamics of microstructure in solids
Arghir Zarnescu (Oxford)
Mathematical problems of the Q-tensor theory of liquid crystals