Research Interaction Team Website
Applied Partial Differential Equations
Spring 2016

Tentative Schedule

Date	Speaker	Topic
8 February	David Levermore	Riccati Equations Arising from Hydrodynamics
15 February	P.-E. Jabin	Navier-Stokes-Fourier System (Snow!)
22 February	Michele Coti Zelati	Mixing and Enhanced Dissipation in Shear Flows
29 February	Jacky Chong	Beyond Mean-Field Equations
7 March	Zhenfu Wang	Mean-Field Limits of Stochastic Particle Systems
14 March	Spring Break
21 March	Zhenning Cai	Spectral Method for the Boltzmann Equation
28 March	Matias Delgadino	The Cahn-Hilliard Equation as a Wasserstein Gradiant Flow
4 April	Eitan Tadmor	Riccati Revisited: Critical Thresholds in Eulerian Dynamics
11 April	Ian Johnson	Diffusion Approximations to Master Equations with Application to Crystal Growth
18 April	Kilian Cooley	ENO and WENO Stability
25 April	Siming He	Keller-Segel Equation
2 May	George Quinn	Biometric Applications of Partial Differential Equations
9 May	Martin Molina	Equilibration Rates for Granular Media and Related Equations

Posting on the Mathematics Department Website

RIT Related Local Activities

• PDE/Applied Math Seminar: 3:30pm Thursdays in MTH 3206
• Numerical Analysis Seminar: 3:30pm Tuesdays in MTH 3206
• CSCAMM Seminar: 2:00pm Wednesdays in CSI 4122
• Student Analysis and PDE Seminar: 2:00pm Fridays in MTH 3206
• Informal Geometric Analysis Seminar: 4:00pm Thursdays in MTH 2300
• February Fourier Talks (FFT) 2016, 18-19 February in MTH 3206
• Avron Douglis Lecture: Laszlo Szekelyhidi
  The H-principle in Fluid Mechanics,
  3:30pm on Thursday, 17 March in MTH 3206
• Workshop on Dynamical Systems and Related Topics, 15-17 April in MTH 3206
• Aziz Lecture: Irene Fonseca, Carnegie Mellon University
  Quantum Dots and Dislocations: Dynamics of Materials,
  3:15pm on Wednesday, 4 May in MTH 3206

Spring 2016 RIT Participants

RIT Plan

Graduate Prerequisites: Analysis (Math 630), or PDEs (Math 673), or ODEs (Math 414 or 670), or numerics (AMSC 666 or 660), or probability (STAT 600). Some knowledge of partial differential equations would be useful. Permission of a Team Director.

Undergraduate Prerequisites: Advanced calculus (Math 410) and differential equations (Math 246). Any of the following are useful but not required: complex variables (Math 463), ODE (Math 414), PDE (Math 462), computation (AMSC 460 or AMSC 466). Permission of a Team Director.

Graduate Program: Team members will make presentations either on readings of fundamental papers or book chapters, or on their own analytical and/or numerical investigations. When appropriate, these may be developed into more formal presentations for seminars, conferences, or publication. Team members will be asked to help mentor more junior team members.

Undergraduate Program: Same as above, as appropriate to the background of the student.

Credit: Students can participate without signing up for credit. Students who sign up for credit typically take one credit; they are expected to attend regularly and to make one presentation. Students who sign up for two credits are expected to attend regularly and to either make three presentations or make one presentation and produce a related written report or project. This last option can be used by AMSC students to prepare for their oral candidacy exam; the written part becomes their AMSC Candidacy Prospectus, and their presentation becomes practice for their oral exam. Students who sign up for three credits will be expected to attend regularly, to make three presentations, and to produce a related written report or project.

Work Schedule: Meetings will be held weekly.

RIT Activity in Past Semesters

Date	Speaker	Topic
14 September	Michele Coti Zelati	Regularity Results for Active Scalar Equations
21 September	Pierre Emmanuel Jabin	Renormalized Solutions: An Introduction to the Well Posedness Theory for Advection Equations
28 September	Alexey Stepanov	Analysis of Dynamical Solutions of 2D Nonlinear Viscoelasticity
5 October	Heyrim Cho	Probability Density Approach for Stochastic Systems with Colored Noise
12 October	Jacky Chong	Derivation of the Nonlinear Schrödinger Equation in R^3
19 October	Dio Margetis	On Classical Solutions of Maxwell's Equations: Ghost Waves on Graphene Sheets
26 October	Zhenfu Wang	Mean-Field Limit for Second-Order Systems with a Bounded Interaction Kernel
2 November	Scott Smith	Global Existence of Renormalized Martingale Solutions to a Stochastic Boltzmann Equation
9 November	Kilian Cooley	Energy-Stable WENO Methods
16 November	Sam Punshon-Smith	Coarsening of One-Dimensional Particle Systems
23 November	Joshua Schneider	Morphological Evolution of Crystal Surfaces: Connecting Atomistic and Continuum Models
30 November	Ian Johnson	A Stochastic Difference Scheme for Step Flow in Crystal Growth Postponed to the Spring Semester
7 December	Jacob Bedrossian	Subcritical Transition for the Three Dimensional Incompressible Navier-Stokes System

Fall 2015 RIT Participants

Topics Covered During Spring 2015

Date	Speaker	Topic
2 February	P-E Jabin	An Introduction to Besov Spaces
9 February	Jacob Bedrossian	Kinetic Theory of Plasmas
16 February	Michele Coti Zelati	Regularity Results for Active Scalar Equations
23 February	Changhui Tan	Presureless Euler Equations
2 March	Dio Margetis	Density Functional Theory
9 March	Siming He	Sub-Critical Keller-Segel Equation
16 March	Spring Break
23 March	Konstantina Trivisa	TBA
30 March	Joshua Schneider	Model of Crystal Growth Arising from a Particle System
6 April	Sam Punshton-Smith	Stochastic Representations of Fluids
13 April	Scott Smith	Concentration Compactness
20 April	Zhenfu Wang	TBA
27 April	Luyu Sun	Self-Organized Dynamics

Spring 2015 RIT Participants

Topics Covered During Fall 2014

Date	Speaker	Topic
15 September	Dio Margetis	Bosons Systems: An Introduction I
22 September	Dio Margetis	Bosons Systems: An Introduction II
29 September	Jacob Bedrossian	Mixing
6 October	Sam Punshon-Smith	Hydrodynamic Limits for Hamiltonian Systems
13 October	P.E. Jabin	Ergodic Theory for Transport Equations
20 October	Maria Cameron	Metastability, Spectra, and Eigencurrents of Networks Representing Energy Landscapes
27 October	Young Researchers Workshop in CSCAMM	Multiscale Phenomena: Modeling, Analysis and Computation
3 November	Manos Grillakis	On the BCS theory of Superconductivity
10 November	Mickey Salins	Stochastic PDE's
17 November	Colleen M. Stock	Seminumeric Approaches to the Eikonal Equation
24 November	Zhenfu Wang	Mean Field Limits for Stochastic Particles
1 December	Jacky Chong	Derivation of the 2-D Nonlinear Schrodinger Equation on the Torus
8 December	Sandra Cerrai	The Exit Problem for PDE Perturbed by Rough Noise

Fall 2014 RIT Participants

Topics Covered During Spring 2014

Date	Speaker	Topic
3 February	Manoussos Grillakis	On the Wave-Map Problem: Geometry and Symmetries
10 February	Spyridon Kamvissis	Introduction to Riemann-Hilbert Methods: Connection to Soliton Equations
17 February	Matei Machedon	Littlewood-Paley Theory
24 February	Spyridon Kamvissis	Applications of Riemann-Hilbert Methods: Orthogonal Polynomials and Random Matrices
3 March	Eitan Tadmor	Entropy Structure and Hyperbolic Systems (snow day)
10 March	David Levermore	Scattering Theory for the Boltzmann Equation and the Arrow of Time
24 March	Pierre Emmanuele Jabin	Well-Posedness for Parabolic Equations and Stochastic Differential Equations with Rough Coefficients
31 March	Matias Delgadino	Introduction to the Harmonic Obstacle Problem with an Application to Interaction Energy Minimizers
7 April	Stefan Doboszczak	Introduction to PDE Existence via Weak Convergence Methods
14 April	Chunting Lu	Acoustic Limit about a Global Maxwellian for Solutions of the Boltzmann Equation that have Finite Second Moments
21 April	Changhui Tan	On the Smoluchowski Coagulation Equation and Gelation Formation
28 April	Ki-Net Conference	Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs
5 May	Scott Smith	On the Katz-Pavlovic Dyadic Model of the Euler Equations
12 May	Mazier Raissi	Multi-Fidelity Stochastic Collocation Method for Parabolic PDEs with Random Forcing

Spring 2014 RIT Participants

Topics Covered During Fall 2013

Date	Speaker	Topic
16 September	Pierre Emmanuele Jabin	Ordinary Differential Equations and Linear Advection Equations: From Cauchy-Lipschitz to Renormalized Solutions
23 September	Matias Delgadino	Introduction to Optimal Transportation
30 September	Pierre Emmanuele Jabin	Introduction to the Classical Theory for Stochastic Differerential Equations and the Connection with Diffusion PDE's
7 October	David Levermore	Statistical Approaches to Modeling Dynamics: Some Background
14 October	CSCAMM Workshop	Kinetic and Macroscopic Models for Complex Systems
21 October	Matias Delgadino	Displacement Convexity and Optimal Transportation
28 October	Eitan Tadmor	Partial Regularity for the Navier-Stokes System of Hydrodynamics
4 November	Sam Punshon-Smith	Boltzmann-Grad Limit for Particles Interacting via Short-Range Potentials: Overview
11 November	Thomas Rey	Perturbative Existence Theories for the Boltzmann Equation
18 November	Scott Smith	Martingales and Fluids
25 November	Elif Kuz	Rate of Convergence to the Mean Field for Interacting Bosons
2 December	Zhenfu Wang	Monge-Mather Shortening Principle
9 December	Stu Antman	A Fluid-Solid Interaction Problem

Fall 2013 RIT Participants

Topics Covered During Spring 2013

Date	Speaker	Topic
4 February	Pierre Emmanuele Jabin	Calderon Zygmund Theory
11 February	Thomas Rey	Hydrodynamic Limit of the Granular Gases Equation
18 February	Kanna Nakamura	Viscosity Solutions with Shocks of Degenerate Parabolic Equations (Postponed)
25 February	Roman Andreev	Stability of Space-Time Petrov-Galerkin Discretizations for Parabolic Equations
4 March	Josh Ballew	Weak-Strong Uniqueness of a Navier-Stokes-Smolkowski System
11 March	Yong-Yong Cai	Bose-Einstein Condensation for Dispersive Equations
25 March	David Levermore	Pseudodifferential Operators
1 April	Thomas Rey	Deterministic Numerical Methods for the Boltzmann Equation
8 April	Ioannis Markou	Diffusive Limit for a Spatially Inhomogeneous Fokker-Planck Equation
15 April	Antoine Mellet	Free Boundary Problem for Thin Films
22 April	Eitan Tadmor	Partial Differential Equations for Image Processing
29 April	Kanna Nakamura	Viscosity Solutions with Shocks of Degenerate Parabolic Equations
6 May	Alexey Stepanov	Global Methods for Problems of Mechanical Growth

Spring 2013 RIT Participants

Topics Covered During Fall 2012

Date	Speaker	Topic
17 September	David Levermore	Coarsening of Particle Systems
24 September	Konstantina Trivisa	On the Doi Model for the Suspension of Rod-Like Molecules
1 October	Maria Cameron	Analysis of the Stochastic Network Associated with the Lennard-Jones-38 Cluster
8 October	Changhui Tan	Macroscopic Flocking Models
15 October	David Levermore	Modeling Profolios with Risky Assets
22 October	Matias Delgadino	Flocking Modeled by Kinetic Equations
29 October	Kanna Nakamura	Remnants of Discrete Dynamics at a Free Boundary in a Continuum Limit
5 November	KI-Net Conference	Kinetic Description of Social Dynamics: From Consensus to Flocking
12 November	Sam Punshon-Smith	Fokker-Planck Model of "Integrate and Fire" Neuronal Networks
19 November	Sandra Cerrai	Pathwise Uniqueness for Stochastic Partial Differential Equations in Banach Spaces
26 November	Doron Levy	Crime Models
3 December	Wenqing Hu	Second-Order Elliptic Equations with a Small Parameter
10 December	Dionisios Margetis	High-Frequency Asymptotics of Feynman Diagrams in Quantum Field Theory: Abelian Case

Fall 2012 RIT Participants

Topics Covered During Spring 2012

Date	Speaker	Topic
20 February	David Levermore	Global Maxwellians over All Space and Their Relation to Converved Quantities of Classical Kinetic Equations
27 February	Eitan Tadmor	Marcinkiewicz Interpolation Theorem and Applications: An Introduction
5 March	Pierre Emmanuele Jabin	Velocity Averaging
12 March	Sebastien Motsch	A Traffic Model for Pedestrians and Its Comparison with Experimental Data
26 March	David Levermore	Kaniel-Shinbrot Iteration and Global Solutions of the Cauchy Problem for the Boltzmann Equation
2 April	Hantaek Bae	Navier-Stokes with Supercritical Initial Data
9 April	Antoine Mellet	Equilibrium Capillary Surfaces and Sliding Drops
16 April	Eitan Tadmor	Compensated Compactness
23 April	Josh Ballew	Low Mach Number Limits to the Navier-Stokes-Smoluchowski System
30 April	Chunting Lu	Velocity Averaging in L^1 for the Transport Equation
7 May	Pierre Emmanuele Jabin	Wasserstein Distance and Optimal Transportation

Spring 2012 RIT Participants

Topics Covered During Fall 2011

Date	Speaker	Topic
19 September	David Levermore	Model Reduction
26 September	Stuart Antman	Degree Theory
3 October	Konstantina Trivisa	Admissibility of Weak Solutions - Entropy
10 October	TBA	TBA
17 October	Ed Yasutake	Aymptotics
24 October	Xuwen Chen	Rigorous Derivation of the 2d Cubic Nonlinear Schroedinger Equation with Anisotropic Switchable Quadratic Traps
31 October	TBA	TBA
7 November	Kanna Nakamura	Homogenization of Heterogeneous Materials
14 November	Ding Zi	Newton Polynomials
21 November	Sandra Cerrai	Gamma Convergence
28 November	Ioannis Markou	Hypocoercivity
5 December	Dionisios Margetis	On High-Frequency Asymptotics of Quantum Field Theories

Fall 2011 RIT Participants

Topics Covered During Spring 2011

Date	Speaker	Topic
14 February	David Levermore	Bose-Einstein Condensation and the Kompaneets Equation
21 February	no speaker	no speaker
28 February	no speaker	no speaker
7 March	Suleyman Ulusoy	Keller-Segel Type Systems in Higher Dimensions
14 March	Xuwen Chen	Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy with a Switchable Quadratic Trap
28 March	Knut Waagan	Stable Numerical Schemes for Nonlinear Elasticity
4 April	Sebastien Motsch	Models of Flocking with Asymmetric Interactions
11 April	Trygve Karper	Convergence of Numerical Methods for Compressible Stokes Flow
18 April	Sandra Cerrai	Small Mass Asymptotics for a Charged Particle in a Magnetic Field and the Long-Time Influence of Small Perturbations
25 April	Hantaek Bae	Analyticity and Time Decay of Solutions to the 3D Navier-Stokes Equations and 2D Quasi-Geostrophic Equations
2 May	Peter Wolfe	Discontinuous Petrov-Galerkin Methods
9 May	Alexey Miroshnikov	Variational Schemes in Nonlinear Elasticity, Convergence and Relative Entropy

Spring 2011 RIT Participants

Topics Covered During Fall 2010

Date	Speaker	Topic
20 September	Stuart Antman	Formal Aymptotics of Heavily-Burdened, Deformable Bodies
27 September	Antoine Mellet	Fractional Diffusion Limits for Kinetic Equations
4 October	David Levermore	Corrections to Diffusion Approximations Derived from Kinetic Equations
11 October	Dionisios Margetis	Notions of Noise in Material Science
18 October	Suleyman Ulusoy	Aymptotics of Heavily-Burdened, Deformable Bodies
25 October	Ioannis Markou	Convergence to Equilibria of Solutions to a Fokker-Planck Equation
1 November	Maria Cameron	Computing Transition Paths for Rare Events
8 November	Josh Ballew	Singular Limits of the Compressible Navier-Stokes System
15 November	Kanna Nakamura	Evolution of Crystal Surface: Boundary Conditions and Decay Estimates
22 November	Eitan Tadmor	Linear PDEs in Critical Regularity Spaces: Hierarchical Construction of their Nonlinear Solutions
29 November	Changhui Tan	Hierarchical Construction of Bounded Solutions to div U = f
6 December	Konstantina Trivisa	Fluid-Particle Interactions (postponed until spring)

Fall 2010 Participants

Topics Covered During Spring 2010

Date	Speaker	Topic
8 February	Brent Baccala	Postponed due to Snow!
15 February	Knut Waagan	Numerical Solution of Astrophysical Magnetohydrodynamics in Multi-Dimensions
22 February	Sandra Cerrai	Normal Fluctuations Around the Averaged Motion for a Class of Reaction-Diffusion Equations Perturbed by a Fast Oscillating Stochastic Term
1 March	Hantaek Bae	Free Boundary-Value Problem of the Navier-Stokes Equations with Surface Tension
8 March	Xuwen Chen	Nonlinear Schroedinger Equations
22 March	Peter Wolfe	An Introduction to Evans Functions
29 March	Stu Antman	TBA
5 April	Brent Baccala	A Stress-Free Introduction to Differential Algebra
12 April	Antoine Mellet	Homogenization of Some Obstacle Problems
19 April	Dave Levermore	Global Classical Solutions of the Boltzmann Equation with Noncutoff Kernels a'la Gressman and Strain I
26 April	Manoussos Grillakis	Global Classical Solutions of the Boltzmann Equation with Noncutoff Kernels a'la Gressman and Strain II
3 May	Animikh Biswas	TBA
10 May	Sebastien Motsch	Models of Flocking: the Cucker-Smale Model and Beyond

Spring 2010 Participants

Topics Covered During Fall 2009

Date	Speaker	Topic
14 September	Matei Machedon	Quantum Dynamics of Many-Body Systems, the Hartree Equation, and Beyond Joint work with M. Grillakis and D. Margetis
21 September	FRG Meeting: Tai-Ping Liu et. al.	Kinetic Description of Multiscale Phenomena Room: CSIC 4122
28 September	Dave Levermore	Dissperive Corrections to the Compressible Navier-Stokes System
5 October	Jae Ryong Kweon	Discontinuity of Solutions to the Compressible Navier-Stokes Equations on Bounded Domains with Corners
12 October	Aziz Lecture: Thomas J.R. Hughes	Isogeometric Analysis: Computational Mechanics based on Modern Developments in Computational Geometry Room: MATH 3206
19 October	Stu Antman	Invariance and Computation for Hyperbolic Conservation Laws
26 October	Konstantina Trivisa	Hyperbolic Balance Laws: Sharp Decay Rates & Consequences
2 November	Suleyman Ulusoy	Asymptotic Equipartition and Long-Time Behavior of Weak Solutions for the Hele-Shaw Flow Problem
9 November	Dio Margetis	Metamaterials and Metasurfaces: A Homogenization (PDE) Perspective
16 November	Sandra Cerrai	postponed to spring due to special seminar
23 November	Animikh Biswas	Analyticity and Gevrey Class Technique for Navier-Stokes and Related Equations
30 November	Hantaek Bae	The Littlewood-Paley Theory and Applications to PDEs
7 December	Knut Waagan	Numerical Solution of Astrophysical Magnetohydrodynamics in Multi-Dimensions postponed to spring due to special seminar

Fall 2009 RIT Participants

Topics Covered During Spring 2009

Date	Speaker	Topic
9 February	J.T. Halbert	Local Equilibrium for Brownian Particles
16 February	David Levermore	Classical Kinetic Equations, Gaussian Moment Closures, and Fluid Regimes
23 February	Konstantinos Spiliopoulos	Large Deviations Principle for Feller Diffusion Processes and Wave Front Propagation
2 March	Stuart Antman	Invariance and Computation for Hyperbolic Conservation Laws (postponed due to snow)
9 March	Ioannis Markou	The Rouse and Zimm Models in Polymer Dynamics
23 March	Eitan Tadmor	A New Approach to the 2D Pressureless Equations
30 March	Dionisios Margetis	Homogenization of Reconstructed Surfaces and Bose-Einstein Condensates
6 April	Sandra Cerrai	Quasipotentials and Exit Times
13 April	Antoine Mellet	Front Propagation in Heterogeneous Media
20 April	Konstantina Trivisa	Asymptotics and Navier-Stokes
27 April	Manoussos Grillakis	Bose-Einstein Condensates
4 May	Arthur Cheng	Two-Phase Euler
11 May	Cynthia Bossard	Mathematical Models for Stock Prices

Spring 2009 RIT Participants

Topics Covered During Fall 2008

Date	Speaker	Topic
17 September	Konstantinos Spiliopoulos	Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection
	Sandra Cerrai	Smoluchowski-Kramers Approximation for Stochastic PDEs
24 September	Alexey Miroshnikov	Radial Shocks in Elastodynamics
	Stuart Antman	Time-Asymptotics for Nonlinear PDEs
1 October	Avanti Athreya	Metastability for Nearly-Hamiltonian Systems
	Weiran Sun	Low Mach Number Limits for Dispersive Navier-Stokes Systems
8 October	J.T. Halbert	Dissipative Particle Dynamics
	David Levermore	Equations-of-State for Pressure
15 October	Konstantinos Spiliopoulos	Reaction-Diffusion Equations in Narrow Domains and Wave Front Propagation
22 October	Avanti Athreya	Large Deviations, Metastability, and Averaging for Diffusion Processes
29 October	Arthur Cheng	The Interaction between Nonlinear Koiter Shells and Viscous Fluids
5 November	Alexey Miroshnikov	A Time Approximation Scheme for the Equations of Elastodynamics in the Radial Case
12 November	Konstantina Trivisa	On the Dynamics of Multicomponent Flows (postponed to 20 November PDE Seminar)
19 November	Sandra Cessai	Fast Diffusion Asymptotics for Stochastic Reaction-Diffusion Equations with Boundary Noise
3 December	Hyejin Kim	Weak Convergence of D_v D_u - Processes
10 December	Weiran Sun	Low Mach Number Limits for Dispersive Navier-Stokes Systems

Fall 2008 RIT Participants