| Weekly Meetings: | 3:00pm - 3:50pm Mondays in MTH 1311 | |
| Team Directors: | Stuart Antman (ssa"at"math) | Maria Cameron (cameron"at"math) |
| Sandra Cerrai (cerrai"at"math) | Manoussos Grillakis (mng"at"math) | |
| Pierre Emmanuele Jabin (pjabin"at"math) | David Levermore (lvrmr"at"math) | |
| Doron Levy (dlevy"at"math) | Matei Machedon (mxm"at"math) | |
| Dionisios Margetis (dio"at"math) | Antoine Mellet (mellet"at"math) | |
| Eitan Tadmor (tadmor"at"cscamm) | Konstantina Trivisa (trivisa"at"math) |
| 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 |
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis, Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa |
| Visitor: | Yongyong Cai |
| Postdocs: | Roman Andreev, Sebastien Motsch, Thomas Rey |
| Students: |
Josh Ballew,
Matias Delgadino,
Stefan Doboszczak,
Akira Horiguchi,
Wenqing Hu, Chunting Lu, Megan Magnoni, Ioannis Markou, Kanna Nakamura, Sam Punshon-Smith, Alexey Stepanov, Nathan Suberi, Changhui Tan, Ignacio Tomas, Ming Zhong |
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 has been 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.
| 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 |
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis, Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa |
| Students: |
Josh Ballew,
Matias Delgadino,
Stefan Doboszczak,
Wenqing Hu,
Elif Kuz, Chunting Lu, Kanna Nakamura, Joshua Parker, Sam Punshon-Smith, Luyu Sun, Changhui Tan, Jinxin Xue, Dongmian Zou |
| 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 |
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis, Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa |
| Postdocs: | Hantaek Bae, Sebastien Motsch |
| Students: |
Josh Ballew,
Xuwen Chen,
Matias Delgadino,
Stefan Doboszczak,
Chen Dong, Chunting Lu, Ioannis Markou, Changhui Tan, Matthew Temba |
| 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
|
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis,
Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Peter Wolfe |
| Postdocs: | Hantaek Bae, Trygve Karper, Sebastien Motsch, Abner Salgado |
| Students: |
Josh Ballew,
Xuwen Chen,
Chunting Lu,
Ioannis Markou,
Kana Nakamura,
Ian Schoch, Funing Shi, Douglas Ulrich, Ed Yasutake, Ding Zi, Ming Zong |
| 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 |
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis,
David Levermore, Doron Levy, Matei Machedon, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Peter Wolfe |
| Postdocs: | Hantaek Bae, Trygve Karper, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan |
| Students: | Josh Ballew, Xuwen Chen, Chunting Lu, Ioannis Markou |
| 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) |
| Faculty: |
Stuart Antman,
Maria Cameron,
Sandra Cerrai,
Manoussos Grillakis,
David Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Peter Wolfe |
| Postdocs: | Suleyman Ulusoy |
| Students: |
Josh Ballew,
Ariel Hafftka,
Ioannis Markou,
Kanna, Nakamura, Changhui Tan, Dan Weinberg |
| 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 |
| Faculty: |
Stuart Antman,
Sandra Cerrai,
Manoussos Grillakis,
David Levermore,
Doron Levy, Matei Machedon, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Peter Wolfe |
| Visitors: | Animikh Biswas |
| Postdocs: | Hantaek Bae, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan |
| Students: | Brent Baccala, Xuwen Chen, Ioannis Markou |
| 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 |
| Faculty: |
Stuart Antman,
Sandra Cerrai,
Manoussos Grillakis,
David Levermore,
Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Athanasios Tzavaras, Peter Wolfe |
| Visitors: | Animikh Biswas, J.T. Halbert, Jae Ryong Kweon |
| Postdocs: | Hantaek Bae, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan |
| Students: | Chungting Lu, Ioannis Markou, Karl Schmitt, Rongrong Wang |
| 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 |
| Faculty: |
Stuart Antman,
Sandra Cerrai,
Manoussos Grillakis,
David Levermore, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa |
| Postdocs: | Arthur Cheng, Weiran Sun |
| Students: | Avanti Athreya, Cynthia Bossard, J.T. Halbert, Ioannis Markou, Hyejin Kim, Karl Schmitt, Konstantinos Spiliopoulos |
| 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 |
| Faculty: | Stuart Antman, Sandra Cerrai, David Levermore, Konstantina Trivisa, Athanasios Tzavaras |
| Postdocs: | Arthur Cheng, Weiran Sun |
| Students: | Avanti Athreya, J.T. Halbert, Ioannis Markou, Hyejin Kim, Alexey Miroshnikov, Konstantinos Spiliopoulos |