## Seminar Categories

- Applied and Computational Math Colloquium (1)
- Applied and Computational Mathematics Seminar (2)
- Climate Seminar (30)
- Colloquium (5)
- Commutative Algebra Seminar (10)
- Differential Geometry and Symplectic Topology Seminar (19)
- IMA Data Science Lab Seminar (4)
- IMA/MCIM Industrial Problems Seminar (4)
- MCFAM Seminar (6)
- Probability Seminar (3)
- Special Events and Seminars (9)
- Student Number Theory Seminar (5)
- Topology Seminar (8)

## Current Series

Wed Sep 11 |
## PDE Seminar3:35pm - Vincent Hall 570Parabolic problems with rough coefficients Pierre Portal,, Australian National University Using form methods, one can solve linear parabolic PDE in divergence form with $L^2$ data in appropriate energy spaces, even when the coefficients are merely bounded measurable in time and space, and no maximum principle is available. This goes back, at least, to the work of Lions and his school in the 1950s. When dealing with $L^p$ data, it is not so clear which $L^p$ like solution space one should use as a replacement of Lions energy space. Depending on the choice, one can solve, for instance, time dependent single equations (Aronson 1968), time independent systems for a range of values of $p$ (Auscher 2005), or stochastic problems with some spatial regularity (starting with Krylov 1994). This summarises joint works with Pascal Auscher, Sylvie Monniaux, Jan van Neerven, and Mark Veraar. |

Wed Sep 25 |
## PDE Seminar3:35pm - Vincent Hall 570Random Tug of War games for the p-Laplacian Marta Lewicka, University of Pittsburgh We propose a new dynamic programming principle related to the Dirichlet problem for the homogeneous p-Laplace equation in connection with the Tug of War games with noise. We also discuss similar approximations in presence of the Robin boundary conditions. For the proofs, we use martingale techniques involving various couplings of random walks and yielding estimates on the involved probabilistic representations. |

Wed Oct 09 |
## PDE Seminar3:35pm - Vincent Hall 570Diffusion in the Mean for a Periodic Schrödinger Equation Perturbed by a Fluctuating Potential Shiwen Zhang, UMN We consider the solution to a tight-binding, periodic Schrödinger equation with a random potential evolving stochastically in time. If the potential evolves according to a stationary Markov process we obtain a positive, finite diffusion constant for the evolution of the solution. More generally, we show that the square amplitude of the wave packet, after diffusive rescaling, converges to a solution of the heat equation. (Joint work with J. Schenker and Z. Tilocco at the Michigan State University). |

Wed Oct 16 |
## PDE Seminar3:35pm - Vincent Hall 570Optimal local well-posedness for the derivative nonlinear Schrodinger's equation Yu Deng, University of Southern California In joint work with Andrea Nahmod and Haitian Yue, we prove local well-posedness for the derivative nonlinear Schrodinger's equation in Fourier-Lebesgue space which has the same scaling as H^s for any s>0. This closes the gap left open by the work of Grunrock-Herr where s>1/4. Here there is no trilinear estimate in any standard function space, instead we will construct the solution in a nonlinear submanifold (of a function space) by exploiting its structure. This is somehow inspired by the theory of para-controlled distributions that Gubinelli et al. developed for stochastic PDEs, but our arguments are purely deterministic. |