Seminars and Colloquia by Series

Wednesday, February 13, 2019 - 13:55 , Location: Skiles 005 , Michael Loss , Georgia Tech , Organizer: Shahaf Nitzan
Wednesday, February 13, 2019 - 12:05 , Location: Skiles 006 , Josephine Yu , Georgia Tech , Organizer: Trevor Gunn
Monday, February 11, 2019 - 14:00 , Location: Skiles 006 , Daniel Álvarez-Gavela , IAS , Organizer: John Etnyre
We will present an h-principle for the simplification of singularities of Lagrangian and Legendrian fronts. The h-principle says that if there is no homotopy theoretic obstruction to simplifying the singularities of tangency of a Lagrangian or Legendrian submanifold with respect to an ambient foliation by Lagrangian or Legendrian leaves, then the simplification can be achieved by means of a Hamiltonian isotopy. We will also discuss applications of the h-principle to symplectic and contact topology.
Monday, February 11, 2019 - 13:55 , Location: Skiles 005 , Prof. Roland Glowinski , University of Houston , roland@math.uh.edu , Organizer: Hao Liu
Monday, February 11, 2019 - 12:50 , Location: TBA , Andrew Obus , Baruch College, CUNY , Andrew.Obus@baruch.cuny.edu , Organizer: Padmavathi Srinivasan
TBA
Monday, February 11, 2019 - 12:45 , Location: Skiles 006 , Daniel Álvarez-Gavela , IAS , Organizer: John Etnyre
The semi-cubical cusp which is formed in the bottom of a mug when you shine a light on it is an everyday example of a caustic. In this talk we will become familiar with the singularities of Lagrangian and Legendrian fronts, also known as caustics in the mathematics literature, which have played an important role in symplectic and contact topology since the work of Arnold and his collaborators. For this purpose we will discuss some basic singularity theory, the method of generating families in cotangent bundles, the geometry of the front projection, the Legendrian Reidemeister theorem, and draw many pictures of the simplest examples.
Thursday, February 7, 2019 - 15:05 , Location: Skiles 006 , Atilla Yilmaz , Temple University , atilla.yilmaz@temple.edu , Organizer: Michael Damron
I will present joint work with Elena Kosygina and Ofer Zeitouni in which we prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear initial conditions have representations involving exponential expectations of controlled Brownian motion in a random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and is explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in a random potential. The proof involves large deviations, construction of correctors which lead to exponential martingales, and identification of asymptotically optimal policies.
Wednesday, February 6, 2019 - 15:00 , Location: Skiles 006 , Anna Lytova , University of Opole , anna.lytova@gmail.com , Organizer: Galyna Livshyts
TBA
Wednesday, February 6, 2019 - 13:55 , Location: Skiles 005 , Dario Alberto Mena , University of Costa Rica , Organizer: Galyna Livshyts
TBA
Wednesday, February 6, 2019 - 12:05 , Location: Skiles 006 , Jennifer Hom , Georgia Tech , Organizer: Trevor Gunn

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