Seminars and Colloquia by Series

Thursday, May 10, 2018 - 15:05 , Location: Skiles 005 , Laurent Miclo , Université de Toulouse , , Organizer: Michael Damron
A Markov intertwining relation between two Markov processes X and Y is a weak similitude relation G\Lambda = \Lambda L between their generators L and G, where \Lambda is a transition kernel between the underlying state spaces. This notion is an important tool to deduce quantitative estimates on the speed of convergence to equilibrium of X via strong stationary times when Y is absorbed, as shown by the theory of Diaconis and Fill for finite state spaces. In this talk we will only consider processes Y taking as values some subsets of the state space of X. Our goal is to present extensions of the above method to elliptic diffusion processes on differentiable manifolds, via stochastic modifications of mean curvature flows.  We will see that Pitman's theorem about the intertwining relation between the Brownian motion and the Bessel-3 process is curiously ubiquitous in this approach.  It  even serves  as an inspiring guide to construct couplings associated to finite Markov intertwining relations via random mappings, in the spirit of the coupling-from-the-past algorithm of Propp and Wilson and of the evolving sets of Morris and Peres.
Monday, April 30, 2018 - 14:00 , Location: Skiles 006 , Michael Harrison , Lehigh University , , Organizer: Mohammad Ghomi
The h-principle is a powerful tool in differential topology which is used to study spaces of functionswith certain distinguished properties (immersions, submersions, k-mersions, embeddings, free maps, etc.). Iwill discuss some examples of the h-principle and give a neat proof of a special case of the Smale-HirschTheorem, using the "removal of singularities" h-principle technique due to Eliashberg and Gromov. Finally, I willdefine and discuss totally convex immersions and discuss some h-principle statements in this context.
Wednesday, April 25, 2018 - 01:55 , Location: Skiles 005 , March Boedihardjo , UCLA , Organizer: Shahaf Nitzan
Series: PDE Seminar
Tuesday, April 24, 2018 - 15:00 , Location: Skiles 006 , Alberto Maspero , SISSA , , Organizer: Yao Yao
Monday, April 23, 2018 - 14:00 , Location: Skiles 006 , Hong Van Le , Institute of Mathematics CAS, Praha, Czech Republic , , Organizer: Thang Le
Novikov  homology was introduced by  Novikov in  the early 1980s motivated by problems  in hydrodynamics.  The Novikov inequalities in the Novikov homology theory give lower bounds for the number of critical points of a Morse  closed 1-form  on a compact  differentiable manifold M. In the first part of my talk  I shall survey  the Novikov homology theory in finite dimensional setting and its  further developments  in infinite dimensional setting with applications in the theory of symplectic fixed points and Lagrangian intersection/embedding problems. In the  second part of my talk I shall report  on my recent joint work with Jean-Francois Barraud  and Agnes Gadbled on construction  of the Novikov fundamental group  associated to a  cohomology class  of a closed 1-form  on M  and its application to obtaining  new lower bounds for the number of critical points of  a Morse 1-form.
Thursday, April 19, 2018 - 15:05 , Location: Skiles 006 , Tomasz Tkocz , Carnegie Mellon University , , Organizer: Michael Damron
 We shall prove that a certain stochastic ordering defined in terms of convex symmetric sets is inherited by sums of independent symmetric random vectors. Joint work with W. Bednorz.
Thursday, April 19, 2018 - 11:00 , Location: Skiles 006 , Tim Austin , UCLA Mathematics Department , Organizer: Mayya Zhilova
Series: PDE Seminar
Tuesday, April 17, 2018 - 15:00 , Location: Skiles 006 , Jian-Guo Liu , Duke University , , Organizer: Yao Yao
Monday, April 16, 2018 - 15:30 , Location: Skiles 005 , Yu Pan , MIT , Organizer: Caitlin Leverson
Monday, April 16, 2018 - 14:00 , Location: Skiles 006 , Ken Baker , University of Miami , /TBA , Organizer: Caitlin Leverson