Tuesday, June 12, 2018 - 15:00 , Location: Skiles 006 , Jean-Christophe Breton , University of Rennes , Organizer: Mayya Zhilova
Random balls models are collections of Euclidean balls whose centers and radii are generated by a Poisson point process. Such collections model various contexts ranging from imaging to communication network. When the distributions driving the centers and the radii are heavy-tailed, interesting interference phenomena occurs when the model is properly zoomed-out. The talk aims to illustrate such phenomena and to give an overview of the asymptotic behavior of functionals of interest. The limits obtained include in particular stable fields, (fractional) Gaussian fields and Poissonian bridges. Related questions will also be discussed.
Thursday, May 10, 2018 - 15:05 , Location: Skiles 005 , Laurent Miclo , Université de Toulouse , Laurent.Miclo@math.univ-toulouse.fr , 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.
Wednesday, May 2, 2018 - 14:00 , Location: Skiles 006 , Hyunki Min , Georgia Tech , firstname.lastname@example.org , Organizer:
Understanding contact structures on hyperbolic 3-manifolds is one of the major open problems in the area of contact topology. As a first step, we try to classify tight contact structures on hyperbolic 3-manifolds. In this talk, we will review the previous classification results and classify tight contact structures on the Weeks manifold, which has the smallest hyperbolic volume. Finally, we will discuss how to generalize this method to classify tight contact structures on general hyperbolic 3-manifolds.
Monday, April 30, 2018 - 14:00 , Location: Skiles 006 , Michael Harrison , Lehigh University , email@example.com , 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.
Series: Combinatorics Seminar
Given a collection of finite sets, Kneser-type problems aim to partition this collection into parts with well-understood intersection pattern, such as in each part any two sets intersect. Since Lovász' solution of Kneser's conjecture, concerning intersections of all k-subsets of an n-set, topological methods have been a central tool in understanding intersection patterns of finite sets. We will develop a method that in addition to using topological machinery takes the topology of the collection of finite sets into account via a translation to a problem in Euclidean geometry. This leads to simple proofs of old and new results.
Series: Analysis Seminar
Abstract: I will state a version of Voiculescu's noncommutative Weyl-von Neumann theorem for operators on l^p that I obtained. This allows certain classical results concerning unitary equivalence of operators on l^2 to be generalized to operators on l^p if we relax unitary equivalence to similarity. For example, the unilateral shift on l^p, 1
Series: Algebra Seminar
The talk reports on joint work with Wayne Raskind and concerns the conjectural definition of a new type of regulator map into a quotient of an algebraic torus by a discrete subgroup, that should fit in "refined" Beilinson type conjectures, exteding special cases considered by Gross and Mazur-Tate.The construction applies to a smooth complete variety over a p-adic field K which has totally degenerate reduction, a technical term roughly saying that cycles acount for the entire etale cohomology of each component of the special fiber. The regulator is constructed out of the l-adic regulators for all primes l simulateously. I will explain the construction, the special case of the Tate elliptic curve where the regulator on cycles is the identity map, and the case of K_2 of Mumford curves, where the regulator turns out to be a map constructed by Pal. Time permitting I will also say something about the relation with syntomic regulators.
Monday, April 23, 2018 - 14:00 , Location: Skiles 006 , Hong Van Le , Institute of Mathematics CAS, Praha, Czech Republic , firstname.lastname@example.org , 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.