Seminars and Colloquia Schedule

Monday, April 23, 2018 - 14:00 , Location: Skiles 006 , Hong Van Le , Institute of Mathematics CAS, Praha, Czech Republic , , Organizer: Thang Le
Novikov&nbsp; homology was introduced by&nbsp; Novikov in&nbsp; the early 1980s motivated by problems&nbsp; in hydrodynamics.&nbsp; The Novikov inequalities in the Novikov homology theory give lower bounds for the number of critical points of a Morse&nbsp; closed 1-form&nbsp; on a compact&nbsp; differentiable manifold M. In the first part of my talk&nbsp; I shall survey&nbsp; the Novikov homology theory in finite dimensional setting and its&nbsp; further developments&nbsp; in infinite dimensional setting with applications in the theory of symplectic fixed points and Lagrangian intersection/embedding problems. In the&nbsp; second part of my talk I shall report&nbsp; on my recent joint work with Jean-Francois Barraud&nbsp; and Agnes Gadbled on construction&nbsp; of the Novikov fundamental group&nbsp; associated to a&nbsp; cohomology class&nbsp; of a closed 1-form&nbsp; on M&nbsp; and its application to obtaining &nbsp;new lower bounds for the number of critical points of&nbsp; a Morse 1-form.
Monday, April 23, 2018 - 15:00 , Location: Skyles006 , , Georgia Tech/Ben-Gurion University ,
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.
Series: PDE Seminar
Tuesday, April 24, 2018 - 15:00 , Location: Skiles 006 , , SISSA , , Organizer: Yao Yao
(Due to a flight cancellation, this talk will be moved to Thursday (Apr 26) 3pm at Skiles 257). We prove an abstract theorem giving a $t^\epsilon$ bound for any $\epsilon> 0$ on the growth of the Sobolev norms in some abstract linear Schrödinger equations. The abstract theorem is applied to&nbsp; nonresonant Harmonic oscillators in R^d. The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. Finally, time permitting, we will show how to construct a perturbation of the harmonic oscillator which provokes growth of Sobolev norms.
Wednesday, April 25, 2018 - 01:55 , Location: Skiles 005 , March Boedihardjo , UCLA , Organizer: Shahaf Nitzan
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<p<\infty, is similar to a compact perturbation of the direct sum of the unilateral shift and the bilateral shift. When p=2, this is a classical result and similarity can be chosen to be unitary equivalence.
Series: PDE Seminar
Thursday, April 26, 2018 - 15:00 , Location: Skiles 257 , , SISSA , , Organizer: Yao Yao
We prove an abstract theorem giving a $t^\epsilon$ bound for any $\epsilon> 0$ on the growth of the Sobolev norms in some abstract linear Schrödinger equations. The abstract theorem is applied to&nbsp; nonresonant Harmonic oscillators in R^d. The proof is obtained by conjugating the system to some normal form in which the perturbation is a smoothing operator. Finally, time permitting, we will show how to construct a perturbation of the harmonic oscillator which provokes growth of Sobolev norms.
Friday, April 27, 2018 - 15:00 , Location: Skiles 202 , Brian Kennedy , School of Physics, Georgia Tech , Organizer: Michael Loss
Electrons possess both spin and charge. In one dimension, quantum theory predicts that&nbsp;systems of interacting electrons may&nbsp;behave as though their charge and spin are transported at different speeds.We discuss examples of how&nbsp; such&nbsp;many-particle effects may be simulated using neutral atoms and radiation fields. Joint work with Xiao-Feng Shi
Friday, April 27, 2018 - 15:00 , Location: Skiles 005 , , Cornell University , Organizer: Lutz Warnke
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.
Friday, April 27, 2018 - 15:05 , Location: Skiles 271 , Bhanu Kumar , GTMath , Organizer: Jiaqi Yang
This talk follows Chapter 4 of the well known text by Guckenheimer and Holmes. It is intended to present the theorems on averaging for systems with periodic perturbation, but slow evolution of the solution. Also, a discussion of Melnikov’s method for finding persistence of homoclinic orbits and periodic orbits will also be given. Time permitting, an application to the circular restricted three body problem may also be included.&nbsp;