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seminars:anal

The seminar meets Wednesdays in WH-100E at 3:30-4:30 p.m. There are refreshments and snacks in WH-102 at 3:15.

The seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

Organizers: Paul Loya, Xiangjin Xu, Gang Zhou , Lu Zhang and Timur M Akhunov

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* **January 17th, Wednesday ** (3:30-4:30pm)

** Speaker **:

* **January 24th, Wednesday ** (3:30-5:00pm)

** Speaker **:

** Abstract**:

* **January 31st, Wednesday ** (3:30-4:30pm)

** Speaker **: Adam Weisblatt (Binghamton University)

** Abstract**: I will present a method to compute various cohomologies of
surfaces.

* **February 7th, Wednesday ** (3:30-4:30pm)(Cancelled due weather)

** Speaker **: Adam Weisblatt (Binghamton University)

** Abstract**: I will present a method to compute various cohomologies of
surfaces.

* **February 14th , Wednesday ** (3:30-4:30pm)(Cancelled)

** Speaker**: Kunal Sharma (Binghamton University)

** Abstract**: We will show how Calderon-Seeley projector comes up in study of boundary values problems for elliptic operators on a compact manifold with boundary. Its properties and applications to address Fredholmness of the operator will be discussed.

* **February 21st, Wednesday ** (3:30-4:30pm)

** Speaker**: Binbin Huang (Binghamton University)

** Abstract**: Manifolds with corners are of little new interest for pure topologists - they are just the manifolds with boundaries. For differential geometers, there are a few intriguing phenomena to study. On the other hand, they are (at least philosophically) unavoidable for analysts who study linear differential operators. In this talk, we will look at some fundamental notions in the theory of manifolds with corners. Some geometric constructions closely related to linear differential operators will be discussed, paving the way to the study of various (pseudo-)differential calculi.

* **February 28th, Wednesday ** (3:30-4:30pm)

** Speaker**: Binbin Huang (Binghamton University)

** Abstract**: Manifolds with corners are of little new interest for pure topologists - they are just the manifolds with boundaries. For differential geometers, there are a few intriguing phenomena to study. On the other hand, they are (at least philosophically) unavoidable for analysts who study linear differential operators. In this talk, we will look at some fundamental notions in the theory of manifolds with corners. Some geometric constructions closely related to linear differential operators will be discussed, paving the way to the study of various (pseudo-)differential calculi.

* **March 7th, Wednesday ** (3:30-4:30pm)(Winter break)

** Speaker**:

** Abstract**:

* **March 14th, Wednesday ** (3:30-4:30pm)

** Speaker**: Timur Akhunov (Binghamton University)

** Abstract**: Dispersive partial equations describe evolution of waves, whose speed of propagation depends on wave frequency. The uncertainty principle of quantum mechanics is intimately tied to the dispersion in the Schrodinger equation. The Korteweg-de Vries (KdV) equation was originally derived in 1890s to explain surface waves in a shallow fluid is among the most studied nonlinear dispersive PDE. Dispersion has since then found a way to connect with harmonic analysis, number theory and algebraic geometry. In a series of papers (the last in collaboration with David Ambrose and Doug Wright from Drexel) we have independently rediscovered and adapted techniques from thin-film equations to the context of KdV.

* **March 21th, Wednesday ** (3:30-4:30pm)

** Speaker**: Shengwen Wang (John Hopkins University)

** Abstract**: The Colding-Minicozzi entropy functional is defined on the space of all hypersurfaces and it measures the complexity of a hypersurface. It is monotonic non-increasing along mean curvature flow and the entropy minimizer among all closed hypersurfaces are round spheres. In this talk I will present a Hausdorff stability result of round spheres under small entropy perturbation.

* **March 28th, Wednesday ** (3:30-4:30pm)

** Speaker**: Binbin Huang (Binghamton University)

** Abstract**: The b-calculus developed by R. Melrose, is among the first materializations of his program of “microlocalizing boundary fibration structures”. Along with other closed related calculi, it provides a convenient framework to study geometric-analytic problems on manifolds with certain singular structures. Due to its nice mapping properties on (b-)Sobolev spaces, techniques from functional analysis can be applied, which makes it a natural choice for the study of index theory. With a more geometric approach initiated by P. Loya, we developed a theory that extends the classical b-calculus. It is obtained by replacing the boundary decay condition by a more modest one. In this talk, we will begin with a brief review of the b-calculus, then we will give a detailed description of our calculus, and study its Fredholm problem.

* **April 4th, Wednesday ** (3:30-4:30pm)(Spring break)

** Speaker**:

** Abstract**:

* **April 11th, Wednesday ** (3:30-4:30pm)

** Speaker**: Kunal Sharma (Binghamton University)

** Abstract**: We will show how Calderon-Seeley projector comes up in study of boundary values problems for elliptic operators on a compact manifold with boundary. Its properties and applications to address Fredholmness of the operator will be discussed.

* **April 18th, Wednesday ** (3:30-4:30pm)

** Speaker**:Benjamin Harrop-Griffiths (NYU)

** Abstract**: We discuss recent work on some quasilinear toy models for the phenomenon of degenerate dispersion, where the dispersion relation may degenerate at a point in physical space. In particular, we present a proof of the existence of solutions using a novel change of variables reminiscent of the classical hodograph transformation. This is joint work with Pierre Germain and Jeremy L. Marzuola.

* **April 24th, Tuesday ** (2:50-4:10pm at WH 309) (Special date, time and location)

** Speaker**: Binbin Huang (Binghamton University)

** Abstract**:

* **April 25th, Wednesday ** (3:30-4:30pm)

** Speaker**: Marius Lemm (Institute for advanced studies, Princeton)

** Abstract**: We consider an elliptic operator on the discrete d-dimensional lattice whose coefficient matrix is a small i.i.d. perturbation of the identity. Recently, Jean Bourgain introduced novel techniques from harmonic analysis to prove the convergence of the Feshbach-Schur perturbation series for the averaged Green's function of this model. Our main contribution is a refinement of Bourgain's approach which yields a conjecturally nearly optimal decay estimate. As an application, we derive estimates on higher derivatives of the averaged Green's function which go beyond the second derivatives considered by Delmotte-Deuschel and related works. This is joint work with Jongchon Kim (IAS).

* **May 2nd, Wednesday ** (3:30-5:00pm)

** Speaker**: Adam Weisblatt (Binghamton University)

** Abstract**:

seminars/anal.txt · Last modified: 2018/04/16 13:14 by xxu

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