Welcome to the home page of the Graduate Analysis Seminar. This page will list the past and upcoming talks for the seminar. For the Spring 2016 Semester, the seminar will run at 5pm on Mondays in the Graduate Student Lounge (Hill 701).
In Fall 2015, the seminar was led by Matt Charnley. Please click here for the information from that semester.
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Speaker: Alexi Hoeft
Date: April 25, 2016
Abstract: Does every Banach space contain an isomorphic copy of a "nice" Banach space? For the longest time, Banach space theorists had been unable to construct a Banach space so wild that it failed to contain an isomorphic copy of one of the classical sequence spaces c_0 or l_p, 1<=p<∞. Hopes for a nice isomorphic structure theory for Banach spaces were shattered, however, when a revolutionary new inductive style of defining a norm suddenly succeeded in yielding such a wild Banach space. But far from being bad news for Banach space theory, this discovery has opened new doors for the field and shed light on the richness of the isomorphic structure of Banach spaces.
Speaker: Érik De Amorim
Date: April 11, 2016
Abstract: After a brief introduction of the necessary concepts from Quantum Mechanics, we will prove that matter is stable. This concerns the mathematical description of a quantum mechanical model of ordinary matter, consisting of particles interacting via gravitational and electric forces, and the proof that such a model has a finite lower bound on its energy. This successful application of the theory of Quantum Physics to the real world fixes a problem with the naive classical approach which was troubling physicists in the early 20th century, namely the conclusion that all atoms should radiate energy and collapse to a point.
Speaker: Matt Charnley
Date: March 28, 2016
Abstract: Polarization Tensors are defined in terms of how an object responds to electrical current on its surface. The initial definition of these tensors was made by Polyá and Szegö in the 1950s, but so called Generalized Polarization Tensors (GPT) were defined more recently and have been shown to have other nice properties in terms of analyzing very small inclusions in an otherwise homogeneous media. In this talk, we will cover the basic definitions of Polarization Tensors, and show how the GPTs are a generalized version of the original case. We will show some sample calculations of the basic polarization tensors for simple geometries. In extending to the GPTs, we will discuss how knowing all of the polarization tensors uniquely determines the geometry of the inclusion, and how these can be used in asymptotic expansions of small inclusions.
Speaker: Jeaheang Bang
Date: March 21, 2016
Abstract: In this talk, we address the boundary value problem of a BGK type model posed in a bounded interval. The existence of the unique mild solution is established when the gas system is sufficiently rarefied. A key ingredient to obtain the existence is Fixed Point Theorem.
Speaker: Mike Breeling
Date: February 8, 2016
Abstract: In this talk we will examine a few consequences of the spectral theorem for bounded self-adjoint operators. This will hopefully be a nice companion lecture to the abstract theory in Dr. Carlen's class; for instance we will begin with the concrete example of the commutative Gelfand-Naimark theorem known as the continuous functional calculus on B(H). Among the applications will be the multiplier operator formulation of the spectral theorem, spectral projections, and Stone's theorem on strongly continuous unitary groups.
Speaker: Matt Charnley
Date: February 1, 2016
Abstract: In this talk, I will most likely discuss the story of existence of solutions to Elliptic PDE's and the eigenvalue problem for these operators. It's one of the things on my oral exam, so I'll either cover this, or something else that I decide would be good to talk about.