Colloquia/Spring2020: Difference between revisions
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Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space. | Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space. | ||
===Jianfeng Lu (Duke University)=== | |||
Title: Density fitting: Analysis, algorithm and applications | |||
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying. | |||
===Aaron Naber (Northwestern)=== | ===Aaron Naber (Northwestern)=== | ||
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Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li. | Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li. | ||
== Past Colloquia == | == Past Colloquia == | ||
Revision as of 19:42, 25 January 2019
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Spring 2019
| date | speaker | title | host(s) | |
|---|---|---|---|---|
| Jan 25 Room 911 | Beata Randrianantoanina (Miami University Ohio) WIMAW | Some nonlinear problems in the geometry of Banach spaces and their applications | Tullia Dymarz | |
| Jan 30 Wednesday | Lillian Pierce (Duke University) | Short character sums | Boston and Street | |
| Jan 31 Thursday | Dean Baskin (Texas A&M) | Radiation fields for wave equations | Street | |
| Feb 1 | Jianfeng Lu (Duke University) | Density fitting: Analysis, algorithm and applications | Qin | |
| Feb 5 Tuesday | Alexei Poltoratski (Texas A&M University) | TBA | Denisov | |
| Feb 8 | Aaron Naber (Northwestern) | A structure theory for spaces with lower Ricci curvature bounds | Street | |
| Feb 15 | TBA | |||
| Feb 22 | Angelica Cueto (Ohio State) | TBA | Erman and Corey | |
| March 4 | Vladimir Sverak (Minnesota) Wasow lecture | TBA | Kim | |
| March 8 | Jason McCullough (Iowa State) | TBA | Erman | |
| March 15 | Maksym Radziwill (Caltech) | TBA | Marshall | |
| March 29 | Jennifer Park (OSU) | TBA | Marshall | |
| April 5 | Ju-Lee Kim (MIT) | TBA | Gurevich | |
| April 12 | Evitar Procaccia (TAMU) | TBA | Gurevich | |
| April 19 | Jo Nelson (Rice University) | TBA | Jean-Luc | |
| April 26 | Kavita Ramanan (Brown University) | TBA | WIMAW | |
| May 3 | Tomasz Przebinda (Oklahoma) | TBA | Gurevich |
Abstracts
Beata Randrianantoanina (Miami University Ohio)
Title: Some nonlinear problems in the geometry of Banach spaces and their applications.
Abstract: Nonlinear problems in the geometry of Banach spaces have been studied since the inception of the field. In this talk I will outline some of the history, some of modern applications, and some open directions of research. The talk will be accessible to graduate students of any field of mathematics.
Lillian Pierce (Duke University)
Title: Short character sums
Abstract: A surprisingly diverse array of problems in analytic number theory have at their heart a problem of bounding (from above) an exponential sum, or its multiplicative cousin, a so-called character sum. For example, both understanding the Riemann zeta function or Dirichlet L-functions inside the critical strip, and also counting solutions to Diophantine equations via the circle method or power sieve methods, involve bounding such sums. In general, the sums of interest fall into one of two main regimes: complete sums or incomplete sums, with this latter regime including in particular “short sums.” Short sums are particularly useful, and particularly resistant to almost all known methods. In this talk, we will see what makes a sum “short,” sketch why it would be incredibly powerful to understand short sums, and discuss a curious proof from the 1950’s which is still the best way we know to bound short sums. We will end by describing new work which extends the ideas of this curious proof to bound short sums in much more general situations.
Dean Baskin (Texas A&M)
Title: Radiation fields for wave equations
Abstract: Radiation fields are rescaled limits of solutions of wave equations near "null infinity" and capture the radiation pattern seen by a distant observer. They are intimately connected with the Fourier and Radon transforms and with scattering theory. In this talk, I will define and discuss radiation fields in a few contexts, with an emphasis on spacetimes that look flat near infinity. The main result is a connection between the asymptotic behavior of the radiation field and a family of quantum objects on an associated asymptotically hyperbolic space.
Jianfeng Lu (Duke University)
Title: Density fitting: Analysis, algorithm and applications
Abstract: Density fitting considers the low-rank approximation of pair products of eigenfunctions of Hamiltonian operators. It is a very useful tool with many applications in electronic structure theory. In this talk, we will discuss estimates of upper bound of the numerical rank of the pair products of eigenfunctions. We will also introduce the interpolative separable density fitting (ISDF) algorithm, which reduces the computational scaling of the low-rank approximation and can be used for efficient algorithms for electronic structure calculations. Based on joint works with Chris Sogge, Stefan Steinerberger, Kyle Thicke, and Lexing Ying.
Aaron Naber (Northwestern)
Title: A structure theory for spaces with lower Ricci curvature bounds.
Abstract: One should view manifolds (M^n,g) with lower Ricci curvature bounds as being those manifolds with a well behaved analysis, a point which can be rigorously stated. It thus becomes a natural question, how well behaved or badly behaved can such spaces be? This is a nonlinear analogue to asking how degenerate can a subharmonic or plurisubharmonic function look like. In this talk we give an essentially sharp answer to this question. The talk will require little background, and our time will be spent on understanding the basic statements and examples. The work discussed is joint with Cheeger, Jiang and with Li.