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 Events
Hong Kong University of Science and Technology
Wed 1 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Solving the high-dimensional Markowitz Optimization Problem: a tale of sparse solutions
ESB 2012
Wed 1 Oct 2014, 3:00pm-4:00pm

Abstract

We consider the high-dimensional Markowitz optimization problem. A new approach combining sparse regression and estimation of optimal returns based on random matrix theory is proposed to solve the problem. We prove that under some sparsity assumptions on the underlying optimal portfolio, our novel approach asymptotically yields the theoretical optimal return, and in the meanwhile satisfies the risk constraint. To the best of our knowledge, this is the first method that can achieve these two goals simultaneously in the high-dimensional setting. We further conduct simulation and empirical studies to compare our method with some benchmark methods, including the equally weighted portfolio, the bootstrap-corrected method by Bai et al. (2009) and the covariance-shrinkage method by Ledoit and Wolf (2004). The results demonstrate substantial advantage of our method, which attains high level of returns while keeping the risk well controlled by the given constraint.

Based on joint work with Mengmeng Ao and Yingying Li.

 
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UBC
Wed 1 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133 (may move to Thursday)
The Status of the Farrell-Jones conjecture
ESB 4133 (may move to Thursday)
Wed 1 Oct 2014, 3:15pm-4:15pm

Abstract

In the beginning of this talk I will use the Farrell-Jones conjecture to express the K-theory of R[Z^2] in Terms of the K-theory of R. Geometric conditions on a Group that imply the conjecture will be mentioned . The class of Groups for which the conjecture is known is quite large I will define it and mention some interesting open cases.
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Université Pierre et Marie Curie
Thu 2 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Points of small height on abelian varieties over function fields
room MATH 126
Thu 2 Oct 2014, 3:30pm-4:30pm

Abstract

An old conjecture of Lang (for elliptic curves) generalized by Silverman, asserts that the Néron-Tate height of a rational point of an abelian variety defined over a number field can be bounded below linearly in terms of the Faltings height of the underlying abelian variety. We shall explore the function field analogue of this problem.
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Université Paris-Sud
Thu 2 Oct 2014, 4:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 (PIMS lounge)
Large Time behavior for the cubic Szego évolution
ESB 4133 (PIMS lounge)
Thu 2 Oct 2014, 4:00pm-5:00pm

Abstract

The cubic Szegö equation is an Hamiltonian evolution on periodic functions with nonnegative Fourier modes, arising as a normal form for the large time behavior of a nonlinear wave equation on the circle. It defines a flow on every Sobolev space with enough regularity. In this talk, I will give the main arguments for the proof of the following theorem. The trajectories of the cubic Szegö equation are almost periodic in the Sobolev energy space, but
are generically unbounded in every more regular Sobolev space.This is a joint work with Sandrine Grellier and Zaher Hani.

Note for Attendees

 Please note unusual time and room.
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UBC
Fri 3 Oct 2014, 3:00pm
Department Colloquium
MATH ANNEX 1100
Recent developments for Ricci flow on non-compact manifolds.
MATH ANNEX 1100
Fri 3 Oct 2014, 3:00pm-4:00pm

Abstract

The Ricci flow is one of the most important equations in geometric analysis, and has been used to solve deep problems in topology and geometry. Through a system of local parabolic PDE's, the flow governs the evolution of a Riemannian metric tensor in space, and it's general theory is fundamentally based on the assumption that the metric is complete with bounded sectional curvatures. I will give an overview of the general theory, then discuss the problem of flowing unbounded curvature metrics on non-compact manifolds. I will then discuss recent results for U(n) invariant Kahler metrics on C^n, and connections to Yau's uniformization conjecture. The talk is based in part on joint work with L.F. Tam and K.F Li.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Kansas State
Mon 6 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
TBA
ESB 4127 (host: UBC)
Mon 6 Oct 2014, 3:00pm-4:00pm

Abstract

 TBA

Note for Attendees

  Note: Today we have a double-header again. Talk one: Gabriel Kerr 15:00-16:00. Talk two: Charlie Beil: 16:30-17:30. Coffee and cookies in between the two talks.
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Director of Institute for Pure & Applied Mathematics, UCLA, Los Angeles
Mon 6 Oct 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
From PDEs to Information Science and Back
LSK 460
Mon 6 Oct 2014, 3:00pm-4:00pm

Abstract

 The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for information science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from PDEs, such as variational principles and numerical diffusion, to image and data analysis. Examples include denoising, segmentation, inpainting and texture extraction for images. The second focus is the development of new ideas in information science, such as wavelets, soft-thresholding, sparsity and compressed sensing. The subsequent application of these ideas to PDEs and numerical computation is the third focus of this talk. Examples include wavelet analysis for turbulent flows, the use of soft-thresholding in computation of PDEs with multi-scale features, and the construction of “compressed modes” (modes that are compactly supported in space) for density functional theory and other PDEs that come from variational principles.

Russel Caflisch is a Professor in the Mathematics Department at UCLA and has a joint appointment in the Department of Materials Science and Engineering. He received his PhD from the Courant Institute at New York University in 1978 and has also held faculty positions at Stanford and NYU. He is currently the director of the Institute for Pure & Applied Mathematics (IPAM), and the Editor-In-Chief for the journal Multiscale Modeling and Simulation. He was a Sloan Foundation Research Fellow, and a fellow of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and the American Academy of the Arts and Sciences. Caflisch’s expertise includes a wide range of topics in applied mathematics, including PDEs, fluid dynamics, plasma physics, materials science, Monte Carlo methods, and computational finance.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building. 
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Bristol
Mon 6 Oct 2014, 4:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Nonlocality and the central geometry of dimer algebras
ESB 4127 (host: UBC)
Mon 6 Oct 2014, 4:30pm-5:30pm

Abstract

A dimer algebra is a type of quiver algebra whose quiver embeds in a torus, with homotopy-like relations.  Dimer algebras with the cancellation property are Calabi-Yau algebras, and their centers are 3-dimensional Gorenstein singularities.  Non-cancellative dimer algebras, on the other hand, are not Calabi-Yau, and their centers are nonnoetherian.  In contrast to their cancellative counterparts, very little is known about these algebras, despite the fact that almost all dimer algebras are non-cancellative.  I will describe how their centers are also 3-dimensional singularities, but with the strange property that they contain positive dimensional 'smeared-out' points.  Furthermore, I will describe how this nonlocal geometry is reflected in the homology of certain vertex simple representations.

Note for Attendees

 Note: Today we have a double-header again. Talk one: Gabriel Kerr 15:00-16:00. Talk two: Charlie Beil: 16:30-17:30. Coffee and cookies in between the two talks.
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UBC
Tue 7 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
TBA
ESB 2012
Tue 7 Oct 2014, 3:30pm-4:30pm

Abstract

 
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