Scientific

Random Maps 2

Speaker: 
Gregory Miermont
Date: 
Tue, Jun 5, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-MPrime Summer School in Probability
Abstract: 

The study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

Class: 
Scientific
Subject: 
Mathematics
Probability

Polya’s Program for the Riemann Hypothesis and Related Problems

Speaker: 
Ken Ono
Date: 
Thu, Nov 9, 2017
Location: 
PIMS, University of British Columbia
Conference: 
PIMS-UBC Math Distinguished Colloquium
Abstract: 

In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity has only been proved for degrees d=1, 2, 3. We prove the hyperbolicity of 100% of the Jensen polynomials of every degree. We obtain a general theorem which models such polynomials by Hermite polynomials. This theorem also allows us to prove a conjecture of Chen, Jia, and Wang on the partition function. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.

Class: 
Scientific
Subject: 
Number Theory

The orbit intersection problem for linear spaces and semiabelian varieties

Speaker: 
Khoa Nguyen
Date: 
Thu, Oct 19, 2017
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 

We will introduce the Dynamical Mordell-Lang problem by Ghioca and Tucker.

After that, we explain the “orbit intersection problem” for linear spaces and semi-abelian varieties. This is joint work with Ghioca.

Class: 
Scientific
Subject: 
Mathematics

Diophantine equations for fun (and profit?)

Speaker: 
Michael Bennett
Date: 
Thu, Sep 21, 2017
Location: 
PIMS, University of Calgary
Conference: 
Louise and Richard K. Guy Lecture Series
Abstract: 

Michael Bennett (President, Canadian Mathematical Society; Professor of Mathematics, University of British Columbia)

Diophantine equations are one of the oldest, frequently celebrated and most abstract objects in mathematics. They crop up in areas ranging from recreational mathematics and puzzles, to cryptography, error correcting codes, and even in studying the structure of viruses. In this talk, Dr. Bennett will attempt to show some of the roles these equations play in modern mathematics and beyond.

Class: 
Scientific
Subject: 
Mathematics

Triangular bases of integral closures

Speaker: 
Jens Bauch
Date: 
Thu, Sep 28, 2017
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 

Triangular bases of integral closures

Class: 
Scientific
Subject: 
Mathematics

Hybrid Krylov Subspace Iterative Methods for Inverse Problems

Speaker: 
James Nagy
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 

Inverse problems arise in many imaging applications, such as image
reconstruction (e.g., computed tomography), image deblurring, and
digital super-resolution. These inverse problems are very difficult
to solve; in addition to being large scale, the underlying
mathematical model is often ill-posed, which means that noise and
other errors in the measured data can be highly magnified in computed
solutions. Regularization methods are often used to overcome this
difficulty. In this talk we describe hybrid Krylov subspace based
regularization approaches that combine matrix factorization methods
with iterative solvers. The methods are very efficient for large scale
imaging problems, and can also incorporate methods to automatically
estimate regularization parameters. We also show how the approaches
can be adapted to enforce sparsity and nonnegative constraints.

We will use many imaging examples that arise in medicine and astronomy
to illustrate the performance of the methods, and at the same time
demonstrate a new MATLAB software package that provides an easy to use
interface to their implementations.

This is joint work with Silvia Gazzola (University of Bath) and
Per Christian Hansen (Technical University of Denmark).

Class: 
Scientific
Subject: 
Mathematics
Applied Mathematics

Rufus Bowen Conference - Lunchtime Speeches

Speaker: 
Brian Marcus
Date: 
Wed, Aug 2, 2017
Location: 
PIMS, University of British Columbia
Conference: 
Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen
Abstract: 

These speeches were given during the remembrance lunch as part of the conference "Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen".

Class: 
Scientific
Subject: 
Mathematics

Rufus Bowen Conference - Lunchtime Slideshow

Speaker: 
Brian Marcus
Date: 
Wed, Aug 2, 2017
Location: 
PIMS, University of British Columbia
Conference: 
Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen
Abstract: 

This slideshow and the accompanying toasts were given during the remembrance lunch as part of the conference "Current Trends in Dynamical Systems and the Mathematical Legacy of Rufus Bowen".

Class: 
Scientific
Subject: 
Mathematics

The Case for T-Product Tensor Decompositions: Compression, Analysis and Reconstruction of Image Data

Speaker: 
Misha Kilmer
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 

Most problems in imaging science involve operators or data that are
inherently multidimensional in nature, yet traditional approaches to
modeling, analysis and compression of (sequences of) images involve
matricization of the model or data. In this talk, we discuss ways in
which multiway arrays, called tensors, can be leveraged in imaging
science for tasks such as forward problem modeling, regularization and
reconstruction, video analysis, and compression and recognition of facial
image data. The unifying mathematical construct in our approaches to
these problems is the t-product (Kilmer and Martin, LAA, 2011) and
associated algebraic framework. We will see that the t-product permits
the elegant extension of linear algebraic concepts and matrix algorithms
to tensors, which in turn gives rise to new, highly parallelizable,
algorithms for the imaging tasks noted above.

Class: 
Scientific
Subject: 
Mathematics
Applied Mathematics

The Geometry of the Phase Retrieval Problem

Speaker: 
Charles Epstein
Date: 
Fri, May 5, 2017
Location: 
PIMS, University of Manitoba
Conference: 
Mathematical Imaging Science
Abstract: 

Phase retrieval is a problem that arises in a wide range of imaging
applications, including x-ray crystallography, x-ray diffraction imaging
and ptychography. The data in the phase retrieval problem are samples of
the modulus of the Fourier transform of an unknown function. To
reconstruct this function one must use auxiliary information to determine
the unmeasured Fourier transform phases. There are many algorithms to
accomplish task, but none work very well. In this talk we present an
analysis of the geometry that underlies these failures and points to new
approaches for solving this class of problems.

Class: 
Scientific
Subject: 
Mathematics
Applied Mathematics

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