Mathematics Dept.
  Events
Tue 2 Sep 2014, 9:00am SPECIAL
Math 125
Qualifying Exams - Analysis
Math 125
Tue 2 Sep 2014, 9:00am-12:00pm

Details

For more information on Qualifying Exams, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
Lunch will be provided in  Math 125 for students writing the Analysis exam.
hide
Tue 2 Sep 2014, 1:00pm SPECIAL
Math 125
Qualifying Exams - Differential Equations
Math 125
Tue 2 Sep 2014, 1:00pm-4:00pm

Details

For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
hide
Tue 2 Sep 2014, 1:00pm SPECIAL
Math 125
Qualifying Exams - Algebra
Math 125
Tue 2 Sep 2014, 1:00pm-4:00pm

Details

For more info, please visit http://www.math.ubc.ca/Grad/QualifyingExams/index.shtml
hide
Tue 2 Sep 2014, 4:30pm SPECIAL
Math 125
Department Graduate Orientation
Math 125
Tue 2 Sep 2014, 4:30pm-5:30pm

Details


hide
University College London
Wed 3 Sep 2014, 3:00pm
Probability Seminar
ESB 2012
Gradient Gibbs measures with disorder
ESB 2012
Wed 3 Sep 2014, 3:00pm-4:00pm

Abstract

We consider - in uniformly strictly convex potentials case - two versions of random gradient models. In model A) the interface feels a bulk term of random fields while in model B) the disorder enters though the potential acting on the gradients itself. It is well known that without disorder there are no Gibbs measures in infinite volume in dimension d = 2, while there are gradient Gibbs measures describing an infinite-volume distribution for the increments of the field, as was shown by Funaki and Spohn. Van Enter and Kuelske proved that adding a disorder term as in model A) prohibits the existence of such gradient Gibbs measures for general interaction potentials in d = 2. Cotar and Kuelske proved the existence of shift-covariant gradient Gibbs measures for model A) when d > 2 and the expectation with respect to the disorder is zero, and for model B) when d > 1. 

In recent work, we prove uniqueness of shift-covariance gradient Gibbs measures with expected given tilt under the above assumptions. We also prove decay of covariances for both models. 

We will also discuss in the talk the case of non-convex potentials with disorder.

This is partly based on joint work with Christof Kuelske.

hide
UBC
Fri 5 Sep 2014, 3:00pm
Department Colloquium
Math Annex 1100
Remarks on the local Langlands conjectures.
Math Annex 1100
Fri 5 Sep 2014, 3:00pm-4:00pm

Abstract

The Langlands program, initiated in the 1960s, is a set of conjectures predicting a unification of number theory and the representation theory
of groups. More precisely, the Langlands correspondence provides a way to interpret results in number theory in terms of group theory, and vice versa.

In this talk we sketch a few aspects of the local Langlands correspondence using elementary examples. We then comment on some questions raised by the emerging "mod p" Langlands program.
hide
Dr. Aria Abubakar
Schlumberger Houston Formation Evaluation, Sugar Land, Texas and SEG 2014 Honorary Lecturer
Mon 8 Sep 2014, 1:00pm SPECIAL
ESB 5104
Joint inversion of multiphysics data for petrophysical and engineering properties
ESB 5104
Mon 8 Sep 2014, 1:00pm-2:00pm

Details

Abstract: A variety of measurements may illuminate the reservoir with varying coverage and resolution such as: electromagnetic (EM); controlled-source EM (CSEM); magnetotelluric (MT), surface-to-borehole EM (STB-EM); crosswell EM; seismic (surface seismic, crosswell seismic, and VSP); gravity (surface and borehole); and production history/well testing data. The interpretation of each measurement on its own will provide incomplete information due to nonuniqueness and limited spatial resolution. However, when integrated and combined with other measurements such as near-wellbore data, they may provide considerable value such as, for example, to enable estimation of reservoir properties, to obtain an improved reservoir model, and to provide a physics-based reservoir upscaling. At the end, it will help us in making appropriate field management decisions with reduced uncertainty. 

This presentation will review joint inversion algorithms and workflows for integrating EM, seismic, and production data. It will analyze challenges, advantages, and disadvantages of these approaches. In particular, for reservoir characterization applications, joint structural and petrophysical algorithms for integrating EM and seismic data (CSEM and surface seismic, and crosswell EM and crosswell seismic) will be presented. For reservoir monitoring applications, the talk will describe EM data (for single-well, crosswell and STB) inversion algorithms constrained by the fluid-flow simulator. In the inversion for both EM and seismic, a full nonlinear approach (the so-called full-waveform inversion) will be employed so that all the information in the data can be utilized. Some test cases will be discussed. 

Biography: Aria Abubakar was born in Bandung, Indonesia, in 1974. He received a master’s degree (cum laude) in electrical engineering and a PhD (cum laude) in technical sciences from Delft University of Technology in 1997 and 2000, respectively. From September 2000 until February 2003 he was a researcher with the Laboratory of Electromagnetic Research and Section of Applied Geophysics of Delft University of Technology. 
He joined Schlumberger-Doll Research in 2003 and his last position there was as a scientific advisor and the Research Program Manager of Multi-Physics Modeling and Inversion Program. While at Schlumberger-Doll Research, he worked on advanced modeling and inversion of electromagnetic and seismic waves. In addition, he has been developing algorithms and workflows for joint inversion of multiphysics data for both reservoir and wellbore-scale measurements. Since early 2013, he has been Interpretation Engineering Manager and Scientific Advisor at Schlumberger Houston Formation Evaluation in Sugar Land, Texas. He currently is leading Schlumberger Wireline and Logging-While-Drilling product development for electromagnetic, nuclear, and resistivity measurements and their joint inversion and interpretation. He is Associate Editor of Radio Science and Geophysics. He has published one book, four book chapters, over 75 scientific articles in refereed journals, 150 conference proceedings papers, and 50 conference abstracts. He holds four US patents and has five US patent applications under review. 

 
hide
Mon 8 Sep 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 306
Institute of Applied Mathematics Welcome Reception
LSK 306
Mon 8 Sep 2014, 3:00pm-5:00pm

Abstract

 Come join us for some food and drink to welcome in the new academic year. Meet old friends and new. 
hide
UIUC
Mon 8 Sep 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Refined and motivic BPS invariants
ESB 4127 (host: UBC)
Mon 8 Sep 2014, 3:00pm-4:00pm

Abstract

The virtual Poincare polynomials of the stable pair moduli spaces of a Calabi-Yau threefold are conjecturally equivalent to the refined BPS numbers of Gopakumar and Vafa.  As an application, stable pair invariants of the del Pezzo surfaces dP_n determine BPS Hilbert spaces which are observed to be representions of the exceptional Lie algebra E_n, consistent with expectations of string theory.  In another direction, string theory on K3 x T^2 leads to a reduced DT theory on K3, hence
corresponding motivic and refined invariants.  Work in progress on the rational elliptic surface dP_9 ("half K3") suggests that a blend of these two examples leads to a BPS Hilbert space with a representation of affine E_8.  This talk includes separate joint works with Choi, Klemm, and Pandharipande.

Note for Attendees

Today the seminar has two talks. Sheldon 3-4pm (as usual) and Masoud 4:30-5:30pm. Coffee and cookies are served in between.
hide
Krystal Taylor
IMA
Mon 8 Sep 2014, 3:00pm
Harmonic Analysis Seminar
MATX 1102
Convolution operators, measures of polynomial growth, and finite point con gurations.
MATX 1102
Mon 8 Sep 2014, 3:00pm-4:00pm

Abstract


hide
Queensland
Mon 8 Sep 2014, 4:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Preservation of depth in local geometric Langlands program
ESB 4127 (host: UBC)
Mon 8 Sep 2014, 4:30pm-5:30pm

Abstract

Local geometric Langlands program aims to establish a relationship between representations of the Galois group of a local field and irreducible representations of the dual group. It is expected that, under mild conditions, this correspondence preserves depths of representations. In this talk, I will explain the geometric analogue of this expectation, in the framework of Frenkel-Gaitsgory's local geometric Langlands correspondence. Based on a joint project with Tsao-Hsien Chen:  http://arxiv.org/abs/1404.0598

Note for Attendees

Today the seminar has two talks. Sheldon 3-4pm (as usual) and Masoud 4:30-5:30pm. Coffee and cookies are served in between.
hide
EHESS, France
Tue 9 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The effect of a line with fast diffusion on biological invasions
ESB 2012
Tue 9 Sep 2014, 3:30pm-4:30pm

Abstract

 
hide
Hokkaido University
Wed 10 Sep 2014, 3:00pm
Probability Seminar
ESB 2012
Critical two-point function for the phi^4 model in dimensions d>4
ESB 2012
Wed 10 Sep 2014, 3:00pm-4:00pm

Abstract

The (lattice) phi^4 model is a scalar field-theoretical model that exhibits a phase transition. It is believed to be in the same universality class as the Ising model. In fact, we can construct the phi^4 model as the N --> infinity limit of the sum of N Ising systems (with the right scaling of spin-spin couplings). Using this Griffiths-Simon construction and applying the lace expansion for the Ising model, we can prove mean-field asymptotic behavior for the critical phi^4 two-point function. In this talk, I will explain the key points of the proof, and discuss possible extensions of the results to the power-law coupling case.
hide
University of Warwick
Wed 10 Sep 2014, 4:00pm SPECIAL
Probability Seminar
ESB 2012
Group walk random graphs
ESB 2012
Wed 10 Sep 2014, 4:00pm-5:00pm

Abstract

I will discuss a new construction of finite random graphs motivated by the study of random walks on infinite groups, and show connections to the Poisson boundary and Sznitman's random interlacements.

Note for Attendees

 This is an extra lecture for the Probability seminar, starting at 4pm rather than the usual 3pm.
hide
University of Washington
Thu 11 Sep 2014, 3:30pm
Number Theory Seminar
room K10908, IRMACS, SFU
Obstructions to the Hasse principle on degree 4 del Pezzo surfaces
room K10908, IRMACS, SFU
Thu 11 Sep 2014, 3:30pm-4:30pm

Abstract

In 1970, Manin showed that the Brauer group can obstruct the existence of rational points. Colliot-Thélène and Sansuc have conjectured that this obstruction completely explains the failure of rational points on del Pezzo surfaces. We show that on degree 4 del Pezzo surfaces, this Brauer-Manin obstruction manifests itself through linear projections. As a consequence of the proof, we obtain a simple and efficient for computing the Brauer classes of a degree 4 del Pezzo surface. This is joint work with Anthony Várilly-Alvarado.
hide
Duncan R. Hewitt
PIMS PDF, UBC
Thu 11 Sep 2014, 4:00pm
Complex Fluids Seminar
ESB 2012
High Rayleigh number convection in porous media
ESB 2012
Thu 11 Sep 2014, 4:00pm-5:00pm

Abstract

Convective flow in porous media can be found in numerous geophysical and industrial processes, and has recently been investigated in the context of geological CO_2 sequestration. I will present high-resolution numerical simulations of statistically steady high-Rayleigh-number convection in a porous medium that is heated at the base and cooled at the upper surface. I will discuss the relationship between the strength of convection, as described by the Rayleigh number, and the transfer of buoyancy, as described by the Nusselt number. I will examine the remarkable dynamical structure of high-Rayleigh-number porous convection: the structure is characterized in the interior by ordered vertical columnar exchange flow with a regular (Rayleigh-number dependent) horizontal wavenumber k(Ra), and near the boundaries by vigorous short-wavelength boundary-layer instabilities . I will investigate the physical control of this structure by performing a stability analysis of the interior columnar flow: the predictions of this analysis give good agreement with the measured horizontal wavenumber k(Ra). Numerical results will be presented in both two-dimensional and three-dimensional porous media.

 

I will then extend these results to consider the more physically relevant context of convection from below one boundary only, and consider the implications of these results for the long-term storage capacity of underground water-saturated porous rocks into which CO_2 has been injected.

hide
UBC
Fri 12 Sep 2014, 3:00pm
Department Colloquium
Math Annex 1100
[N choose k] equals [N choose N-k]
Math Annex 1100
Fri 12 Sep 2014, 3:00pm-4:00pm

Abstract

We explore and take advantage of hidden structure behind the binomial identity above. This will lead us through some basic representation theory of sl(2), categorical equivalences and quantum knot invariants.
hide
UBC Zoology and Mathematics
Mon 15 Sep 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Evolutionary Dynamics in High-Dimensional Phenotype Spaces
LSK 460
Mon 15 Sep 2014, 3:00pm-4:00pm

Abstract

Adaptive dynamics is a general framework to study long-term evolutionary dynamics. It is typically used to study evolutionary scenarios in low-dimensional phenotype spaces, such as the important phenomenon of evolutionary branching (adaptive diversification). I will briefly recall the basic theory of evolutionary branching and present a well-studied empirical example. Because birth and death rates of individuals are likely to be determined by many different phenotypic properties, it is important to consider evolutionary dynamics in high-dimensional phenotype spaces. I will present some results about evolutionary branching in high-dimensional phenotype spaces, as well as results about more general types of non-equilibrium evolutionary dynamics, such as chaos. Finally, I will compare the deterministic adaptive dynamics in high-dimensional phenotype spaces to individual-based simulations of the underlying stochastic birth-death process.
 

Note for Attendees

Michael Doebeli is the winner of the 2014 CAIMS Research Prize. 
hide
Mainz
Mon 15 Sep 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Canonical Coordinates from Tropical Curves
ESB 4127 (host: UBC)
Mon 15 Sep 2014, 3:00pm-4:00pm

Abstract

Morrison defined canonical coordinates near a maximal degeneration point in the moduli of Calabi-Yau manifolds using Hodge theory. Gross and Siebert introduced a logarithmic-tropical algorithm to provide a canonically parametrized smoothing of a degenerate Calabi-Yau. We show that the Gross-Siebert coordinate is a canonical coordinate in the sense of Morrison. The coordinates are given by period integrals which we compute explicitly integrating over cycles constructed using tropical geometry. This is joint work with Siebert.

hide
Rustum Choksi
Department of Mathematics and Statistics, McGill University
Tue 16 Sep 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Self-Assemby: Variational Models and Energy Landscapes
ESB 4133 (PIMS Lounge)
Tue 16 Sep 2014, 12:30pm-1:30pm

Abstract

Self-assembly, a process in which a disordered system of preexisting components forms an organized structure or pattern, is both ubiquitous in nature and important for the synthesis of many designer materials. In this talk, we will address two variational paradigms for self-assembly from the point of view of analysis and computation. The first variational model is a nonlocal perturbation (of Coulombic-type) to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. The functional has a rich and complex energy landscape with many metastable states. We present recent joint work with Dave Shirokoff (NJIT) and J.C. Nave (McGill) on developing a method for assessing whether or not a particular (computed) metastable state is a global minimizer. Our method is based upon a very simple idea of using a ``suitable" global convex envelope of the energy. We present full details for global minimality of the constant state, and then present a few partial results on the application to non-constant, computed metastable states.
 
The second variational model is purely geometric and finite-dimensional: Centroidal Voronoi Tessellations (CVT) of rigid bodies. Using a level set formulation, we a priori fix the geometry for the structures and consider self-assembly entirely dictated by distance functions. We introduce a novel fast algorithm for simulating CVTs of rigid bodies in any space dimension. The method allows us to empirically explore the CVT energy landscape. This is joint work with Lisa Larsson (Courant) and J.C. Nave (McGill).
 
hide
John Ma
UBC
Tue 16 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Singularities in Lagrangian Mean Curvature Flow
ESB 2012
Tue 16 Sep 2014, 3:30pm-4:30pm

Abstract

Lagrangian Mean Curvature Flow (LMCF) is a geometric flow, aiming to deform a Lagrangian immersion to a minimal one. To understand the flow, it is important to understand the formation of singularity in LMCF. In this talk, I will introduce the concept of a self-shrinker (a local model for singularity), how it is formed in LMCF, and give some examples of Lagrangian self-shrinkers. Then I will discuss a recent work with Jingyi Chen concerning the space of all compact Lagrangian self-shrinkers in \mathbb C^2.
hide
University of Washington
Tue 16 Sep 2014, 4:00pm
Discrete Math Seminar
ESB 4133
Coxeter-Knuth Graphs and a signed Little map
ESB 4133
Tue 16 Sep 2014, 4:00pm-5:00pm

Abstract

We propose an analog of the Little map for reduced expressions for signed permutations. We show that this map respects the transition equations derived from Chevellay's formula on Schubert classes. We discuss many nice properties of the signed Little map which generalize recent work of Hamaker and Young in type A where they proved Lam's conjecture.   As a key step in this work, we define shifted dual equivalence graphs building on work of Assaf and Haiman and prove they can be characterized by axioms.   These graphs are closely related to both the signed Little map and to the Coxeter-Knuth relations of type B due to Kraskiewicz.
 
This talk is based on joint work with Zach Hamaker, Austin Roberts and Ben Young.
 
hide
National University of Mexico
Thu 18 Sep 2014, 2:15pm SPECIAL
Topology and related seminars
ESB 4133
On the Chern classes of singular varieties
ESB 4133
Thu 18 Sep 2014, 2:15pm-3:15pm

Abstract

Chern classes of complex manifolds play a key role in geometry and topology. In this talk we shall discuss how these classes extend to singular varieties. In fact there are various possible extensions, depending on which properties of Chern classes you want to preserve. This is closely related to asking who plays the role of the tangent bundle at the singular points (where there is no tangent bundle).
hide
Hebrew University of Jerusalem
Thu 18 Sep 2014, 3:30pm
Number Theory Seminar
room MATH 126
From Ramanujan graphs to Ramanujan complexes
room MATH 126
Thu 18 Sep 2014, 3:30pm-4:30pm

Abstract

Ramanujan graphs are optimal expanders (from spectral point of view). Explicit constructions of such graphs were given in the 80's as quotients of the Bruhat-Tits tree associated with GL(2) over a local field F, by suitable congruence subgroups. The spectral bounds were proved using works of Hecke, Deligne and Drinfeld on the "Ramanujan conjecture" in the theory of automorphic forms. The work of Lafforgue, extending Drinfeld from GL(2) to GL(n), opened the door for the construction of Ramanujan complexes as quotients of the Bruhat-Tits buildings. This gives finite simplical complxes which on one hand are "random like" and at the same time have strong symmetries. Recently various applications have been found in combinatorics, coding theory and in relation to Gromov's overlapping properties. We will describe these developments and give some details on recent applications. 
hide
Hebrew University of Jerusalem
Fri 19 Sep 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
High dimensional expanders and Ramanujan complexes (PIMS-UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 19 Sep 2014, 3:00pm-4:00pm

Abstract

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.
                  We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }
hide
Mathematics, SFU
Mon 22 Sep 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Challenges and Opportunities in ”Mathematics for Industry”
LSK 460
Mon 22 Sep 2014, 3:00pm-4:00pm

Abstract

Industrial mathematics is a field that spans a broad spectrum of activity ranging from applied R&D performed by mathematicians employed in industry, to purely academic research projects undertaken by university mathematics professors. In this talk, I will survey several research projects I have been involved with that fall under the heading of what I’ll call ”mathematics *for* industry”, which relates specifically to direct collaborations between university mathematicians and non-academic partner organizations. These projects encompass a diverse collection of mathematical techniques (ranging from simple algebra to partial differential equations, finite volume methods, inverse problems and homogenization theory) as well as applications from many scientific disciplines (such as fluid mechanics, image processing, atmospheric science and plant biology). In the process, I will attempt to characterize the job of an industrial mathematician and to identify the qualities and skills that are most desirable for anyone interested in making significant contributions to research at the interface between university and industry. I also hope to convince you that industrial collaborations can be a rich source of challenging and novel mathematical problems for academic mathematicians. 

Note for Attendees

John Stockie is the winner of the 2014 CAIMS/Mprime Industrial Mathematics Prize. 
hide
Bonn
Mon 22 Sep 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Graded quiver varieties and derived categories
ESB 4127 (host: UBC)
Mon 22 Sep 2014, 3:00pm-4:00pm

Abstract

Nakajima's quiver varieties are important geometric objects in representation theory that can be used to give geometric constructions of quantum groups. Very recently,  graded quiver varieties also found application to monoidal categorification of cluster algebras. Nakajima's original construction uses geometric invariant theory. In my talk, I will give an alternative representation theoretical definition of graded quiver varieties. I will show that the geometry of graded quiver varieties is governed by the derived category of the quiver. This is joint work with Berhard Keller. 

hide
Baptiste Devyver
UBC
Tue 23 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
General Hardy-type inequalities on manifolds.
ESB 2012
Tue 23 Sep 2014, 3:30pm-4:30pm

Abstract

Given a general second-order, elliptic operator P on a general domain, we discuss the question of finding an "optimal", or "asymptotically optimal", Hardy inequality for P. Such an inequality can be considered as a gneralized spectral gap inequality of P. If time allows, we will also consider the $L^p$ case.
hide
Kyoto University
Wed 24 Sep 2014, 3:00pm
Probability Seminar
ESB 2012
Quenched Invariance Principle for a class of random conductance models with long-range jumps
ESB 2012
Wed 24 Sep 2014, 3:00pm-4:00pm

Abstract

We study random walks on Z^d among random conductances {C_{xy}: x,y in Z^d} that permit jumps of arbitrary length. Apart from joint ergodicity with respect to shifts, we assume only that the nearest-neighbor conductances are uniformly positive and that sum_{x in Z^d} C_{0x} |x|^2 is integrable.
Our focus is on the Quenched Invariance Principle (QIP) which we establish in all d >= 3 by a combination of corrector methods and heat-kernel technology. We also show that our class contains examples where the corrector is not sublinear everywhere and yet the QIP holds. Thus, although the recent work of Andres, Slowik and Deuschel can be extended to long-range models, it cannot cover all cases for which the QIP is conjectured to hold. Notwithstanding, a combination of their methods with ours proves the QIP for random walks on long-range percolation graphs with exponents larger than d+2 in all d >= 2, provided all nearest-neighbor edges are present.
 
This is an ongoing joint work with Marek Biskup (UCLA).
hide
UBC
Wed 24 Sep 2014, 3:15pm
Topology and related seminars
ESB 4133
Algebraic K-Theory of Group rings and its applications
ESB 4133
Wed 24 Sep 2014, 3:15pm-4:15pm

Abstract

In this talk I will mention some conjectures about group rings (Idempotent conjecture, unit conjecture) and mention their stable versions. Those involve algebraic K-theory. I will explain how the Farrell-Jones conjecture implies those stable versions. I will then finish with the status of the Farrell-Jones conjecture. The cheapest way to prove it for a certain group is to use its inheritance properties, but this also touches very interesting questions in (geometric) group theory.
hide
Department of Mathematics, University of California, San Diego
Thu 25 Sep 2014, 12:00pm
Mathematics of Information and Applications Seminar
ESB 4133 (PIMS Lounge)
Quantization and near-optimal encoding of linear measurements
ESB 4133 (PIMS Lounge)
Thu 25 Sep 2014, 12:00pm-1:00pm

Abstract

Frames generalize the notion of bases and provide a useful tool for modeling the measurement (or sampling) process in several modern signal processing applications. In the digital era, such a measurement process is typically followed by quantization, or digitization.  We discuss the quantization of frame coefficients using a scheme known as Sigma-Delta quantization. We show that a simple encoding via a discrete random Johnson-Lindenstrauss embedding of the integrated bit-stream yields near-optimal approximation error (as a function of the number of bits used). The result holds with high probability on the draw of the embedding, allows efficient reconstruction, and holds for a wide class of frames including random frames and deterministic smooth frames.

In addition, we show that if the same encoding scheme is applied to quantized compressed sensing measurements (albeit with a different reconstruction scheme), it also yields near-optimal approximation accuracy as a function of the bit-rate.  Our results hold for Gaussian and sub-Gaussian compressed sensing matrices.

Note for Attendees

Pizza and pop will be provided.
hide
South Carolina
Thu 25 Sep 2014, 1:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Wall crossing in moduli problems and semi-orthogonal decompositions
ESB 4127 (host: UAlberta)
Thu 25 Sep 2014, 1:00pm-2:00pm

Abstract

We discuss how the derived category of a smooth algebraic stack of finite type changes as one removes certain types of closed substacks. As an application, we show how wall-crossing in moduli of stable sheaves and Bridgeland stable objects yields semi-orthogonal decompositions of relating their derived categories.

Note for Attendees

 Note the unusual day and time.
hide
UBC
Thu 25 Sep 2014, 1:05pm
Graduate Student Seminar
Math 225
What is... a CW-Complex?
Math 225
Thu 25 Sep 2014, 1:05pm-2:00pm

Abstract

In the Lego world, everything is built out of simple blocks fitting together in a prescribed way. In the mathematical world, you can just as easily think of cubes (or hypercubes) as Lego blocks and build away!

Note for Attendees

Notice the special time! This is to accommodate participation in the TA Union Orientation meeting:
Date(for above event): Thursday, September 25
Time: 12:30-1:30
Location: Leonard S. Klinck Building (LSK) (6356 Agricultural Road) Room 200


Sushi and pop will be provided in our seminar.
hide
UBC
Thu 25 Sep 2014, 3:30pm
Number Theory Seminar
room MATH 126
Primitive and doubly primitive divisors in dynamical sequences
room MATH 126
Thu 25 Sep 2014, 3:30pm-4:30pm

Abstract


hide
Miami
Fri 26 Sep 2014, 2:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Decomposing Landau-Ginzburg Models
ESB 4127 (host: UAlberta)
Fri 26 Sep 2014, 2:00pm-3:00pm

Abstract

One version of homological mirror symmetry relates the algebraic geometry of certain varieties to the symplectic topology of a Lefschetz pencil. Extracting symplectic (i.e. Floer theoretic) invariants from these fibrations is quite difficult, even in simple examples. I'll review some recent proposals (particularly from Kapranov-Kontsevich-Soibelman and Diemer-Kerr-Katzarkov) for deforming symplectic fibrations into more tractable components. The corresponding mirror theory appears to be closely related to birational geometry and the Mori program.

Note for Attendees

 Note the unusual day and time.
hide
UBC
Fri 26 Sep 2014, 3:00pm
Department Colloquium
Mathematics Annex 1100
The Dynamical Mordell-Lang problem
Mathematics Annex 1100
Fri 26 Sep 2014, 3:00pm-4:00pm

Abstract

A space X is called Noetherian if there is no infinite descending chain of closed subsets of X. Let X be a Noetherian space, let f be a continuous self-map on X, let Y be a closed subset of X, and let x be a point in X. We show that the set containing all positive integers n such that the n-th iterate of x under f lands in Y is a union of at most finitely many arithmetic progressions along with a set of Banach density 0. This result has various consequences from the distribution of zeros in recurrence sequences to questions in arithmetic geometry.

Note for Attendees

Refreshments will be served at 2:45 p.m. in the Math Lounge area, MATH 125 before the colloquium.
hide
Stanford
Mon 29 Sep 2014, 3:30pm
CRG Geometry and Physics Seminar
ESB 2012
Stabilization of discriminants in the Grothendieck ring
ESB 2012
Mon 29 Sep 2014, 3:30pm-4:30pm

Abstract

We consider the ``limiting behavior'' of {\em discriminants}, by which we mean informally the closure of the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on a variety X, and linear systems on X. These are connected --- we use the first to understand the second. We describe their classes in the "ring of motives", as the number of points gets large, or as the line bundle gets very positive. They stabilize in an appropriate sense, and their stabilization can be described in terms of the motivic zeta values. The results extend parallel results in both arithmetic and topology. I will also
present a conjecture (on ``motivic stabilization of symmetric powers'') suggested by our work. Although it is true in important cases, Daniel Litt has shown that it contradicts other hoped-for statements. This is joint work with Melanie Wood. 

Note for Attendees

 Note the unusual place, ESB 2012, and the unusual time, 3:30-4:30pm.
hide
Chen Greif
Computer Sciences, UBC
Tue 30 Sep 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Null-Space Based Block Preconditioners for Saddle-Point Systems with a Maximally Rank-Deficient Leading Block
ESB 4133 (PIMS Lounge)
Tue 30 Sep 2014, 12:30pm-1:30pm

Abstract

We consider nonsingular saddle-point matrices whose (1,1) block is maximally rank deficient, and show that the inverse in this case has unique mathematical properties. We then develop a class of indefinite block preconditioners that rely on approximating the null space of the leading block. Under certain conditions, even though the preconditioned matrix is a product of two indefinite matrices, the conjugate gradient method can be applied and is rapidly convergent. Spectral properties of the preconditioners are observed, which are validated by numerical experiments.

This is joint work with Ron Estrin.

hide
University of Minnesota
Tue 30 Sep 2014, 2:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
Geometry of shrinking Ricci solitons
ESB 4127
Tue 30 Sep 2014, 2:30pm-3:30pm

Abstract

This talk concerns the geometry of shrinking Ricci solitons, a class of self-similar solutions to the Ricci flows. We plan to provide some general background results and explain a recent work with Ovidiu Munteanu on the curvature estimates of four dimensional solitons.

Note for Attendees

 Please note unusual time and room.
hide
Universite de Cergy-Pontoise
Tue 30 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Stationary Kirchhoff systems in closed manifolds
ESB 2012
Tue 30 Sep 2014, 3:30pm-4:30pm

Abstract

 We investigate various issues for stationary Kirchhoff systems in closed manifolds, such as the questions of existence, non-existence and compactness of solutions to the equations.
hide